mm-4009 === Subject: Re: root finding > Does anyone know if there exist an analytical solution for the > following expression? > Ax+Bsin(Cx) = D >> There is no elementary or analytical expression for the value of x >> in terms of A, B and C for arbitrary A, B, and C. Nor does there seem to be any using any sort of > known or accepted mathematical operation. There is. Kepler's equation is exactly solvable if one uses the generalized Hyper Lambert functions. -- I.N. Galidakis === Subject: Engineering Circuit Analysis, 6th Edition, Hyat I need the solutions manual for Engineering Circuit Analysis, 6th Edition, Hyat. Please that would be great. === Subject: Re: Engineering Circuit Analysis, 6th Edition, Hyat > I need the solutions manual for Engineering Circuit Analysis, 6th > Edition, Hyat. Please that would be great. It would be ven better if you did a bit of hard work, for a change. === Subject: I have the Solution Manual Many Solutions Manuals and Ebooks in Electronic (PDF)Format! PS: These are part of my solutions, if the solution you want isnOt on the list, do not give up, just contact with me: My email is solutionpay(at)hotmail.com( please replace the (at) with @ ) NOTE: if the solutions you want is on the list renewed, please mention in your email,thank you! Solution manual for the list:.81B http://rapidshare.com/files/52408080/list.doc I will reply with your Email within 12 hours!! advanced engineering mathematics (8/e) by ERWIN KREYSZIG advanced engineering mathematics.81i9/e.81j by ERWIN KREYSZIG advanced macroeconomics Analytical Mechanics (7/e) By Grant R. Fowles, George L. Cassiday applied mathematics and modelling forchemical engineers(8/e) Applied Strength of Materials (4th Edition) by Robert MoTT Boyce Elementary Differential Equations and Boundary Value Problems by Willian E.Boyce C How to Program, 3RD Edition 2000 By Harvey M. Deitel Calculus I, II, Transidentals 10e BY George B. Thomas Calculus with Analytic Geometry Calculus, 4th edition by James Stewart Computational Techniques for Fluid Dynamics By Karkenahalli Srinivas, Clive A. J. Fletcher Computer Organization and Design: The Hardware/Software Interface93/e) by David A. Patterson, John L. Hennessy Design of Analog CMOS Integrated Circuit by B. Razavi Digital and Analog Communication Systems by LEON W. COUCH Digital and Analog Communication Systems .81C5th, by Leon W. Couch, Leon W., II Couch . DISCRETE-TIME SIGNAL PROCESSING/2e by Oppenheim.81ASchafer Econometric Analysis (6/e) by willian H.GREENE Econometric Analysis ,5th Edition, by William H. Greene Electric Machinery Fundamentals 4/e By Stephen J. Chapman Electric Machinery Fundamentals, 4/e , by S. J. Chapman. Electrical Circuits (7/e) by James W. Nilsson, and Susan A. Elementary Differential Equations and Boundary Value Problems , 8th.81Cby William E. Boyce (Author), Richard C Elementary Principles of Chemical Processes Elements of Chemical Reaction Engineering By H Fogler Elements of Chemical Reaction Engineering (3rd)by H.Scott Fogler Engineering electromagnetics (6/e) by HAYT Engineering electromagnetics (7/e) by HAYT Engineering Fluid Mechanics, 7th Edition By Clayton T. Crowe, Donald F. Elger, John A. Roberson Engineering Mathematics, 4th Edition ,by John Bird Engineering Mechanics - Dynamics (11th ) by R.C.HIBBELER Engineering Mechanics - Statics (11th ) by R.C.HIBBELER Engineering Mechanics - Statics and Dynamics,11th, by Russell C Hibbeler. Engineering Mechanics, Dynamics 5th By J. L. Meriam, L. G. Kraige Engineering Mechanics: Statics By R.C. Hibbeler Engineering Mechanics: Statics ,10th ,by R.C.Hibbeler, field and wave electromagnetics (2/e) by David Cheng Fundamentals of Logic Design 5Ed by CharlesRoth Fundamentals of Chemical Reaction Engineering By Mark E. E. Davis, Robert J. J. Davis Fundamentals of Fluid Mechanics, 5th by By Bruce R. Munson, Donald, Theodore H. Okiishi, Fundamentals of Organic Chemistry, 5E Fundamentals of Thermodynamics 6ed By Richard E. Sonntag Heat Transfer: A Practical Approach Hornback's Organic Chemistry, 2nd Introduction to Electrodynamics(3/e) by David J. Griffiths Introduction to Heat Transfer 4th Edition By Frank P. Incropera, David Introduction to Solid State Physics (8 ED) by Charles.Kittel__ MATHEMATICAL ANALYSIS (2/e) (chapter1-9) by Tom M. Apostol Mechanical Engineering Design By Joseph Shigley, Charles Mischke, Mechanics of Materials 96/E) by R.C.Hibbeler Microeconomic Analysis, 3rd Edition, by Hal R. Varian Microeconomic Theory by Andreu Mas-Colell, Michael D. Whinston, Modern Control Engineering/ 4E by K.OGATA Modern Digital and Analog Communication Systems (3/e) Organic Chemistry, 2th by Hornback Physica Chemistry 7th.Ed. by Atkins Physical Chemistry (7/e) by Peter Atkins and Julio de Paula Physical Chemistry (7th) by P.W.Atkins Physics for Scientists and Engineers by Serway'& Jewett Probability & Statistics for Engineers & Scientists, 8th by Sharon Myers , Keying Ye, Walpole Probability and Statistics for Engineering and the Sciences 7/e JAY L.DEVORE Probability, Random Variables and Stochastic Processes,3rd, by Athanasios Papoulis Signals and Systems (2nd Edition) Thermodynamics: An Engineering Approach,5th Ed. by Cengel Thermodynamics: An Engineering Approach,6th Ed. by Cengel Thomas' Calculus (11th Edition) by George B Thomas University Physics with Modern Physics By Hugh D. Young Vector Mechanics for Engineers: Statics, 7th By Ferdinand P. Beer Visual C++ How to Program, (3rd Edition) ,by Harvey & Paul Deitel & Associates Zill's a First Course in Differential Equations with Modeling Applicants 7/e http://pdfsolution.spaces.live.com === Subject: Many Solutions Manuals and Ebooks in Electronic (PDF)Format! Many Solutions Manuals and Ebooks in Electronic (PDF)Format! PS: These are part of my solutions, if the solution you want isnOt on the list, do not give up, just contact with me: My email is solutionpay(at)hotmail.com( please replace the (at) with @ ) NOTE: if the solutions you want is on the list renewed, please mention in your email,thank you! Solution manual for the list:.81B http://rapidshare.com/files/52408080/list.doc I will reply with your Email within 12 hours!! advanced engineering mathematics (8/e) by ERWIN KREYSZIG advanced engineering mathematics.81i9/e.81j by ERWIN KREYSZIG advanced macroeconomics Analytical Mechanics (7/e) By Grant R. Fowles, George L. Cassiday applied mathematics and modelling forchemical engineers(8/e) Applied Strength of Materials (4th Edition) by Robert MoTT Boyce Elementary Differential Equations and Boundary Value Problems by Willian E.Boyce C How to Program, 3RD Edition 2000 By Harvey M. Deitel Calculus I, II, Transidentals 10e BY George B. Thomas Calculus with Analytic Geometry Calculus, 4th edition by James Stewart Computational Techniques for Fluid Dynamics By Karkenahalli Srinivas, Clive A. J. Fletcher Computer Organization and Design: The Hardware/Software Interface93/e) by David A. Patterson, John L. Hennessy Design of Analog CMOS Integrated Circuit by B. Razavi Digital and Analog Communication Systems by LEON W. COUCH Digital and Analog Communication Systems .81C5th, by Leon W. Couch, Leon W., II Couch . DISCRETE-TIME SIGNAL PROCESSING/2e by Oppenheim.81ASchafer Econometric Analysis (6/e) by willian H.GREENE Econometric Analysis ,5th Edition, by William H. Greene Electric Machinery Fundamentals 4/e By Stephen J. Chapman Electric Machinery Fundamentals, 4/e , by S. J. Chapman. Electrical Circuits (7/e) by James W. Nilsson, and Susan A. Elementary Differential Equations and Boundary Value Problems , 8th.81Cby William E. Boyce (Author), Richard C Elementary Principles of Chemical Processes Elements of Chemical Reaction Engineering By H Fogler Elements of Chemical Reaction Engineering (3rd)by H.Scott Fogler Engineering electromagnetics (6/e) by HAYT Engineering electromagnetics (7/e) by HAYT Engineering Fluid Mechanics, 7th Edition By Clayton T. Crowe, Donald F. Elger, John A. Roberson Engineering Mathematics, 4th Edition ,by John Bird Engineering Mechanics - Dynamics (11th ) by R.C.HIBBELER Engineering Mechanics - Statics (11th ) by R.C.HIBBELER Engineering Mechanics - Statics and Dynamics,11th, by Russell C Hibbeler. Engineering Mechanics, Dynamics 5th By J. L. Meriam, L. G. Kraige Engineering Mechanics: Statics By R.C. Hibbeler Engineering Mechanics: Statics ,10th ,by R.C.Hibbeler, field and wave electromagnetics (2/e) by David Cheng Fundamentals of Logic Design 5Ed by CharlesRoth Fundamentals of Chemical Reaction Engineering By Mark E. E. Davis, Robert J. J. Davis Fundamentals of Fluid Mechanics, 5th by By Bruce R. Munson, Donald, Theodore H. Okiishi, Fundamentals of Organic Chemistry, 5E Fundamentals of Thermodynamics 6ed By Richard E. Sonntag Heat Transfer: A Practical Approach Hornback's Organic Chemistry, 2nd Introduction to Electrodynamics(3/e) by David J. Griffiths Introduction to Heat Transfer 4th Edition By Frank P. Incropera, David Introduction to Solid State Physics (8 ED) by Charles.Kittel__ MATHEMATICAL ANALYSIS (2/e) (chapter1-9) by Tom M. Apostol Mechanical Engineering Design By Joseph Shigley, Charles Mischke, Mechanics of Materials 96/E) by R.C.Hibbeler Microeconomic Analysis, 3rd Edition, by Hal R. Varian Microeconomic Theory by Andreu Mas-Colell, Michael D. Whinston, Modern Control Engineering/ 4E by K.OGATA Modern Digital and Analog Communication Systems (3/e) Organic Chemistry, 2th by Hornback Physica Chemistry 7th.Ed. by Atkins Physical Chemistry (7/e) by Peter Atkins and Julio de Paula Physical Chemistry (7th) by P.W.Atkins Physics for Scientists and Engineers by Serway'& Jewett Probability & Statistics for Engineers & Scientists, 8th by Sharon Myers , Keying Ye, Walpole Probability and Statistics for Engineering and the Sciences 7/e JAY L.DEVORE Probability, Random Variables and Stochastic Processes,3rd, by Athanasios Papoulis Signals and Systems (2nd Edition) Thermodynamics: An Engineering Approach,5th Ed. by Cengel Thermodynamics: An Engineering Approach,6th Ed. by Cengel Thomas' Calculus (11th Edition) by George B Thomas University Physics with Modern Physics By Hugh D. Young Vector Mechanics for Engineers: Statics, 7th By Ferdinand P. Beer Visual C++ How to Program, (3rd Edition) ,by Harvey & Paul Deitel & Associates Zill's a First Course in Differential Equations with Modeling Applicants 7/e http://pdfsolution.spaces.live.com === Subject: Re: Writing solutions manual Since I noticed there is such an interest in these books, I have decided > to write a solutions manual. I invite you to help me--we should make > 10^9s... Here are my first 3 solutions or answers... To make this joint > work (is that the new standard?), please limit your solutions to 3 per > person/day. 1. 42 > 2. By studying > 3. Yes, it is rude to call somebody a crackpot 4. Yes, it does seem a flagrantly disrespectful to an author to indiscriminately disseminate solutions manuals to his or her efforts without appropriate permissions. 5. Truth is not a popularity contest--the notion of surrogate factoring is likely not a diamond in the rough.... 6. The antiderivative of (1/cabin) is a houseboat. === Subject: Re: Five Sided Dice > [...] the faces cover equal solid angles with respect > to the center of gravity. For a center of gravity in the obvious > place, I > get that the six triangle edges should be longer than the other three > edges > by a ratio of sqrt[(15 + 9 sqrt(5)) / 10] ~ 1.87. >> I'd rather use physics and say that a thoroughly thrown die will go >> through a lot of bounces and end up in a stable position of potential >> energy W with probability proportional to exp(-kT/W). >> Since W is proportional to height, the center of gravity should be the >> center of a sphere touching all (stable) faces. Interesting. This (obviously) gives a ratio of sqrt(3) ~ 1.73. I'm not > convinced that this is a good model of the final low-energy > settling-down part of the toss, but then I don't find my model very > convincing either. Now I feel like doing an experiment. (But I'm not > going to.) What I don't get is why anyone would design or use a shape like this in > the first place rather than one that's manifestly symmetrical. Can you imagine a symmetrical 5-sided 3D shape? I can't. === Subject: Re: Five Sided Dice > Can you imagine a symmetrical 5-sided 3D shape? I can't. Not with five planar faces, but you needn't limit yourself to those. Take, for example, five copies of the rounded lozenge defined in the plane by 5/6 - sqrt(1-x^2) < y < sqrt(1-x^2) - 5/6 and make them the curved faces of a banana-shaped die. I'd even trust the six-sided version of this more than I'd trust a regular die -- I've never understood how to spin the usual design in a way that doesn't appear to favor some faces over others, but with this design you can obviously just spin it around the axis of n-fold symmetry. You could also use a gamer's d10 with the faces labeled with two copies of the digits 1 through 5, or an icosahedron labeled with four copies. A dreidel would also work -- that strikes me as the fairest design of them all. -- Ben === Subject: Re: Five Sided Dice >> [...] the faces cover equal solid angles with respect >> to the center of gravity. For a center of gravity in the obvious >> place, I >> get that the six triangle edges should be longer than the other >> three edges >> by a ratio of sqrt[(15 + 9 sqrt(5)) / 10] ~ 1.87. I'd rather use physics and say that a thoroughly thrown die will go > through a lot of bounces and end up in a stable position of potential > energy W with probability proportional to exp(-kT/W). > Since W is proportional to height, the center of gravity should be the > center of a sphere touching all (stable) faces. >> Interesting. This (obviously) gives a ratio of sqrt(3) ~ 1.73. I'm not >> convinced that this is a good model of the final low-energy >> settling-down part of the toss, but then I don't find my model very >> convincing either. Now I feel like doing an experiment. (But I'm not >> going to.) >> What I don't get is why anyone would design or use a shape like this >> in the first place rather than one that's manifestly symmetrical. Can you imagine a symmetrical 5-sided 3D shape? I can't. Suppose we have a pyramid with a square base and four congruent isosceles or equilateral triangles sharing a vertex at the summit of the pyramid. We could make the square have sides of unit length. The one parameter left would be the height h of the summit above the base. Let's simply assume the four triangular faces have the same chance of ending down. ( The downside face would be the selected one ...) For large h, the chance of landing triangle down would be > 4/5. For small enough h, I'm not sure what would happen. I guess the square base could be generalized to a rhombus-shaped base, keeping the four congruent triangle feature. For a generic rhombus, it seems the triangles would no longer be isosceles/equilateral. David Bernier === Subject: Block Linear System I have a block linear system (I put linear in quotes because I don't know how to better describe it) of the form / / / | A | | C D | | A B | | | = | | | | | B | | E F | | I | / / / X = M Y where A through F are square matrices and I is the identity matrix. I currently solve the above system via iteration and it converges just fine. The desired end product is the matrix A. I am trying to prove that it will always converge for certain parameters that generate the matrices C -F. I am pretty sure that the matrix M has a spectral radius less than or equal to 1 for the parameters of interest. With a spectral radius less than 1, that would be sufficient to demonstrate convergence for a typical iterative method. The A B term on the right hand side makes this a little different than the typical iterative method. Question: 1) If the spectral radius of M is less than 1, does that prove the iteration will converge? 2) Is there a name for a system of this form? === Subject: Analysis with integral. Hello sir~ If f is a bounded function defined on a closed, bounded interval [a, b] and f is continuous except at countably many points, then f is Riemann integrable. ---------------------------------------------------- I know it. My question is.... If f(x) is a bounded and continuous on [a,b] and f(x) = g(x) at except countably discontinuous points, (Namely, g(x) = f(x) , (x not x_1, x_2, x_3, ....) and g(x) is not continuous at x_1, x_2, x_3, .....) Then int_{a to b} f(x) dx = int{a to b} g(x) dx. is this possible ? If f(x) is a bounded and continuous on [a,b] and g(x) = f(x) , (x in (a,b]), g(a) =/= f(a), Then int_{a to b} f(x) dx = int{a to b} g(x) dx. is this possible ? === Subject: Re: Analysis with integral. > If f(x) is a bounded and continuous on [a,b] > and f(x) = g(x) at except countably discontinuous points, > (Namely, g(x) = f(x) , (x not x_1, x_2, x_3, ....) and > g(x) is not continuous at x_1, x_2, x_3, .....) Then int_{a to b} f(x) dx = int{a to b} g(x) dx. is this possible ? It's certainly possible (let the countable exceptional set be the empty set), so I think you mean: Is it possible for the integrals to be different? No for Lebesgue integration, yes for Riemann integration. One counterexample for Riemann integration is: f(x) = 0 for all values of x g(x) = characteristic function of the rational numbers In this case, the Riemann integrals are not equal because the Riemann integral of g does not exist (g is too discontinuous). Another counterexample for Riemann integration is: f(x) = 0 for all values of x g(x) = q if x = p/q (p,q relatively prime integers) g(x) = 0 if x=0 or x is irrational Again, the Riemann integrals are not equal because the Riemann integral of g does not exist (g is not bounded). However, for your assumptions about f and g, if both Riemann integrals exist, then the integrals will be equal. Dave L. Renfro === Subject: Re: Analysis with integral. My question is.... If f(x) is a bounded and continuous on [a,b] and f(x) = g(x) at except countably discontinuous points, (Namely, g(x) = f(x) , (x not x_1, x_2, x_3, ....) and g(x) is not continuous at x_1, x_2, x_3, .....) Then int_{a to b} f(x) dx = int{a to b} g(x) dx. is this possible ? It is true, if that is what you mean: Informally, if you have only countably many non-zero points, you can make the partition width small-enough so that the sum becomes 0 . consider h(x)= g(x)-f(x)=0 except at x_1,...,x_n,.... Consider a Riemann sum in which the values x_i* , i.e, the values in the i-th element of the partition that you select for : Sum (n=1,..,oo)f(x_i*)dx_i Let M=maxf(x) over [a,b] (assume wolg that f>=0) Them above sum is bounded above by: Sum(n=1,...,oo)Mdx_i = M[ Sum(n=1,...,oo)dx_i]<=M(b-a) Now make the partition width |P|=maxdx_i small-enough, and the Riemann sum is zero. () === Subject: Re: Analysis with integral. > My question is.... If f(x) is a bounded and continuous on [a,b] >and f(x) = g(x) at except countably discontinuous points, >(Namely, g(x) = f(x) , (x not x_1, x_2, x_3, ....) and >g(x) is not continuous at x_1, x_2, x_3, .....) Then int_{a to b} f(x) dx = int{a to b} g(x) dx. is this possible ? It is true, if that is what you mean: Informally, if you have only countably many non-zero > points, you can make the partition width small-enough > so that the sum becomes 0 . > consider h(x)= g(x)-f(x)=0 except at x_1,...,x_n,.... Consider a Riemann sum in which the values x_i* , i.e, the values in the i-th element of the partition that you select for : > Sum (n=1,..,oo)f(x_i*)dx_i > Let M=maxf(x) over [a,b] (assume wolg that f>=0) > Them above sum is bounded above by: Sum(n=1,...,oo)Mdx_i = > M[ Sum(n=1,...,oo)dx_i]<=M(b-a) Now make the partition width |P|=maxdx_i small-enough, and the Riemann sum is zero. () Hehe, and the Legesgue integral is even more zero. Brian === Subject: Finding binary irreducible polynomials Hi there!, I am looking if there is a simple numerical algorith that could be used to see if a binary polynomial is irreducible. for example: the CCIT CRC32 polynomial f(x) = 1+x^1+x^2+x^4+x^5+x^7+x^8+x^10+ x^11+x^12+x^16+x^22+x^23 +x^26+x^32 Also known with the binary 0x04C11DB7 from the binary bits. If I generate my own custom polynomials how do I know if they are irreducible ? Iakovos === Subject: Re: Finding binary irreducible polynomials >Hi there!, I am looking if there is a simple numerical algorith that could >be used to see if a binary polynomial is irreducible. for example: >the CCIT CRC32 polynomial f(x) = 1+x^1+x^2+x^4+x^5+x^7+x^8+x^10+ > x^11+x^12+x^16+x^22+x^23 +x^26+x^32 Also known with the binary 0x04C11DB7 from the binary bits. If I generate my own custom polynomials how do I know if they are >irreducible ? >Iakovos Ah yes, you want to factor the polynomial and each of the factors has coefficients equal to either 0 or 1. Try this link http://en.wikipedia.org/wiki/Berlekamp's_algorithm Brian === Subject: Re: Polynomials prime in relation one to secound ? > message > mathforum.org... > 4p7*r -p8*r = 9xy +9y^2 = 9y(x +y) = p9*r > 2p8*r +p7*r = 9x^2 -9xy = 9x(x -y) = p10*r I followed the post somewhat until here. Then I > hen I got p9*r = 9xy-9y^2 = 9y(x-y) (?) > p10*r = 9x^2-9xy = 9x(x-y) (as you > s you claimed) The reasoning x+y is prime to x-y and r will be 3 > or 9 no longer > went through. I see P1(x,x) = P2(x,x) = 0. Let > (x,y) = (1,12) . Then > P1 = -3^2*11*19 and P2 = -5^2*11 are divisible by r = > 11. > I also some similarity with S-polynomial > omial calculations of the Grobner > basis algorithm. Combine with factorization of > Grobner basis elements > using the Hensel-Berlekamp algorithm. Repeat into a > case analysis tree. > You might be able to develop an algorithm this way > that produces useful > knowledge about r . I tried this intriguing approach > out myself for just > a small spin. It leads to some interesting > conclusions, but maybe not > all the way to a solution without some further > thought. I hope once to see mentioned by You methods. In the meantime I've used to follow another kinds of developments from the basic set of equations: eg.(1): r^3 +4xr^2 +6x^2r + 3x^3 -x^2y -xy^2 -y^3 = 0 eq.(2): r^2 -3yr -x^2 -xy +2y^2 = 0 Where it is to find: P1 = 3x^3 -x^2y -xy^2 -y^3 P2 = -x^2 -xy +2y^2 And so on I've tried to find these polynomials P1 and P2 prime in relation one to another for to achieve some statement, that following system of eq.(1) and eq.(2) is under the field of rational numbers for some integer x;y of gcd=1. Also lately I've noticed: P1 = 3x^3 -x^2y -xy^2 -y^3 = (3x^2 +2xy +y^2)(x-y) then eq.(1) for r=y-x could be reduced to: eq.(1)': r^2 +4xr +6x^2 -3x^2 -2xy -y^2 eq.(1)': r^2 +4xr +3x^2 -2xy - y^2 = 0 eq.(2) : r^2 -3yr -x^2 -xy +2y^2 = 0 Then calculating determinants for eq.(1) and eq.(2): D1 = 4x^2 +8xy +4y^2 D2 = 4x^2 +4xy +y^2 For rational solutions: D1 = A^2 D2 = B^2 A^2 -B^2 = 4xy +3y^2 = y(4x-3y) (A-B)(A+B) = y(4x-3y) once we let y>x so should be taken: (B-A)(B+A) = y(3y-4x)........................(*) but anyhow it looks for some confusion for to achieve the last sentence... I can assure also, that there are some more general developments and more clear results claiming just from the beginning that eq.(1) or eq.(2) even separately have not rational solutions for x;y of gcd=1 . In such circumstances (*) should have also its clear picture or some method ? Meanwhile I can't find in (*) something so clear as I used to find with some similar equations providing just: (A-B)(A+B) = n(x-y)(x+y) Does the last one equation could be true for n as prime number and n>=3 ? Simple interesting ? Ro-Bin === Subject: COME ON !!! 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My actions and * comments do not reflect in any way on MIT. Also, I am nowhere near Boston. === Subject: Re: Paul R Halmos, Measure Theory, Sec 36, Question (2) Each iterated integral is 0. BTW: is there any way to prove the conclusion without fubini's law? Say, through the definition of Lebesque measure? Wei > Fubinate > -- > Ignorantly, > Allan Adler * comments do not reflect in any way on MIT. Also, I am nowhere near Boston. === Subject: Re: Paul R Halmos, Measure Theory, Sec 36, Question (2) Please help.... > If (X,S,u) and (Y,T,v) are the unit interval with Lebesgue measure, > and if E is a subset of X*Y such that Ex and X-(Y Section of E) are > countable for every x and y, then E is not measurable. === Subject: dont have solutions anymore.Old computer is fried! asdda === Subject: Re: Some vector math for computational geometry. > Not knowing how this group represents vectors when boldfacing isn't > possible, I'll use my own notation. p(t) = p0 + tdv (NOTE: dv is a single variable. I need to > differentiate between the scalar and vector expression of d) > p dot n = ds (ds is the scalar expression of d) > dv (an unadvised notation) is a variable over what? Scalars or vectors? Let p,u,v,w be vectors and s,t,x,y,z real variables. p(t) = p0 + tv describes a line as t varies over the reals, a line passing through p0 with the slope of v. > Since we want the point at where the ray/line and plane intersect, we > do some subbing and solve for t. > What plane? What's subbing? > (p0 + tdv) dot n = ds What's ds? Another vector? What's n? No, ds is a scalar. n is the normal to the mystery plane? > p0 dot n + tdv dot n = ds > tdv dot n = ds - (p0 dot n) > t = (ds - (p0 dot n))/(dv dot n) > Let s = p(t) * n = (p0 + tv) * n = (p0 * n) + (tv * n) Ok. t = (s - (p0 * n))/(v * n). So what? > Now, I understand a few things about this: p0 is the point of origin. No, p0 is a point through which the line p(t) passes. At t = 0, p(t) = p0. > dv is the vector that describes the full length of the ray. No, v is a vector that describes the direction of the line, determines it slope. > dv dot n gives the angular relationship between the plane's normal > vector and the ray. > What's n? A normal to a plane? What plane? v * n = |v||n| cos angle v,n. > One question: does p0 dot n tell me anything useful in and of > itself? > Not off hand. > It seem I could use it to determine from what side of the plane the > ray starts: front side or back side, thus, taken in conjunction with > dv dot n, I could use it to determine if I'm advancing on or > retreating from the plane. > You haven't indicated where the plane is located. This advancing and retreating would be in according to increasing t? If v was the reverse of what you thought, then advancing and retreating would be just the opposite. Calculate the distance s(t) from p(t) to the plane. If at t = t0, s(t) is increasing with increasing t, then p(t) is retreating from the plane. If at t = t0, s(t) is decreasing with increasing t, then p(t) is advancing toward the plane. Advancing or retreating will change according to what t0 you pick. You may also have the situation where the line lies on the mystery plane, in which case p(t) is neither advancing nor retreating for any t0. === Subject: Re: Some vector math for computational geometry. Not knowing how this group represents vectors when boldfacing isn't > possible, I'll use my own notation. > p(t) = p0 + tdv (NOTE: dv is a single variable. I need to > differentiate between the scalar and vector expression of d) > p dot n = ds (ds is the scalar expression of d) dv (an unadvised notation) is a variable over what? Since the forums can't do boldfacing, the notation used for vectors, what is the alternative? Telling people and hoping they can keep it straight? Now, since in the next line I said ds is the scalar expression...perhaps I'm assuming too much to no explicitly state dv is the vector expression? > Since we want the point at where the ray/line and plane intersect, we > do some subbing and solve for t. What plane? What's subbing? Um, the plane of intersection? The plane expressed by the three points that define the triangle contained within the plane. Subbing is shorthand for substitution or substitute. Sometimes it's sufficient to say sub rather than substitute, especially when my handwriting is better than my typing skills (didn't have a keyboard or typewriter when I was a boy). > (p0 + tdv) dot n = ds What's ds? Another vector? What's n? Forget I said anything. Disregard the remainder. === Subject: Re: JSH: Surrogate factoring, periodic behavior > Having completed better analysis on surrogate factoring I found the > equations > Having completed better analysis on surrogate factoring I found the > equations > James Harris > . Direct calculation of n in JSH's Surrogate, S=2*k^2 + n*T given p, T, and k where > T is an odd composite integer > p is an integer divisor of T > k is an integer Let A, B, C, D be elements of matrix M: B D > A C If > A = (p+k) - T mod (p+k) > C = T mod (p+k) > and Det M = -[2*k^2 mod(p+k)] = B*C - A*D then n = B + D > --------------------------------------------- > Example: T = 20303 > p = 79 > k = 23 > Factored trying 5 surrogates on the fifth surrogate using k=1 where the start was with n=7. Part of the problem I've run into with comments about surrogate factoring have been repeated claims it works only as good as trial division, but hey, I programmed the damn thing. I know you people are lying. The current algorithms I'm trying now are actually crappier than what I had before which would factor out small numbers with only a couple of surrogates. So, the problem here is that I have a Java program where I can stick in your numbers and watch the damn thing do better than you claim it can do. So I KNOW you are lying while it's not clear why. But people who don't program this thing for themselves need to understand that these people are not telling you the real truth here, and God only knows exactly why. If surrogate factoring had worked really crappy all along I'd have given up on it myself, but instead I found it crapped out with slightly bigger numbers, and definitely not with primes less than 100. James Harris === Subject: Re: JSH: Surrogate factoring, periodic behavior >Factored trying 5 surrogates on the fifth surrogate using k=1 where >the start was with n=7. I ran my usual tests again on 500 random composite odd numbers that are multiples of two different primes, each in the range 500 to 1000. The results are compared to Fermat's method, trial factorisation (both forward and reverse) and random picking. Fermat average = 7.58 probes. JSH average = 1635.83 probes. Probe ratio = 1 : 215.752 Trial average = 118.52 probes. Reverse average = 12.12 probes. Random average = 727.79 probes. 500 trials, 0 misfactors found. Average k's tried per factorisation: 1.000 Average n's tried per factorisation: 47.040 k was fixed at 1 and n was 7, 8, 9, ... >Part of the problem I've run into with comments about surrogate >factoring have been repeated claims it works only as good as trial >division, but hey, I programmed the damn thing. Any chance of seeing your code? Mine is below. It is Java. This is not compilable as-is because there are a few external classes and functions that I use. They are all pretty obvious. // -- Begin Code -- // JSH method - August 07 static FactorData jshFactor(int target) { FactorData retData = new FactorData(); retData.factor1 = 0; retData.factor2 = 0; retData.probeCount = 0; int k = 1; int n = 7; while(true) { // Surrogate to factor = 2k^2 + nT long surrogate = Math.abs(2L * k * k + n * target); ArrayList sFactors = allFactorPairs(surrogate); ++nCount; // Try possible solutions long g_1, g_2, trialFac; for (int i = 0; i < sFactors.size(); ++i) { g_1 = sFactors.get(i).first; g_2 = sFactors.get(i).second; // fac1, positive trialFac = Maths.GCD(g_1 - k, target); ++retData.probeCount; if (trialFac > 1 && trialFac < target) { retData.factor1 = trialFac; retData.factor2 = target / trialFac; break; } // end if // fac1, negative trialFac = Maths.GCD(-g_1 - k, target); ++retData.probeCount; if (trialFac > 1 && trialFac < target) { retData.factor1 = trialFac; retData.factor2 = target / trialFac; break; } // end if // fac2, positive trialFac = Maths.GCD(g_2 - k, target); ++retData.probeCount; if (trialFac > 1 && trialFac < target) { retData.factor1 = trialFac; retData.factor2 = target / trialFac; break; } // end if // fac2, negative trialFac = Maths.GCD(-g_2 - k, target); ++retData.probeCount; if (trialFac > 1 && trialFac < target) { retData.factor1 = trialFac; retData.factor2 = target / trialFac; break; } // end if } // end for if (retData.factor1 != 0) { break; } ++n; } // end while return retData; } // end jshFactor() // -- End Code -- rossum === Subject: Re: JSH: Surrogate factoring, periodic behavior Factored trying 5 surrogates on the fifth surrogate using k=1 where >the start was with n=7. I ran my usual tests again on 500 random composite odd numbers that > are multiples of two different primes, each in the range 500 to 1000. > The results are compared to Fermat's method, trial factorisation (both > forward and reverse) and random picking. Fermat average = 7.58 probes. > JSH average = 1635.83 probes. > Probe ratio = 1 : 215.752 > Trial average = 118.52 probes. > Reverse average = 12.12 probes. > Random average = 727.79 probes. 500 trials, 0 misfactors found. Average k's tried per factorisation: 1.000 > Average n's tried per factorisation: 47.040 k was fixed at 1 and n was 7, 8, 9, ... > To support a position that surrogate factoring is worse than any other method, which is kind of odd, to the thinking person, as how is that possible? Consider a calculator given to scribes in Old England, like it was sent backwards through time, and some scribes bang on it, and even manage to turn it on, but think it is just a weird gizmo with funny lights. While one plays with it carefully and figures out how to get it to work. Or give a computer to someone who hasn't a clue about what a computer is and watch them bang on the keyboard. Surrogate factoring to be worse than random must not be being used properly as if it were random then it would behave randomly. Random means chaos, no reason. The worst you SHOULD get from something that cannot work better. Can you force Fermat's method to behave worse than random if you try, by changing how you use it? Yes, if you're smart enough and willing to do the exercise, you can. Your evidence is just indication that you do not know what you are doing. Like that imaginary scribe banging at a modern calculator. >Part of the problem I've run into with comments about surrogate >factoring have been repeated claims it works only as good as trial >division, but hey, I programmed the damn thing. Any chance of seeing your code? > No. I put it up a while back but that code didn't work that well anyway. I'm making adjustments based on the new theory and have decided it would be irresponsible to just put that out there. I think it fascinating though that people like you could present a worse than random position as indication that surrogate factoring is a bad idea when that is intriguing, as how does the math know? Why does it care to give you results WORSE than random if the method cannot be made better, if not to tell you that you are doing something wrong? It reminds me of this episode of Star Trek, where Capt. Kirk is seduced by a women from a primitive culture, in that they don't have weapons much beyond sticks and stones, using some kind of love potion to make him obey her, who realizes there is all this power in his phaser, so she steals it to give to a man she deems more worthy of power than Kirk, and confronting an armed group they go down as they can't get it to work! The phaser is technology beyond their primitive ability to get it to work, which always interested me as guns are rather simple--you pull a trigger. So did phasers have some kind of locking mechanism maybe? Or did the writers think them more complicated than just pulling the trigger? In any event, worse than random is a clue, as how can a factoring method be worse than random? Why? is a great question to ask, if you have normal human curiosity. It is how we build things, and figure things out, because someone asks why. James Harris === Subject: Re: JSH: Surrogate factoring, periodic behavior >>Factored trying 5 surrogates on the fifth surrogate using k=1 where >>the start was with n=7. >> I ran my usual tests again on 500 random composite odd numbers that >> are multiples of two different primes, each in the range 500 to 1000. >> The results are compared to Fermat's method, trial factorisation (both >> forward and reverse) and random picking. >> Fermat average = 7.58 probes. >> JSH average = 1635.83 probes. >> Probe ratio = 1 : 215.752 >> Trial average = 118.52 probes. >> Reverse average = 12.12 probes. >> Random average = 727.79 probes. >> 500 trials, 0 misfactors found. >> Average k's tried per factorisation: 1.000 >> Average n's tried per factorisation: 47.040 >> k was fixed at 1 and n was 7, 8, 9, ... To support a position that surrogate factoring is worse than any other >method, which is kind of odd, to the thinking person, as how is that >possible? I do not say that surrogate factoring is worse than any other method. I say that it is worse than some other methods. I show my evidence for this above. Do you have any evidence to show that I am wrong? >Consider a calculator given to scribes in Old England, like it was >sent backwards through time, and some scribes bang on it, and even >manage to turn it on, but think it is just a weird gizmo with funny >lights. While one plays with it carefully and figures out how to get it to >work. Or give a computer to someone who hasn't a clue about what a computer >is and watch them bang on the keyboard. Surrogate factoring to be worse than random must not be being used >properly as if it were random then it would behave randomly. Surrogate factoring was not designed as a PRNG, hence I am not surprised that it performs badly as a PRNG. I suspect the problem is that it is generating repeats more often than the PRNG (which is statistically limited in the number of repeats it can generate). If you repeatedly generate an unsuccessful trial factor then you are doind unneccessary work since that trial factor has already been tried and failed. Random means chaos, no reason. The worst you SHOULD get from >something that cannot work better. No. I can try 1, 1, 1, 1, 1, 1, ... as factors and I will never find a proper factor. If a proposed method gives more repeats of non-factors then a PRNG would then it is likely to perform worse than a PRNG. You might like to analyse the number of times you method throws up the same potential factor. Can you force Fermat's method to behave worse than random if you try, >by changing how you use it? Yes, if you're smart enough and willing >to do the exercise, you can. No, then it would no longer be Fermat's method. Fermat's method works systematically through the options without repeating. Your evidence is just indication that you do not know what you are >doing. Like that imaginary scribe banging at a modern calculator. >Part of the problem I've run into with comments about surrogate >>factoring have been repeated claims it works only as good as trial >>division, but hey, I programmed the damn thing. >> Any chance of seeing your code? No. I put it up a while back but that code didn't work that well >anyway. I'm making adjustments based on the new theory and have decided it >would be irresponsible to just put that out there. I think it fascinating though that people like you could present a >worse than random position as indication that surrogate factoring is a >bad idea when that is intriguing, as how does the math know? Why does it care to give you results WORSE than random if the method >cannot be made better, if not to tell you that you are doing something >wrong? You have seen my code, so you tell me what I am doing wrong. One change I have made since my last post is that you have now made it clear that you use both positive and negative values of k. Rerunning my tests using both k = +1 and k = -1 gave the results: Fermat average = 8.06 probes. JSH average = 3597.41 probes. Probe ratio = 1 : 446.107 Trial average = 119.65 probes. Reverse average = 12.59 probes. Random average = 771.60 probes. 500 trials, 0 misfactors found. Average k's tried per n: 1.9618 Average n's tried per factorisation: 52.372 This is worse than before. As the figure of 1.96 k's per n shows, you are not gaining a lot by using the second value of k, it just add more unsuccessful trials before moving on to the next n. If that figure was closer to 1.1 then you would be gaining something by using the negative value of k. >In any event, worse than random is a clue, as how can a factoring >method be worse than random? Easily, if it takes no steps to avoid repeating failed trial factors. Both Fermat and Trial Factorisation work systematically through the options, without repeating. Your method is generating factors of each surrogate with no provision for avoiding numbers that have appeared before as a factor of a previous surrogate. By repeating work already done any method can be made as bad as random or worse. rossum Why? is a great question to ask, if you have normal human curiosity. It is how we build things, and figure things out, because someone asks >why. >James Harris === Subject: Re: JSH: Surrogate factoring, periodic behavior <3f3jd3d9g535dj5dl1s56egmok55sl783l@4ax.com >>Factored trying 5 surrogates on the fifth surrogate using k=1 where >>the start was with n=7. >> I ran my usual tests again on 500 random composite odd numbers that >> are multiples of two different primes, each in the range 500 to 1000. >> The results are compared to Fermat's method, trial factorisation (both >> forward and reverse) and random picking. >> Fermat average = 7.58 probes. >> JSH average = 1635.83 probes. >> Probe ratio = 1 : 215.752 >> Trial average = 118.52 probes. >> Reverse average = 12.12 probes. >> Random average = 727.79 probes. >> 500 trials, 0 misfactors found. >> Average k's tried per factorisation: 1.000 >> Average n's tried per factorisation: 47.040 >> k was fixed at 1 and n was 7, 8, 9, ... >To support a position that surrogate factoring is worse than any other >method, which is kind of odd, to the thinking person, as how is that >possible? I do not say that surrogate factoring is worse than any other > method. I say that it is worse than some other methods. I show my > evidence for this above. Do you have any evidence to show that I am > wrong? > Yes. >Consider a calculator given to scribes in Old England, like it was >sent backwards through time, and some scribes bang on it, and even >manage to turn it on, but think it is just a weird gizmo with funny >lights. >While one plays with it carefully and figures out how to get it to >work. >Or give a computer to someone who hasn't a clue about what a computer >is and watch them bang on the keyboard. >Surrogate factoring to be worse than random must not be being used >properly as if it were random then it would behave randomly. Surrogate factoring was not designed as a PRNG, hence I am not > surprised that it performs badly as a PRNG. I suspect the problem is > that it is generating repeats more often than the PRNG (which is > statistically limited in the number of repeats it can generate). If > you repeatedly generate an unsuccessful trial factor then you are > doind unneccessary work since that trial factor has already been tried > and failed. > Hand waving. Wouldn't a detailed analysis give an answer? >Random means chaos, no reason. The worst you SHOULD get from >something that cannot work better. No. I can try 1, 1, 1, 1, 1, 1, ... as factors and I will never find > a proper factor. If a proposed method gives more repeats of > non-factors then a PRNG would then it is likely to perform worse than > a PRNG. You might like to analyse the number of times you method > throws up the same potential factor. Why? What in the math would indicate that is the way to go? >Can you force Fermat's method to behave worse than random if you try, >by changing how you use it? Yes, if you're smart enough and willing >to do the exercise, you can. No, then it would no longer be Fermat's method. Fermat's method works > systematically through the options without repeating. > You show lack of imagination. Can anyone ELSE figure out a way to use Fermat's method in a way that would make it worse than random? James Harris === Subject: Re: JSH: Surrogate factoring, periodic behavior Factored trying 5 surrogates on the fifth surrogate using k=1 where >the start was with n=7. > I ran my usual tests again on 500 random composite odd numbers that > are multiples of two different primes, each in the range 500 to 1000. > The results are compared to Fermat's method, trial factorisation (both > forward and reverse) and random picking. > Fermat average = 7.58 probes. > JSH average = 1635.83 probes. > Probe ratio = 1 : 215.752 > Trial average = 118.52 probes. > Reverse average = 12.12 probes. > Random average = 727.79 probes. > 500 trials, 0 misfactors found. > Average k's tried per factorisation: 1.000 > Average n's tried per factorisation: 47.040 > k was fixed at 1 and n was 7, 8, 9, ... To support a position that surrogate factoring is worse than any other > method, which is kind of odd, to the thinking person, as how is that > possible? Consider a calculator given to scribes in Old England, like it was > sent backwards through time, and some scribes bang on it, and even > manage to turn it on, but think it is just a weird gizmo with funny > lights. While one plays with it carefully and figures out how to get it to > work. Or give a computer to someone who hasn't a clue about what a computer > is and watch them bang on the keyboard. Surrogate factoring to be worse than random must not be being used > properly as if it were random then it would behave randomly. Random means chaos, no reason. The worst you SHOULD get from > something that cannot work better. Can you force Fermat's method to behave worse than random if you try, > by changing how you use it? Yes, if you're smart enough and willing > to do the exercise, you can. Your evidence is just indication that you do not know what you are > doing. Like that imaginary scribe banging at a modern calculator. >Part of the problem I've run into with comments about surrogate >factoring have been repeated claims it works only as good as trial >division, but hey, I programmed the damn thing. > Any chance of seeing your code? No. Because you can't? Because you left all that behind when you left Atlanta? Because you got fired for ing around on a company computer instead of doing your job? > I put it up a while back but that code didn't work that well > anyway. I'm making adjustments based on the new theory and have decided it > would be irresponsible to just put that out there. In other words you CAN'T program anymore. I think it fascinating though that people like you could present a > worse than random position as indication that surrogate factoring is a > bad idea when that is intriguing, as how does the math know? Why does it care to give you results WORSE than random if the method > cannot be made better, if not to tell you that you are doing something > wrong? It reminds me of this episode of Star Trek, where Capt. Kirk is > seduced by a women from a primitive culture, in that they don't have > weapons much beyond sticks and stones, using some kind of love potion > to make him obey her, who realizes there is all this power in his > phaser, so she steals it to give to a man she deems more worthy of > power than Kirk, and confronting an armed group they go down as they > can't get it to work! Kind of like JSH with a Java compiler, eh? The phaser is technology beyond their primitive ability to get it to > work, Like writing programs is beyond your capability. > which always interested me as guns are rather simple--you pull a > trigger. That explains a lot. So did phasers have some kind of locking mechanism maybe? Like a safety? > Or did the writers think them more complicated > than just pulling the trigger? Could it be that factoring is more complicated that surrogates? In any event, worse than random is a clue, as how can a factoring > method be worse than random? Easy. Not that primitives would ever understand that. Why? is a great question to ask, Could it be that your program thinks composites are primes? > if you have normal human curiosity. It is how we build things, and figure things out, because someone asks > why. What you mean we, Kemosabe? James Harris === Subject: Re: JSH: Surrogate factoring, periodic behavior > Having completed better analysis on surrogate factoring I found the > equations > James Harris > . > Direct calculation of n in JSH's Surrogate, > S=2*k^2 + n*T > given p, T, and k where > T is an odd composite integer > p is an integer divisor of T > k is an integer > Let A, B, C, D be elements of matrix M: > B D > A C > If > A = (p+k) - T mod (p+k) > C = T mod (p+k) > and Det M = -[2*k^2 mod(p+k)] = B*C - A*D > then n = B + D > --------------------------------------------- > Example: > T = 20303 > p = 79 > k = 23 Factored trying 5 surrogates on the fifth surrogate using k=1 where > the start was with n=7. > I cannot duplicate your result. If you would be kind enough to provide a list of S from n = 7 to n = the one that gave a factor then I can see if my program comes up with the same numbers. If it doesn't, then we're using different routines. I'm assuming that you used T=20303, k=1, n=7,8,9,10,11 and had success at n=11. Is your factor of the surrogate that worked equal to k + a factor of T? In my example, 79 as a factor of T=20303 was found with the factor k+79 = 23+79=102, a factor of S at n=74; S=1503480 = 102*14740 Enrico === Subject: Re: JSH: Surrogate factoring, periodic behavior > Having completed better analysis on surrogate factoring I found the > equations > James Harris > . > Direct calculation of n in JSH's Surrogate, > S=2*k^2 + n*T > given p, T, and k where > T is an odd composite integer > p is an integer divisor of T > k is an integer > Let A, B, C, D be elements of matrix M: > B D > A C > If > A = (p+k) - T mod (p+k) > C = T mod (p+k) > and Det M = -[2*k^2 mod(p+k)] = B*C - A*D > then n = B + D > --------------------------------------------- > Example: > T = 20303 > p = 79 > k = 23 > Factored trying 5 surrogates on the fifth surrogate using k=1 where > the start was with n=7. I cannot duplicate your result. > If you would be kind enough to provide a list > of S from n = 7 to n = the one that gave a factor > then I can see if my program comes up with the > same numbers. If it doesn't, then we're using > different routines. > I do use +/-k as it's easy enough to just check both, and my f's can be fractions with a 2 in the denominator. Try again. If you can't duplicate then I'll think about going to the program to pull out in more detail what it's doing. > I'm assuming that you used T=20303, k=1, n=7,8,9,10,11 > and had success at n=11. > I used k=1 or -1, since the program automatically checks both, and the rest is probably correct but I haven't adjusted the program to tell me what n it is using as that only just recently came up as important, so it was n=11 or n=12, probably n=11. Previously I thought only the k/T ratio was important. > Is your factor of the surrogate that worked equal to > k + a factor of T? In my example, 79 as a factor of > T=20303 was found with the factor k+79 = 23+79=102, > a factor of S at n=74; S=1503480 = 102*14740 Enrico I've been more focused on theory than the program, but am just now getting back to the question of implementation. My guess is that my checking plus or minus k should explain how I see much better success, so maybe I jumped the gun by calling you a liar. That effectively doubles checks, though with a very light impact since it is just a matter of first adding k to 2f_1 or 2f_2 and checking the gcd with T and then subtracting, so it is the kind of simple optimization that any serious coders would use. Even with that doubling I needed only 10 surrogates to check, again that is much worse than what I've seen with previous code. But you see, experiments only told me so much so I shelved things for a while and went on to other things. If they did show this idea was just total crap then I might still do analysis to figure out why, as with all previous surrogate factoring equations I could always pull them apart to find out why I wasn't getting the desired behavior. And that behavior I remind is the ability to factor an RSA sized number in under 10 minutes on a standard desktop computer. Recently I came back to do a detailed analysis which includes new info like the decision relations this thread is ACTUALLY about, and next I'll see if the new info leads to better working code. That's how it's done. You people instead just want to come out every once and a while and claim it doesn't work well, without being able to explain why. Your lack of curiosity is what I am using to get people suspicious of you. So, yeah, maybe surrogate factoring is a bum idea that will never work well, but why? Why? That simple question is a driver of human evolution. Without asking it, you cannot truly be an intellectual if you are criticizing an idea. If you don't care, fine. But if you care enough to attack an idea, if you are a real researcher you need to care enough to figure out why it doesn't work! That's why political hacks are so annoying!!! They don't give a damn about anything but maybe their paychecks and satisfaction at winning at any costs, so start a war? Who cares if you're a political hack and that's your job. People starving as a result of policies you help implement? Who cares if you are a political hack as hey, that's their problem, right? Political hacks are people who do not care about the truth, and cannot be bothered to ask, why. It's a mindless and narrow worldview that sees people as things and cares nothing at all about what actually is true. It is the anti-thesis of the scientist to simply take a position, have talking points, and care only about convincing people without knowing the 'why'. Science is all about why. James Harris === Subject: Re: JSH: Surrogate factoring, periodic behavior > If they did show this idea was just total crap then I might still do > analysis to figure out why, as with all previous surrogate factoring > equations I could always pull them apart to find out why I wasn't > getting the desired behavior. And that behavior I remind is the ability to factor an RSA sized > number in under 10 minutes on a standard desktop computer. Recently I came back to do a detailed analysis which includes new info > like the decision relations this thread is ACTUALLY about, and next > I'll see if the new info leads to better working code. That's how it's done. You people instead just want to come out every once and a while and > claim it doesn't work well, without being able to explain why. Your lack of curiosity is what I am using to get people suspicious of > you. So, yeah, maybe surrogate factoring is a bum idea that will never work > well, but why? Why? That simple question is a driver of human evolution. Without asking > it, you cannot truly be an intellectual if you are criticizing an > idea. If you don't care, fine. But if you care enough to attack an idea, if > you are a real researcher you need to care enough to figure out why it > doesn't work! No, that is not how real researchers work. If you were a doctor and somebody came up to you and suggested that maybe one could cure brain cancer by eating two pounds of fudge before stroking a tree while facing north, would you drop what you were doing and devote your time to figuring out why that isn't going to work? Or would you first ask the guy why on Earth he thinks it *would* work? The fact is that any algorithm that generates integers and then calculates their GCD with a target T *might* reveal non-trivial factors of T. Moreover if that algorithm checks enough numbers then it is very likely that eventually it *will* reveal a non-trivial factor of T. But a simple counting argument suggests that if T is RSA-sized and has no small factors then for most such algorithms the time taken to find a non-trivial factor of T is prohibitively large. If you want anybody to believe that your method is any kind of breakthrough then you must present some reason to believe that it might find factors of T faster than existing methods, or else you will be taken no more seriously than a man who claims with no justification that fudge- eating and tree-stroking can cure cancer. But you haven't - in fact when Marcus asked you to do so you chose instead to rant about how sub- human we all are. I know it's probably futile but I'll ask again: why do you believe that your method should work better than trial division or random-GCD? [snip social crap] === Subject: Re: JSH: Surrogate factoring, periodic behavior > If they did show this idea was just total crap then I might still do > analysis to figure out why, as with all previous surrogate factoring > equations I could always pull them apart to find out why I wasn't > getting the desired behavior. > And that behavior I remind is the ability to factor an RSA sized > number in under 10 minutes on a standard desktop computer. > Recently I came back to do a detailed analysis which includes new info > like the decision relations this thread is ACTUALLY about, and next > I'll see if the new info leads to better working code. > That's how it's done. > You people instead just want to come out every once and a while and > claim it doesn't work well, without being able to explain why. > Your lack of curiosity is what I am using to get people suspicious of > you. > So, yeah, maybe surrogate factoring is a bum idea that will never work > well, but why? > Why? > That simple question is a driver of human evolution. Without asking > it, you cannot truly be an intellectual if you are criticizing an > idea. > If you don't care, fine. But if you care enough to attack an idea, if > you are a real researcher you need to care enough to figure out why it > doesn't work! No, that is not how real researchers work. If you were a doctor and > somebody came up to you and suggested that maybe one could cure brain > cancer by eating two pounds of fudge before stroking a tree while > facing north, would you drop what you were doing and devote your time > to figuring out why that isn't going to work? Or would you first ask > the guy why on Earth he thinks it *would* work? > If that person drove traffic in medical subjects from around the world and had a dedicated mob of respondents who argued with him day and night over medical topics, I might. Google searches shift on a day to day basis on what I talk about on sci.math which is an impact far beyond what most of you can even imagine. The issue is not whether or not there are people who are interested in what I say, as the evidence is overwhelming that there are. > The fact is that any algorithm that generates integers and then > calculates their GCD with a target T *might* reveal non-trivial > factors of T. Moreover if that algorithm checks enough numbers then it > is very likely that eventually it *will* reveal a non-trivial factor > of T. But a simple counting argument suggests that if T is RSA-sized > and has no small factors then for most such algorithms the time taken > to find a non-trivial factor of T is prohibitively large. If you want > anybody to believe that your method is any kind of breakthrough then > you must present some reason to believe that it might find factors of > T faster than existing methods, or else you will be taken no more > seriously than a man who claims with no justification that fudge- > eating and tree-stroking can cure cancer. But you haven't - in fact > when Marcus asked you to do so you chose instead to rant about how sub- > human we all are. > Surrogate factoring is kind of mysterious because people can do these checks as they have posted about that indicate very much worse than random! But how is that possible? Isn't random the bottom? > I know it's probably futile but I'll ask again: why do you believe > that your method should work better than trial division or random-GCD? [snip social crap] Sigh. Years ago I wondered, might you be able to factor one number by instead factoring another? That's it dude. I wondered that years ago and started looking to see what the math said. Can you comprehend asking a question and then going looking? So yeah, I question your basic human curiosity because I have to keep repeating that over and over again for you so you clearly DO NOT GET IT. Somehow your brain seizes up on the possibility of someone just wondering about something and going to go see if it is possible, which to me does not make you a candidate for an evolutionary leap in the human species as I think MOST people on the planet WOULD get it. Or do you disagree? James Harris === Subject: Re: JSH: Surrogate factoring, periodic behavior > No, that is not how real researchers work. If you were a doctor and > somebody came up to you and suggested that maybe one could cure brain > cancer by eating two pounds of fudge before stroking a tree while > facing north, would you drop what you were doing and devote your time > to figuring out why that isn't going to work? Or would you first ask > the guy why on Earth he thinks it *would* work? If that person drove traffic in medical subjects from around the world > and had a dedicated mob of respondents who argued with him day and > night over medical topics, I might. Google searches shift on a day to day basis on what I talk about on > sci.math which is an impact far beyond what most of you can even > imagine. The issue is not whether or not there are people who are interested in > what I say, as the evidence is overwhelming that there are. We all know what you consider overwhelming evidence. Recently, for example, you repeatedly claimed that the fact that your posts appeared in web searches for DMESE was hard evidence that people were interested in your ideas. You never explained why, in that case, the results of a web search for CSTMY weren't equally hard evidence for the obviously nonsensical proposition that the world was interested in a garbage five-letter string that Tim Peters made up. As for having a dedicated mob of respondents, why not try going to a high-activity medical newsgroup and stating that fudge can cure cancer? If people disagree with you, call them liars, tell them they will be killed when the truth comes out, point out that you are a true, living super- genius, threaten to destroy the world as they know it using your great powers, and generally act like a psychological train wreck. I'm guessing that you will get plenty of attention there just like you do here - will that prove that people are taking your ideas about medicine seriously? > The fact is that any algorithm that generates integers and then > calculates their GCD with a target T *might* reveal non-trivial > factors of T. Moreover if that algorithm checks enough numbers then it > is very likely that eventually it *will* reveal a non-trivial factor > of T. But a simple counting argument suggests that if T is RSA-sized > and has no small factors then for most such algorithms the time taken > to find a non-trivial factor of T is prohibitively large. If you want > anybody to believe that your method is any kind of breakthrough then > you must present some reason to believe that it might find factors of > T faster than existing methods, or else you will be taken no more > seriously than a man who claims with no justification that fudge- > eating and tree-stroking can cure cancer. But you haven't - in fact > when Marcus asked you to do so you chose instead to rant about how sub- > human we all are. Surrogate factoring is kind of mysterious because people can do these > checks as they have posted about that indicate very much worse than > random! But how is that possible? Isn't random the bottom? Don't you even understand how random-GCD works? Of course it isn't the bottom. There are many reasons why a method of the type I described above would perform worse than random. I see that rossum has already given an obvious example. Another would be a method which preferentially picked powers of two, none of which would reveal a non- trivial factor of an odd number. > I know it's probably futile but I'll ask again: why do you believe > that your method should work better than trial division or random-GCD? > [snip social crap] Sigh. Years ago I wondered, might you be able to factor one number by > instead factoring another? That's it dude. I wondered that years ago and started looking to see > what the math said. You didn't answer the question. Why do you think that factoring one number by instead factoring another is a better idea than, say, random- GCD? > Can you comprehend asking a question and then going looking? So yeah, I question your basic human curiosity because I have to keep > repeating that over and over again for you so you clearly DO NOT GET > IT. Somehow your brain seizes up on the possibility of someone just > wondering about something and going to go see if it is possible, which > to me does not make you a candidate for an evolutionary leap in the > human species as I think MOST people on the planet WOULD get it. Or do you disagree? Wondering about something and going to see if it is possible is just fine. It would be fine, for example, to wonder whether fudge can be used to cure cancer and trying to find out. On the other hand, spending four years researching the topic without ever coming up with a reason to believe that fudge is better at curing cancer than, say, toffee, would seem rather daft. And insulting anybody who didn't join you in spending their time trying to find which flavour of fudge was best for curing cancer, and accusing them of not having basic human curiosity, would seem downright idiotic. === Subject: Re: JSH: Surrogate factoring, periodic behavior > No, that is not how real researchers work. If you were a doctor and > somebody came up to you and suggested that maybe one could cure brain > cancer by eating two pounds of fudge before stroking a tree while > facing north, would you drop what you were doing and devote your time > to figuring out why that isn't going to work? Or would you first ask > the guy why on Earth he thinks it *would* work? > If that person drove traffic in medical subjects from around the world > and had a dedicated mob of respondents who argued with him day and > night over medical topics, I might. > Google searches shift on a day to day basis on what I talk about on > sci.math which is an impact far beyond what most of you can even > imagine. > The issue is not whether or not there are people who are interested in > what I say, as the evidence is overwhelming that there are. We all know what you consider overwhelming evidence. Recently, for > example, you repeatedly claimed that the fact that your posts appeared > in web searches for DMESE was hard evidence that people were > interested in your ideas. You never explained why, in that case, the > results of a web search for CSTMY weren't equally hard evidence for > the obviously nonsensical proposition that the world was interested in > a garbage five-letter string that Tim Peters made up. As for having a > dedicated mob of respondents, why not try going to a high-activity > medical newsgroup and stating that fudge can cure cancer? If people > disagree with you, call them liars, tell them they will be killed when > the truth comes out, point out that you are a true, living super- > genius, threaten to destroy the world as they know it using your great > powers, and generally act like a psychological train wreck. I'm > guessing that you will get plenty of attention there just like you do > here - will that prove that people are taking your ideas about > medicine seriously? > Nope. I'd be ignored. People spend energy on what interests them, one way or another. Working to convince readers otherwise is a stupid political hack. I'm disappointed in you. You should know better. Better to say nothing than say something that your readers know intuitively is wrong, as if, as if medical doctors would waste their time as you claim. ___JSH === Subject: Re: JSH: Surrogate factoring, periodic behavior > We all know what you consider overwhelming evidence. Recently, for > example, you repeatedly claimed that the fact that your posts appeared > in web searches for DMESE was hard evidence that people were > interested in your ideas. You never explained why, in that case, the > results of a web search for CSTMY weren't equally hard evidence for > the obviously nonsensical proposition that the world was interested in > a garbage five-letter string that Tim Peters made up. As for having a > dedicated mob of respondents, why not try going to a high-activity > medical newsgroup and stating that fudge can cure cancer? If people > disagree with you, call them liars, tell them they will be killed when > the truth comes out, point out that you are a true, living super- > genius, threaten to destroy the world as they know it using your great > powers, and generally act like a psychological train wreck. I'm > guessing that you will get plenty of attention there just like you do > here - will that prove that people are taking your ideas about > medicine seriously? Nope. I'd be ignored. Try it. Or don't - it's not like you need to look far to find evidence that people will happily spend their time arguing with obvious nonsense. Take a few other sci.math posters for example. Do you believe that the universe is a giant plutonium atom? I'm guessing not. So how do you explain the fact that people have been arguing with Archimedes Plutonium since long before you came along, and still do? Do you think that Cantor's diagonal argument is flawed? If not, then how do you explain the fact that the thread Cantor Confusion reached almost 8000 posts (making the energy people expend arguing with you look pretty lame by comparison)? > People spend energy on what interests them, one way or another. > Working to convince readers otherwise is a stupid political hack. I'm not working to convince readers otherwise. Readers know full well that people spend energy on what interests them. I expect that every reader except you is also well aware that many people find lunatics interesting. > I'm disappointed in you. LOL. How can I go on now? I live for your approval, James. === Subject: Re: JSH: Surrogate factoring, periodic behavior >> Having completed better analysis on surrogate factoring I found the >> equations > James Harris >> . >> Direct calculation of n in JSH's Surrogate, >> S=2*k^2 + n*T >> given p, T, and k where >> T is an odd composite integer >> p is an integer divisor of T >> k is an integer >> Let A, B, C, D be elements of matrix M: >> B D >> A C >> If >> A = (p+k) - T mod (p+k) >> C = T mod (p+k) >> and Det M = -[2*k^2 mod(p+k)] = B*C - A*D >> then n = B + D >> --------------------------------------------- >> Example: >> T = 20303 >> p = 79 >> k = 23 >> Factored trying 5 surrogates on the fifth surrogate using k=1 where >> the start was with n=7. >> I cannot duplicate your result. >> If you would be kind enough to provide a list >> of S from n = 7 to n = the one that gave a factor >> then I can see if my program comes up with the >> same numbers. If it doesn't, then we're using >> different routines. I do use +/-k as it's easy enough to just check both, and my f's can > be fractions with a 2 in the denominator. Try again. If you can't duplicate then I'll think about going to the > program to pull out in more detail what it's doing. >> I'm assuming that you used T=20303, k=1, n=7,8,9,10,11 >> and had success at n=11. I used k=1 or -1, since the program automatically checks both, and the > rest is probably correct but I haven't adjusted the program to tell me > what n it is using as that only just recently came up as important, so > it was n=11 or n=12, probably n=11. so you need to fix your buggy code first, right? Previously I thought only the k/T ratio was important. > Is your factor of the surrogate that worked equal to >> k + a factor of T? In my example, 79 as a factor of >> T=20303 was found with the factor k+79 = 23+79=102, >> a factor of S at n=74; S=1503480 = 102*14740 >> Enrico I've been more focused on theory than the program, but am just now > getting back to the question of implementation. My guess is that my checking plus or minus k should explain how I see > much better success, so maybe I jumped the gun by calling you a liar. but he IS a liar. That effectively doubles checks, though with a very light impact since > it is just a matter of first adding k to 2f_1 or 2f_2 and checking the > gcd with T and then subtracting, so it is the kind of simple > optimization that any serious coders would use. Even with that doubling I needed only 10 surrogates to check, again > that is much worse than what I've seen with previous code. for T<10 ? But you see, experiments only told me so much so I shelved things for > a while and went on to other things. so it dosent work and you gave up? If they did show this idea was just total crap then I might still do > analysis to figure out why, as with all previous surrogate factoring > equations I could always pull them apart to find out why I wasn't > getting the desired behavior. So you admit that it dosent work ? > And that behavior I remind is the ability to factor an RSA sized > number in under 10 minutes on a standard desktop computer. Recently I came back to do a detailed analysis which includes new info > like the decision relations this thread is ACTUALLY about, and next > I'll see if the new info leads to better working code. That's how it's done. so you are a hacker that dosent know math ? > You people instead just want to come out every once and a while and > claim it doesn't work well, without being able to explain why. show that it does work. > Your lack of curiosity is what I am using to get people suspicious of > you. Your lack of mathamatics is what I am using to get people suspicious of you. So, yeah, maybe surrogate factoring is a bum idea that will never work > well, but why? you admit that ...surrogate factoring is a bum idea that will never work... Why? When? That simple question is a driver of human evolution. Without asking > it, you cannot truly be an intellectual if you are criticizing an > idea. but you are not an intellectual, you stuck in basic algebra, ha! > If you don't care, fine. But if you care enough to attack an idea, if > you are a real researcher you need to care enough to figure out why it > doesn't work! then get busy, lard ass. That's why political hacks are so annoying!!! then why do you persist at it? They don't give a damn about anything but maybe their paychecks and > satisfaction at winning at any costs, so start a war? WTF are you talking about, lame ass Mathless Bimbo? > Who cares if > you're a political hack and that's your job. People starving as a > result of policies you help implement? Who cares if you are a > political hack as hey, that's their problem, right? Political hacks > are people who do not care about the truth, and cannot be bothered to > ask, why. JSH is a HUGE political HACK, for YEARS and YEARS. It's a mindless and narrow worldview that sees people as things and > cares nothing at all about what actually is true. You should change your preception. It is the anti-thesis of the scientist to simply take a position, have > talking points, and care only about convincing people without knowing > the 'why'. What? Science is all about why. WRONG. It is about the HOW. James Harris - the dufus on sci.math === Subject: Re: JSH: Surrogate factoring, periodic behavior >> Having completed better analysis on surrogate factoring I found the >> equations that explain a periodic behavior at least one person has >> noted in posts, where for a given k and n, if you find a prime factor >> p of your target T with that n, then you will find other solutions by >> adding multiples of p to n. >> Two of the equations determining that behavior are >> Cw = n + (k + 2xr_1*p_1)( k + 2xr_2*p_2) - ((k + 2xr_1*p_1)( k + >> 2xr_2*p_2) - 2k^2)/T >> and >> w = k + 2xr_2*p_2 mod T >> where if the second equation is true for a given n, then you will have >> a solution to the surrogate factoring equations at that n, but that is >> an only if. There C doesn't matter but is just some non-zero integer, >> as w just needs to be any factor of the right side--which is an >> integer I should note as the T must divide through--for which the >> second condition is met. >> That is the primary decision relation that determines if a surrogate >> factorization can work or not. >> Remember the surrogate factorization involves factoring a target >> composite T by solving >> (x+k)^2 = y^2 + 2k^2 + nT >> where the primary question has been, how do you pick k and n? >> If they are picked correctly then some solution for x and y will also >> be a solution for >> x^2 = y^2 mod p >> where p is a prime factor of T. >> James Harris >> . You've never explained what x and y are supposed > to be or how they are supposed to be used. > How are they? > Duh! They are in a quadratic! === Subject: Re: JSH: Surrogate factoring, periodic behavior There does seem to be a periodicity to your mania. But is it really periodic, or is it chaotic? An interesting problem ... === Subject: Re: JSH: Surrogate factoring, periodic behavior periodic, or is it chaotic? An interesting problem ... I've got JSH's number. Its > 3.57 but probably around 1+ sqrt(8) Try this: http://en.wikipedia.org/wiki/Logistic_map Enrico === Subject: Re: JSH: Surrogate factoring, periodic behavior periodic, or is it chaotic? An interesting problem ... I've got JSH's number. Its > 3.57 but probably around 1+ 8 Try this: http://en.wikipedia.org/wiki/Logistic_map Enrico === Subject: Re: JSH: Surrogate factoring, periodic behavior > Having completed better analysis on surrogate factoring I found the > equations that explain a periodic behavior at least one person has > noted in posts, where for a given k and n, if you find a prime factor > p of your target T with that n, then you will find other solutions by > adding multiples of _p_ *** This is not true *** to n. > Last line should be: > adding multiples of (p + k) to n. Enrico === Subject: Re: JSH: Surrogate factoring, periodic behavior >*** Different Example Here Say T = 21. Let k = 1, n = 1. Then S = 2*k + n*T = 2 + 21 = 23. This is prime, Yes, but that gives you factors of 1 * 23 and -1 * -23. This gives F1 = 1, F2 = 23 F1 - 1 = 0 -> GCD(0, 21) so nothing. F2 - 1 = 22 -> GCD(22, 21) nothing again. we also have F1 = -1, F2 = -23 F1 - 1 = -2 -> GCD(-2, 21) again nothing. F2 - 1 = -24 -> GCD(-24, 21) = 3 BINGO! In my tests I include 1 * S as my first pair of factors of S, and I allow for both factors to be negative since James has never said that only positive factors of S are allowed. As an aside, James tends to factor S differently. He usually has: S = 4 * f_1 * f_2 I am not sure why he insists on the 4, since there is no guarantee that S is a multiple of 4, and his use of it gets him into fractional values later on (one of his examples has f_1 = 7/2). He would do better to drop the 4 and just split S into two factors. It may be that the factor of 4 was required by one of the earlier iterations of his method and he has never got round to taking it out. It is always possible to pick k and n so that S is a multiple of 4 if that is a requirement, but in the example above that would have missed the factor for S = 23. It is also worth noting that in this case trial factorisation gives: 21 mod 2 = 1 21 mod 3 = 0 BINGO! Again, trial factorisation is faster than James' method. > so increment n by 1 and try again: S = 2*k + 2*T = 2 + 42 = 44 = 4 * 11. Thus let F1 = 11, F1 = 4. X = (F1 + F2 - 2)/2 = (11 + 4 - 2)/2 = 13/2. Y = (F1 - F2)/2 = 7/2. Then X + Y = F1 - 1 = 10, and X - Y = F2 - 1 = 3. Thus g1 = GCD(F1 - 1, T) = GCD(10, 21) = 1 and g2 = GCD(F2 - 1, T) = GCD(3, 21) = 3, the latter of which leads to the factorization of T. The central question is still: why should this process >have a high probability of working? Agreed. The different iterations of the Surrogate method all find factors, but do so inefficiently. Unless James can either eliminate some of his free variables or limit the range of choices allowed for them the method is probably going to remain inefficient. The more free choices there are the more different choices need to be tried before hitting on the right combination. His current track seems to be to try to limit the values allowed for k and n. In principle this is the right thing to do. rossum >The rationale seems >lacking. This is unlike, say, the quadratic sieve process, >where a rationale is given. The lack of rationale accounts, >I think for two things: (1) why your method is not being >taken seriously by most people interested in factoring, and >(2) why so far it does not seem to work. You seem to be >hoping that either there is hidden magic in what you are >doing, or maybe you will just get lucky. It could happen. >But neither of these is a logical basis for an algorithm. > Marcus. > Marcus. === Subject: Re: JSH: Surrogate factoring, periodic behavior As an aside, James tends to factor S differently. He usually has: S = 4 * f_1 * f_2 I am not sure why he insists on the 4, since there is no guarantee > that S is a multiple of 4, and his use of it gets him into fractional > values later on (one of his examples has f_1 = 7/2). He would do > better to drop the 4 and just split S into two factors. Thats what I do. Never liked the idea of fractional factors of an integer. I sometimes get fractional X and Y, but Enrico === Subject: Re: JSH: Surrogate factoring, periodic behavior > Having completed better analysis on surrogate factoring I found the > equations that explain a periodic behavior at least one person has > noted in posts, where for a given k and n, if you find a prime factor > p of your target T with that n, then you will find other solutions by > adding multiples of p to n. > Two of the equations determining that behavior are > Cw = n + (k + 2xr_1*p_1)( k + 2xr_2*p_2) - ((k + 2xr_1*p_1)( k + > 2xr_2*p_2) - 2k^2)/T > and > w = k + 2xr_2*p_2 mod T > where if the second equation is true for a given n, then you will have > a solution to the surrogate factoring equations at that n, but that is > an only if. There C doesn't matter but is just some non-zero integer, > as w just needs to be any factor of the right side--which is an > integer I should note as the T must divide through--for which the > second condition is met. > That is the primary decision relation that determines if a surrogate > factorization can work or not. > Remember the surrogate factorization involves factoring a target > composite T by solving > (x+k)^2 = y^2 + 2k^2 + nT > where the primary question has been, how do you pick k and n? > If they are picked correctly then some solution for x and y will also > be a solution for > x^2 = y^2 mod p > where p is a prime factor of T. > James Harris > . > Here is how I understand your algorithm. > You want to factor integer T. > You choose k and n, and let > S = 2*k + n*T. > S is your 'surrogate'. Perhaps S is easier to factor than T. You > then hope that the factors of S lead to a nontrivial factorization of > T. > Specifically, suppose k = 1, and S = F1 * F2. > Let X = (F1 + F2 - 2)/2 > Let Y = (F1 - F2)/2. > You hope that X^2 - Y^2 has factors in common with T. > Since X^2 - Y^2 = (X + Y) * (X - Y), you consider X + Y > and X - Y. > You note that > X + Y = F1 - 1 and > X - Y = F2 - 1. > So the question is: what are > g1 = GCD(F1 - 1, T) and > g2 = GCD(F2 - 1, T). > If 1 < g1 < T, you have a nontrivial factor. Similarly > for g2. > Of course it may happen that S factors in several different > ways. That is, there may be other choices for F1 and F2. > If your first choice for F1 and F2 don't work, you try the > others. > If none of those work, you increment n and compute a new > S and start over. > Is that the surrogate factoring process? *** Different Example Here Say T = 21. Let k = 1, n = 1. Then S = 2*k + n*T = 2 + 21 = 23. This is prime, so increment n > by 1 and try again: > Why? Who cares if the surrogate is prime? It might still factor. Even trivial factorizations of the surrogate may work. > The central question is still: why should this process > have a high probability of working? The rationale seems Yes, questions, the mark of true researchers and human beings in general, as human curiosity is such a wonderful thing. We wonder why and in looking for answers humanity finds new things. So yeah, like I mentioned in another thread, the question in my mind for some time has been how so many of you seem to lack basic human curiosity. Does the idea work at all? If not, why not? If so, how? Learning begins with questions. Now I have worked for years at answering questions presented by an idea, which was, could you factor one number with another, and I kept at it despite derision and insults from people like you. You are the jocks of the schoolyard who tease that strange little boy who is so fascinated with his books. Whether you wanted to be or not, or thought you hated those people growing up, that is your behavior against me and always has been. Maybe you hated them growing up because you wanted to BE them, and given the slightest excuse they are who you became. You are the cruel jocks picking on the kid you call nothing. And I am the genius. James Harris === Subject: Re: JSH: Surrogate factoring, periodic behavior >> for some time has been how so many of you seem to lack basic human > curiosity. Does the idea work at all? If not, why not? If so, how? no it does not, too many guessing variables. no real structure. > Learning begins with questions. do you need a question? > Now I have worked for years at answering questions presented by an > idea, which was, could you factor one number with another, and I kept > at it despite derision and insults from people like you. I have never insulted you. You are self-insulting. You are always insulting yourself with your posts that you know are nonsense. > You are the jocks of the schoolyard who tease that strange little boy > who is so fascinated with his books. you may believe you are a strange little boy, but you do not read books, especially math books. > Whether you wanted to be or not, or thought you hated those people > growing up, that is your behavior against me and always has been. the windmills in your mind are grinding up making a wierd screaching noise that comes out your ears as green goo. > Maybe you hated them growing up because you wanted to BE them, and > given the slightest excuse they are who you became. projecting again, you always do that. wiki for it. You are the cruel jocks picking on the kid you call nothing. the kid that has nothing and says he does needs to be cruelly picked upon. And I am the genius. Prove it, What did you score on the SAT ? > James Harris > === Subject: Re: JSH: Surrogate factoring, periodic behavior > Having completed better analysis on surrogate factoring I found the > equations that explain a periodic behavior at least one person has > noted in posts, where for a given k and n, if you find a prime factor > p of your target T with that n, then you will find other solutions by > adding multiples of p to n. > Two of the equations determining that behavior are > Cw = n + (k + 2xr_1*p_1)( k + 2xr_2*p_2) - ((k + 2xr_1*p_1)( k + > 2xr_2*p_2) - 2k^2)/T > and > w = k + 2xr_2*p_2 mod T > where if the second equation is true for a given n, then you will have > a solution to the surrogate factoring equations at that n, but that is > an only if. There C doesn't matter but is just some non-zero integer, > as w just needs to be any factor of the right side--which is an > integer I should note as the T must divide through--for which the > second condition is met. > That is the primary decision relation that determines if a surrogate > factorization can work or not. > Remember the surrogate factorization involves factoring a target > composite T by solving > (x+k)^2 = y^2 + 2k^2 + nT > where the primary question has been, how do you pick k and n? > If they are picked correctly then some solution for x and y will also > be a solution for > x^2 = y^2 mod p > where p is a prime factor of T. > James Harris > . >> Here is how I understand your algorithm. >> You want to factor integer T. >> You choose k and n, and let >> S = 2*k + n*T. >> S is your 'surrogate'. Perhaps S is easier to factor than T. You >> then hope that the factors of S lead to a nontrivial factorization of >> T. >> Specifically, suppose k = 1, and S = F1 * F2. >> Let X = (F1 + F2 - 2)/2 >> Let Y = (F1 - F2)/2. >> You hope that X^2 - Y^2 has factors in common with T. >> Since X^2 - Y^2 = (X + Y) * (X - Y), you consider X + Y >> and X - Y. >> You note that >> X + Y = F1 - 1 and >> X - Y = F2 - 1. >> So the question is: what are >> g1 = GCD(F1 - 1, T) and >> g2 = GCD(F2 - 1, T). >> If 1 < g1 < T, you have a nontrivial factor. Similarly >> for g2. >> Of course it may happen that S factors in several different >> ways. That is, there may be other choices for F1 and F2. >> If your first choice for F1 and F2 don't work, you try the >> others. >> If none of those work, you increment n and compute a new >> S and start over. >> Is that the surrogate factoring process? >> *** Different Example Here >> Say T = 21. Let k = 1, n = 1. Then >> S = 2*k + n*T = 2 + 21 = 23. This is prime, so increment n >> by 1 and try again: Why? Who cares if the surrogate is prime? It might still factor. Even trivial factorizations of the surrogate may work. > The central question is still: why should this process >> have a high probability of working? The rationale seems > Yes, questions, the mark of true researchers and human beings in > general, as human curiosity is such a wonderful thing. We wonder why and in looking for answers humanity finds new things. So yeah, like I mentioned in another thread, the question in my mind > for some time has been how so many of you seem to lack basic human > curiosity. Does the idea work at all? If not, why not? If so, how? Learning begins with questions. Now I have worked for years at answering questions presented by an > idea, which was, could you factor one number with another, and I kept > at it despite derision and insults from people like you. You are the jocks of the schoolyard who tease that strange little boy > who is so fascinated with his books. Whether you wanted to be or not, or thought you hated those people > growing up, that is your behavior against me and always has been. > Maybe you hated them growing up because you wanted to BE them, and > given the slightest excuse they are who you became. You are the cruel jocks picking on the kid you call nothing. And I am the genius. So, how does 4773695331839566234818968439734627784374274207965089 factor? David Bernier === Subject: Re: JSH: Surrogate factoring, periodic behavior > Having completed better analysis on surrogate factoring I found the > equations that explain a periodic behavior at least one person has > noted in posts, where for a given k and n, if you find a prime factor > p of your target T with that n, then you will find other solutions by > adding multiples of p to n. > Two of the equations determining that behavior are > Cw = n + (k + 2xr_1*p_1)( k + 2xr_2*p_2) - ((k + 2xr_1*p_1)( k + > 2xr_2*p_2) - 2k^2)/T > and > w = k + 2xr_2*p_2 mod T > where if the second equation is true for a given n, then you will have > a solution to the surrogate factoring equations at that n, but that is > an only if. There C doesn't matter but is just some non-zero integer, > as w just needs to be any factor of the right side--which is an > integer I should note as the T must divide through--for which the > second condition is met. > That is the primary decision relation that determines if a surrogate > factorization can work or not. > Remember the surrogate factorization involves factoring a target > composite T by solving > (x+k)^2 = y^2 + 2k^2 + nT > where the primary question has been, how do you pick k and n? > If they are picked correctly then some solution for x and y will also > be a solution for > x^2 = y^2 mod p > where p is a prime factor of T. > James Harris > . > Here is how I understand your algorithm. > You want to factor integer T. > You choose k and n, and let > S = 2*k + n*T. > S is your 'surrogate'. Perhaps S is easier to factor than T. You > then hope that the factors of S lead to a nontrivial factorization of > T. > Specifically, suppose k = 1, and S = F1 * F2. > Let X = (F1 + F2 - 2)/2 > Let Y = (F1 - F2)/2. > You hope that X^2 - Y^2 has factors in common with T. > Since X^2 - Y^2 = (X + Y) * (X - Y), you consider X + Y > and X - Y. > You note that > X + Y = F1 - 1 and > X - Y = F2 - 1. > So the question is: what are > g1 = GCD(F1 - 1, T) and > g2 = GCD(F2 - 1, T). > If 1 < g1 < T, you have a nontrivial factor. Similarly > for g2. > Of course it may happen that S factors in several different > ways. That is, there may be other choices for F1 and F2. > If your first choice for F1 and F2 don't work, you try the > others. > If none of those work, you increment n and compute a new > S and start over. > Is that the surrogate factoring process? > *** Different Example Here > Say T = 21. Let k = 1, n = 1. Then > S = 2*k + n*T = 2 + 21 = 23. This is prime, so increment n > by 1 and try again: Why? Who cares if the surrogate is prime? It might still factor. > Good point. I should have tried it. > Even trivial factorizations of the surrogate may work. > The central question is still: why should this process > have a high probability of working? The rationale seems Yes, questions, the mark of true researchers and human beings in > general, as human curiosity is such a wonderful thing. We wonder why and in looking for answers humanity finds new things. > This is just empty pontification. I asked a reasonable question. You come back with blather. I didn't ask for a condescending fatuous sermon. > So yeah, like I mentioned in another thread, the question in my mind > for some time has been how so many of you seem to lack basic human > curiosity. > might work? > Does the idea work at all? If not, why not? If so, how? > Right. Do you have some insight or some basis for a hunch? Is there an underlying idea, just as there is an underlying idea (several, actually) with the quadratic sieve algorithm? If so, what is this idea? The surrogate is a function of T, but why should that mean that factors of the surrogate have a special relationship to factors of T? > Learning begins with questions. > Debatable, actually. But anyway, I can't tell here if you are saying I should ask questions (which I did), or I shouldn't. > Now I have worked for years at answering questions presented by an > idea, which was, could you factor one number with another, and I kept > at it despite derision and insults from people like you. You are the jocks of the schoolyard who tease that strange little boy > who is so fascinated with his books. > You are fascinated with books?? Just not math books, apparently. > Whether you wanted to be or not, or thought you hated those people > growing up, that is your behavior against me and always has been. > Maybe you hated them growing up because you wanted to BE them, Be YOU??? Never. > and > given the slightest excuse they are who you became. You are the cruel jocks picking on the kid you call nothing. And I am the genius. > If you are the genius, why do you keep erasing your posts? Is that what geniuses do? Here's what looks interesting to me in what you are trying. You find a surrogate S with factors F1 and F2. If the process works, then gcd(F1 - 1, T) or gcd(F2 - 1, T) is not equal 1 or T. Since in some cases of interest, T is a product of primes, say T = p1 * p2, then say e.g., gcd(F1 - 1, p1) = p1. Which means, p1 is a divisor of F1 - 1. Which implies, p1 is a divisor of S - F2. Not that I can see what that gets you. I still don't see why you think this scheme is likely to work. Marcus. > James Harris- Hide quoted text - - Show quoted text - === Subject: Wholesale / Sell Gucci Moon Bag @btbsell.com Louis Vuitton, Fendi SPY Bags, Fendi B bag, Chloe Paddington bags, Chloe Silverado bags, Chloe Edith Bag, Balenciaga, Goyard, miumiu, mulberry, prada, Marc Jacobs, Gucci 85th, Dior Gaucho, Jimmy choo, Gucci, Chanel, YSL, Hermes, Loewe, Versace, Mqueen, Thomaswylde , We accept Paypal www.btbsell.com MSN: ebaynt@gmail.com luggages Bottega loewe chloe Fendi LV Gucci Versace YSL Thomaswylde Mqueen Belt | Necklace | Finger Ring | Key Ring & Phone Strap | SCARF Fendi watches | Dior watches | Armani watches | Burberry watches | LV watches | Bottega Veneta Bag | goyard | Loewe bag | MiuMiu Prada BALENCIAGA HANDBAGS Twiggy Duffle | 34cm | 45cm | 51cm | 38cm | Kooba | Mulberry | Fendi B Bag | Fendi | FendiSpy | GUCCI HANDBAGS 85th Anniversary | Gucci Jolicoeur Tote | NEW ARRIVAL | Gucci Boston Bag | Gucci Hobo | Scarf Collection | Guccissima Collection | Gucci Moon Bag | Gucci D Bag | Gucci Bag | Marc Jacobs | Chloe Paddington Shopper | New Chloe | Chloe Paddington Color Hardware | Chloe Paddington With Shoulder Strap | Chloe Paddington With Silver Hardware | Chloe Doctor Bag | Chloe Betty | Chloe Silverado | Chloe Hampton | Chloe Horse Collection | Chloe Tote With Lock and Key | Chloe IT Edith Bag | Chloe Paddington | Suhali | Monogram Multicolore | Monogram Denim | Damier Canvas | Monogram Ceries | Taiga | Damier Geant | Epi | Monogram Canvas | Winter 2005 / 2006 Collection | Waltz Oskar | Antigua | Cruise Collection | Onatah | NEW ARRIVALS | Mini | vernis | Trapeze | LV Stamped | Perforated | HERMES HANDBAG ostrich | 35cm Hermes Birkin Crocodile | 42cm JPG Birkins | Hermes Tote | 35cm Birkin Togo Leather CHANEL HANDBAGS Chanel Bag | Cambon Collection | CHRISTAIN DIOR HANDBAGS Dior Detective | Dior Rebelle | Dior bag | Dior Gaucho | BOTIKER HANDBAGS Luella | Jimmy Choo | Bulga | Chanel Wallet | Marc Jacobs Wallet | Chloe wallet | Louis vuitton Wallet | Gucci wallet | Miumiu Shoes | HERMES Shoes | TODS Shoes | Salvafove Fenagamo Shoes | D&G Shoes | Dior Shoes | Chanel Shoes | Prada shoes | Gucci Shoes | LV shoes | chloe shoes ------------------------------------ === Subject: #31C fourth way of proving Earth is 2X older than Jupiter; twin stars are mostly 2X age different?? Re: ATOM TOTALITY (Atom Universe) THEORY REPLACES BIG BANG THEORY IN PHYSICS Nope, I do not think this method is going to be as productive as zircon dating or core dating or radioactive element abundance. The trouble with twin stars as much of astronomy has the trouble of such huge distances away and the unwarranted assumptions that goes into the data. When astronomy can not tell whether a star is a binary system in many cases, then that leads to little confidence on my part that binary stars can tell us age differences. If we find a zircon crystal from Vesta asteroid that measures the age of the Solar System at 8 billion years old is about the best evidence we can find. Or if we find Earth having twice as much radioactive elements like thorium or uranium than does Jupiter in parts per billion would be strong evidence. Another search for ages of companion stars in binary systems http://adsabs.harvard.edu/abs/2000PhDT.........7P http://www.astrophysicsspectator.com/topics/stars/BinaryPulsar.html One of those sites mentions an age difference of 1 billion years of companion stars. But that is not a large enough difference for what I am looking for. So I think that binary stars can be supporting evidence that Earth is twice as old as Jupiter, but I suspect binary star studies cannot be the primary lead evidence. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: #31D historical-physics that electron must be (-1) charge value; fourth way of proving Earth is 2X older than Jupiter; twin stars are mostly 2X age different?? Re: ATOM TOTALITY (Atom Universe) THEORY REPLACES BIG BANG THEORY IN PHYSICS I am going to leave this binary star method from this book for now. Perhaps some news will come forth before the 3rd edition of this book which says that companions of binary stars are about 1/2 as old. Or that most companions to binary stars have 1/2 the radioactive elements such as strontium or rubidium or thorium or uranium in parts per billion which again implies an age of 1/2 as old. Much of this discussion of our Solar System should be a separate big book written by me titled something to the effect Growing Solar System Theory: via Dirac Radioactivity We see this Growing Solar System throughout the Cosmos and we rarely have any evidence of the Nebular Dust Cloud Theory. When I write the above book I should start it out by saying that when Science and Scientist enter a big field of science to explain a phenomenon, they usually get it mistakenly and big wrong the first time. The first time scientists explained Earth was as a flat object in the center of the Cosmos. The first time scientists explained the Solar System was the Ptolemy model of epicycles. The first time scientists explained disease was some humour inside the body that had to be sucked out by leeches. The point of this exercise is given a world class phenomenon to be explained for the first time by scientists, that they usually get it very badly wrong and the origin of the Solar System as a Nebular Dust Cloud Theory is another one of those huge gaffes. Back to Twin Stars. One website says 50% of all stars are twin stars and another says 90%. Which is correct? Well, let us not worry which is correct but concern ourselves with the idea that if 50% are binary stars then life in 50% of the possible star systems has just been eliminated because binary stars are not stable enough of a environment for life to become established. And if 90% is the more accurate figure, then only 10% of stars can possibly accommodate life. So planet Earth and our Solar System are rare phenomenon provided that most stars are binary stars. I think I should write this book now, since it is fresh on my mind, at least get it started. And added impetus is the idea that the age of the Solar System is a fact which if Earth is twice as old as Jupiter would be the very best evidence that destroys the Big Bang theory and the Nebular Dust Cloud theory all in one news report of a zircon crystal. So where the science of geology takes precedence over astronomy and cosmology. Geology is more believable because we are right here and not separated by light years of distance and the huge paper bag of assumptions. But I am not quite finished with this 2nd edition of this book. One topic that was raised recently is the question of when the electron was assigned the value of (-1). I believe the history of physics goes back to Ben Franklin as to positive and negative charges but the electron was not fully developed until about the late 1800s and early 1900s. So the question is: was it arbitrary to assign the electron as (-1) or was it a lucky guess for which the laws of physics can only have the electron as (-1)? In the 1990s I vaguely remember my mind traversing this question but I could not remember what my answer was back then. I have a fishy feeling that some feature of physics demanded that the electron be assigned the (-1) value in order for satisfying some physics equations. Was it the negative sign in the Maxwell Equation Theory of Faraday's Law? If the electron had been assigned a (+1) value, would the Maxwell Equations not come out properly? I have forgotten what my answer to this assigning of electron as (-1) was in the history of physics, but I am going to venture into proving that the electron has to be assigned (-1) due to the Atom Totality theory. Notice that the number (i) appears alot in physics and is the sqrt(-1). Notice that mathematics is incomplete unless it has a sqrt(-1). Now imagine if physics history had assigned the electron as (+1) instead of (-1). And then humanity discovers the Atom Totality theory. And then humanity realizes that the Euler Identity of e^(pi)(i) = -1 is the math description of the Observable Cosmos where the (-1) is the fact that we are living in the last electron of the 5f6. And the (i) within that Identity is the fact of orthogonal energy term of the electron space universe. What I am trying to say quickly is that the Atom Totality Theory proves that the assigning of the electron as (-1) was never an arbitrary exercise. That the electron had to have the value of (-1) and could never take the value of (+1). But I do suspect that other parts of physics already found out that the electron charge value had to be (-1) such as the Maxwell Equations. If not, well, then this post is a historic post because it shows us that the charge value of the electron has to be (-1). Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: Re: #28F perhaps an easy path to a proof that (pi) and (e) are the only two independent Transcendental Numbers Re: ATOM TOTALITY (Atom Universe) THEORY REPLACES BIG BANG THEORY IN PHYSICS , > Who says, though, that temperature was meant to be measured in Kelvin? > After all, Kelvin is only a shift of Celsius, and Celsius temperatures > are based on one particular compound in the universe. Maybe temperature should be based on a single unit which is based on > the melting/boiling temperature of hydrogen (the most plentiful > material in the universe). Temperature is defined by an ideal gas, a fluid of operating in a heat engine running a reversible cycle. The amount of work extracted from two reservoirs at temperatures t_1 and t_2 is the difference between the amount of heat absorbed from the two reservoirs, Q_2 - Q_1. It turns out that there is a universal function of temperature f(t_1, t_2) such that Q_2/Q_1 = f(t_1, t_2) and f(t_0, t_2) f(t_1, t_2) = ----------- = f(t_0, t_1) By choosing once and for all t_0 and K we have theta(t) = K.f(t_0, t). The function theta is the absolute thermodynamic scale of temperature. K can be chosen so that the difference between the boiling point and freezing point of water is 100 degree. -- Michael Press === Subject: #28F why Kelvin is special; perhaps an easy path to a proof that (pi) and (e) are the only two independent Transcendental Numbers Re: ATOM TOTALITY (Atom Universe) THEORY REPLACES BIG BANG THEORY IN PHYSICS <46CD344A.5080607@dtgnet.com> (snipped) Temperature is defined by an ideal gas, a fluid of > operating in a heat engine running a reversible cycle. The amount of work extracted from two reservoirs at > temperatures t_1 and t_2 is the difference between the > amount of heat absorbed from the two reservoirs, > Q_2 - Q_1. It turns out that there is a universal function of temperature > f(t_1, t_2) such that Q_2/Q_1 = f(t_1, t_2) and f(t_0, t_2) > f(t_1, t_2) = ----------- > = f(t_0, t_1) By choosing once and for all t_0 and K we have theta(t) = K.f(t_0, t). The function theta is the absolute thermodynamic > scale of temperature. Well you threw the knockout punch but noone fell down. Or, another metaphor, you did everything sweet to the girl but forgot to ask the question: will you marry me. Kelvin temperature is different from any other temperature scale in that it is as basic as mass or distance. Celsius or Fahrenheit are arbitrary, but Kelvin is not arbitrary. Kelvin is fixed to a physics property where there is no motion. Where you have Absolute Zero corresponding to no motion. So when the Cosmic Background Microwave Radiation comes back as a number that equals (e) of 2.71...... degrees Kelvin and blackbody radiation is very significant and important and as fixed as that of saying the hydrogen atom has one proton or that the atomic number for helium is 2. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: Re: #28F perhaps an easy path to a proof that (pi) and (e) are the only two independent Transcendental Numbers Re: ATOM TOTALITY (Atom Universe) THEORY REPLACES BIG BANG THEORY IN PHYSICS <46CD344A.5080607@dtgnet.com> Who says, though, that temperature was meant to be measured in Kelvin? > After all, Kelvin is only a shift of Celsius, and Celsius temperatures > are based on one particular compound in the universe. > Maybe temperature should be based on a single unit which is based on > the melting/boiling temperature of hydrogen (the most plentiful > material in the universe). Temperature is defined by an ideal gas, a fluid of > operating in a heat engine running a reversible cycle. The amount of work extracted from two reservoirs at > temperatures t_1 and t_2 is the difference between the > amount of heat absorbed from the two reservoirs, > Q_2 - Q_1. It turns out that there is a universal function of temperature > f(t_1, t_2) such that Q_2/Q_1 = f(t_1, t_2) and f(t_0, t_2) > f(t_1, t_2) = ----------- > = f(t_0, t_1) By choosing once and for all t_0 and K we have theta(t) = K.f(t_0, t). The function theta is the absolute thermodynamic > scale of temperature. K can be chosen so that the difference between > the boiling point and freezing point of water > is 100 degree. But it doesn't have to, which was the point of my post. You could choose K so that the difference [yada yada yada] is 10, not 100. Or you could use a different compound, other than water. --- Christopher Heckman === Subject: Re: #28F perhaps an easy path to a proof that (pi) and (e) are the only two independent Transcendental Numbers Re: ATOM TOTALITY (Atom Universe) THEORY REPLACES BIG BANG THEORY IN PHYSICS > , > Who says, though, that temperature was meant to be measured in Kelvin? > After all, Kelvin is only a shift of Celsius, and Celsius temperatures > are based on one particular compound in the universe. > Maybe temperature should be based on a single unit which is based on > the melting/boiling temperature of hydrogen (the most plentiful > material in the universe). > Temperature is defined by an ideal gas, a fluid of > operating in a heat engine running a reversible cycle. > The amount of work extracted from two reservoirs at > temperatures t_1 and t_2 is the difference between the > amount of heat absorbed from the two reservoirs, > Q_2 - Q_1. > It turns out that there is a universal function of temperature > f(t_1, t_2) such that Q_2/Q_1 = f(t_1, t_2) and > f(t_0, t_2) > f(t_1, t_2) = ----------- > = f(t_0, t_1) > By choosing once and for all t_0 and K we have > theta(t) = K.f(t_0, t). > The function theta is the absolute thermodynamic > scale of temperature. > K can be chosen so that the difference between > the boiling point and freezing point of water > is 100 degree. But it doesn't have to, which was the point of my post. You could > choose K so that the difference [yada yada yada] is 10, not 100. Or > you could use a different compound, other than water. My point is that the the definition of temperature is not based on water. You said Kelvin is only a shift of Celsius, and Celsius temperatures are based on one particular compound in the universe. -- Michael Press === Subject: Re: Geometrical Quaternions I have another question. How can you define a quat's position and orientation? For example: If I have a vector3 (20,20,20), and I want to rotate it to somewhere else... how would you put/convert this vector to a quat? I ask this because If I have a quat let's say (1.0f, 1.0f, 1.0f, 1.0f) how can you know where it is in the world space? Jack === Subject: Re: Geometrical Quaternions > I have another question. > How can you define a quat's position and orientation? > For example: > If I have a vector3 (20,20,20), and I want to rotate it to > somewhere else... how would you put/convert this vector to a quat? > I ask this because If I have a quat let's say (1.0f, 1.0f, 1.0f, 1.0f) > how can you know where it is in the world space? > Jack Its possible to define a quaternion in terms of an axis of rotation and an angle around the axis: q = (cos(a/2), x * sin(a/2), y * sin(a/2), z * sin(a/2)) where: * a=angle of rotation. * x,y,z = vector representing axis of rotation. More here: http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/ === Subject: Re: Error det & corr > Can any one help me out to find me what methods are exactly used to do > following: 1. 2-bit error correction > 2. 2-bit error detection > 3. 3-bit error correction > 4. 3-bit error detection i know only abt single bit ECC & EDC but do specify their names/ > methods to do above said...... > of codes known as Reed-Solomon codes, after the names of their discoverers. Current implementations of Reed-Solomon codes in CD technology are able to cope with error bursts as long as 4000 consecutive bits. < http://www.eccpage.com/reed_solomon_codes.html > David Bernier === Subject: Convolution f*f=f Let f be a function fron L^1(R) such that f * f = f, here * stands for the convolution. Does this imply that f = 0 a.e. ? What if we just suppose f to be in R/Z ? === Subject: Re: Convolution f*f=f > Let f be a function fron L^1(R) such that f * f = f, here * > stands for the convolution. Does this imply that f = 0 a.e. ? What if we just suppose f to be in R/Z ? If this is homework the author could have dropped the hint Fourier transformation ... === Subject: Convolution f*f=f Let f be a function fron L^1(R) such that f * f = f, here * stands for the convolution. Does this imply that f = 0 a.e. ? What if we just suppose f to be in R/Z ? === Subject: Convolution f*f=f Let f be a function fron L^1(R) such that f * f = f, here * stands for the convolution. Does this imply that f = 0 a.e. ? What if we just suppose f to be in R/Z ? === Subject: heterosis is the flaw of the master race !! Well Tooly, I appreciate your passion, and agree that Liberals are !! misguided. But so are conservatives. !! !! But rather than write of what I think should happen, let me lay out !! what I see coming, whether we like it or not. Both liberal and !! conservative frames of thot are too distorted to fit the facts. !! !! Might still makes Right. but now, after 5000 years of the brave heart, !! strong right arm, sword in hand, that just dont cut it any more. Smith !! & Wesson guarantee equal rights for smart women. Most guys dont get !! it. !! !! But the other thing smart women have, is cunts. And they still work as !! well as they ever did in getting guys to go along with whatever agenda !! a smart woman has. And what the smart bitches are doing, is ignoring !! the warriors, and ing the geeks. Its the geeks who have the !! innovative minds that is empowering their mutual ventures, and !! allowing them to laff all the way to the bank. !! !! The geeks invented the internet and the hardware that puts this !! message in front of your face. But it is the women who ran the offices !! and kept track of the inventory, and... increasingly, they see they !! can get along without the high cost of CEO male management. !! !! Smart women have also seen that the men of their station who they'd !! consider as husbands, are already married to sexy bimbos. So, they are !! going to fertility clinics, selecting among thousands of the most !! promising Y chromosome lines on the planet, and have already given !! birth to some of the most talented young minds around. !! !! They are, consciously or not, selecting fair haird Nordic lines way !! more than all others, and giving birth to lotsa trophy blondes. These, !! my friends, are the Uberwench. And they dont *have* family values. !! They will, as we've already seen, some lech for the last few !! years of his life, then inherit his empire. !! !! I see lesbians moving in with each other, and likewise using !! fertility clinics. I've also see witches host a safe sex orgy, and !! then noted how a warrior type forgot everything he knew about weapons, !! and only wanted to do whatever he could to advance their agenda. I !! also filled my freezer with venison shot by a witch. She dressed it !! out in her bathtub. She can shoot as well as you can, but the demand !! for her sexual services are waaaaaay ahead of yours. You have friends !! to help you move. She has friends to help her move bodies. !! !! All this Nazi racist bull is pissing in the wind. The Uberwench !! will overwhelmingly select Northern European sperm donors, so their !! demise has been premature, and exaggerated. They will also be !! accepting women from whatever race, into their ranks so long as the !! ladies in question are talented enuf. They have a bottom line, and !! they want as much talent as they can find. They will no doubt find !! some from every race, but the East Asians will be much more common. !! !! But the more mysogenistic a culture has been, the stupider the women. !! smart women figured out how to get out. sex magick is a battlefield these days and i do not think any strain will survive the process separably hybrid vigor is observed and measured regularly i think that reason is why topaz tooly the infamous 71 bigots of alt.politics the actual historical nazi's and their influence today have very flawed goals it is why the magicians turned that late night in the winter when it was decided fundamentally it is a magick that fails the reason is heterosis is beneficial and inbreeding depression only harms a culture there can be no master race because it will be the end of the human race it will make us frail homogeneity festers and fails to innovate that's why america has been so successful it has always been one of the most heterogeneous populations many great men and many great women have lived before from many different races all our ancestors are our inheritance all learning all clever little new behaviors that brought us to this verbal age the capacity for greatness is found in all places of the world because it is a learned topology in our neurodynamics greatness as you know, day is a linguistic phenomenon effort with potential .. among magicians there is a deep conflict on miscegenation it was always crowley stirring it up playing with the wotanists and their bloated sense of importance this was ultimately why leah hirsig cried ^,.^ this can even been formalised mathematically inbreeding depression is a well known consequence of the magnification of homozygous deleterious genes and hybridisation provides control robustness gaia in her eukaryotic avatar has learned several suppression dynamics which through possible involvement of epigenetic neolamarckian mechanisms has found ways to prevent expression of genes that do not become fit when a gene or epigene that is fit is present undergrad genetics course speak of dominant and recessive genes but the dynamic is more general and complex the expression suppression mechanism allows dynamics which move the fitness of a population to the fitness near the intersection of their selection events given two strings S1, S2 we can define a measure of distance d(S1, S2) ( eg. levenshtein ) inbreeding depression is a result of: -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ Theorem: The metabolic dynamical structure will likely have a fitness F that is decreasing as the epigenetic span distance d(P) across a population P goes to 0. -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ the most basic derivation is pretty standard and mathematically very simple but there are tangents necessary to fully formalise which genetic alphabet is dynamically relevant which means that we don't look at string of nucleic acid compounds but functionally relevant codons to translation and at any position x in genetic space G we can consider the collection of stimuli or events K(x) for which that organism would be selected before procreating with variation in a population there is some likelihood to be some subpopulation fit to a stimulus and in general the existence of a difference between two genetic loci x and y can (with some extra preconditions) imply | K(x) - K(y) | > 0 defining a fitness F is basically defining a measure space over which the K form a lattice of course those tangents are where the full intracacy of the theory develops but even remaining with this simple framework there are many purely empirical systems in which the effect is commonly measured corn for example and hormesis is synergetic with heterosis so there is a good deal of universality in this phenomenon %%%%%%%%%%..$$$ the problem is the racial purity virus accomodates the private man ashamed and hiding, eager for justification in their position and peers there are always plenty of weak men unable to display themselves often called macho because of their aggressions when reveal is immanent the neophilia virus requires a man strong enough to know his weaknesses and take full adult responsibility to learn the geeks who do not assert with arrogance but progress through plans and handle well when plans fail the cunts of some women are shaved in neotenic defense refusing to face adulthood cultivating their defensive men in paranoias and obsessions some cunts though proceed to a natural fur comfortable with its mammalian intensions these differences may seem slight but the spells take wildly different paths... -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: Re: heterosis is the flaw of the master race !! Well Tooly, I appreciate your passion, and agree > that Liberals are > !! misguided. But so are conservatives. > !! > !! But rather than write of what I think should > happen, let me lay out > !! what I see coming, whether we like it or not. Both > liberal and > !! conservative frames of thot are too distorted to > fit the facts. > !! > !! Might still makes Right. but now, after 5000 years > of the brave heart, > !! strong right arm, sword in hand, that just dont > cut it any more. Smith > !! & Wesson guarantee equal rights for smart women. > Most guys dont get > !! it. > !! > !! But the other thing smart women have, is cunts. > And they still work as > !! well as they ever did in getting guys to go along > with whatever agenda > !! a smart woman has. And what the smart bitches are > doing, is ignoring > !! the warriors, and ing the geeks. Its the geeks > who have the > !! innovative minds that is empowering their mutual > ventures, and > !! allowing them to laff all the way to the bank. > !! > !! The geeks invented the internet and the hardware > that puts this > !! message in front of your face. But it is the women > who ran the offices > !! and kept track of the inventory, and... > increasingly, they see they > !! can get along without the high cost of CEO male > management. > !! > !! Smart women have also seen that the men of their > station who they'd > !! consider as husbands, are already married to sexy > bimbos. So, they are > !! going to fertility clinics, selecting among > thousands of the most > !! promising Y chromosome lines on the planet, and > have already given > !! birth to some of the most talented young minds > around. > !! > !! They are, consciously or not, selecting fair haird > Nordic lines way > !! more than all others, and giving birth to lotsa > trophy blondes. These, > !! my friends, are the Uberwench. And they dont > *have* family values. > !! They will, as we've already seen, some lech > for the last few > !! years of his life, then inherit his empire. > !! > !! I see lesbians moving in with each other, and > likewise using > !! fertility clinics. I've also see witches host a > safe sex orgy, and > !! then noted how a warrior type forgot everything he > knew about weapons, > !! and only wanted to do whatever he could to advance > their agenda. I > !! also filled my freezer with venison shot by a > witch. She dressed it > !! out in her bathtub. She can shoot as well as you > can, but the demand > !! for her sexual services are waaaaaay ahead of > yours. You have friends > !! to help you move. She has friends to help her move > bodies. > !! > !! All this Nazi racist bull is pissing in the > wind. The Uberwench > !! will overwhelmingly select Northern European sperm > donors, so their > !! demise has been premature, and exaggerated. They > will also be > !! accepting women from whatever race, into their > ranks so long as the > !! ladies in question are talented enuf. They have a > bottom line, and > !! they want as much talent as they can find. They > will no doubt find > !! some from every race, but the East Asians will be > much more common. > !! > !! But the more mysogenistic a culture has been, the > stupider the women. > !! smart women figured out how to get out. sex magick is a battlefield these days > and i do not think any strain will survive the > he process separably hybrid vigor is observed and measured regularly i think that reason is why > topaz > tooly > the infamous 71 bigots of alt.politics > the actual historical nazi's > and their influence today have very flawed goals it is why the magicians turned > that late night in the winter when it was decided fundamentally > it is a magick that fails the reason is > heterosis is beneficial > and inbreeding depression only harms a culture there can be no master race > because it will be the end of the human race it will make us frail homogeneity festers and fails to innovate that's why america has been so successful > it has always been one of the most heterogeneous > populations many great men and many great women have lived before > from many different races all our ancestors are our inheritance > all learning > all clever little new behaviors that brought us to > to this verbal age the capacity for greatness is found in all places of > the world > because it is a learned topology in our > ur neurodynamics greatness > as you know, day > is a linguistic phenomenon effort with potential .. among magicians there is a deep conflict on > miscegenation it was always crowley stirring it up > playing with the wotanists and their bloated sense of > importance this was > ultimately > why leah hirsig cried ^,.^ this can even been formalised mathematically inbreeding depression is a well known consequence > of the magnification of homozygous deleterious > us genes > and hybridisation provides control robustness gaia > in her eukaryotic avatar > has learned several suppression dynamics > which through possible involvement of epigenetic > neolamarckian mechanisms > has found ways to prevent expression of genes that > at do not become fit > when a gene or epigene that is fit is present undergrad genetics course speak of dominant and > recessive genes > but the dynamic is more general and complex the expression suppression mechanism > allows dynamics which move the fitness of a > a population > to the fitness near the intersection of their > ir selection events given two strings S1, S2 > we can define a measure of distance d(S1, S2) > ( eg. levenshtein ) inbreeding depression is a result of: -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ > -+-+-+-+-+-+-+-+-+-+-+ > Theorem: The metabolic dynamical structure will > likely have a fitness F > that is decreasing as the epigenetic span distance > d(P) across a population > P goes to 0. > -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ > -+-+-+-+-+-+-+-+-+-+-+ the most basic derivation is pretty standard and > mathematically very simple > but there are tangents necessary to fully formalise > which genetic alphabet is dynamically relevant > which means that we don't look at string of > g of nucleic acid compounds > but functionally relevant codons to translation > and at any position x in genetic space G > we can consider the collection of stimuli or events > K(x) for which that organism > would be selected before procreating with variation in a population > there is some likelihood to be some subpopulation > on fit to a stimulus > and in general > the existence of a difference between two genetic > etic loci x and y > can (with some extra preconditions) imply | K(x) > K(x) - K(y) | > 0 defining a fitness F is basically defining a measure > space > over which the K form a lattice of course those tangents are where the full intracacy > of the theory develops but even remaining with this simple framework > there are many purely empirical systems in which > ch the effect is commonly measured corn > for example and hormesis is synergetic with heterosis > so there is a good deal of universality in this > is phenomenon %%%%%%%%%%..$$$ the problem is > the racial purity virus accomodates the private man > ashamed and hiding, eager for justification in > n in their position and peers there are always plenty of weak men unable to > e to display themselves > often called macho because of their aggressions > ions when reveal is immanent the neophilia virus requires a man strong enough to > know his weaknesses > and take full adult responsibility to learn the geeks who do not assert with arrogance > but progress through plans > and handle well when plans fail the cunts of some women are shaved in neotenic > defense > refusing to face adulthood > cultivating their defensive men in paranoias and > nd obsessions some cunts > though > proceed to a natural fur > comfortable with its mammalian intensions these differences may seem slight > but the spells take wildly different paths... -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- > galathaea: prankster, fablist, magician, liar > I got a big guilty laugh out of all this, but I essentially agree with you--the purity of a race is its weakness. Demonstrably, from a POV of complex systems (of which humanity forms a component in this world), the number of survival options is proportional to the genetic variety. Tom === Subject: Re: heterosis is the flaw of the master race <4h0Ci.25443$7e6.18190@bignews4.bellsouth.net> I certainly dont expect to see any pure blood Galathaea. The most indicative lesson from History I know of is that of Kucha, The pre- eminent city of the Silk Road, a few hundred miles WNW of the hegemony of China & the Jade Gate. For at least 1500 years, until over run by the Mongols on their way to sweeping across most of Asia, Kucha retained a matriarchic system that occassionally was garissoned by Chinese troops with the velvet glove to help put down banditry. They were Aryan, as was proven by the DNA of the natural mummies still being found in their graveyards. But among them are some Chinese, buried in Aryan clothes with Aryan grave goods. But both The Chinese and the Tocharians despised the barbaric Tibetans, Zongnu ( who became the Mongols), and the arrogant sakyas (the mysogenistic warlords who still run lots of central Asia. Part of what was going on, is that the Silk Road was mostly a string of independent city states, and no matter how each was run, a talented person could, and did, vote with their feet to wherever the government was honest and less tyrannic. At the top of that list was Kucha. There were no slums. The grave yards dont have the lavish graves of kings or chieftains, but grave after grave of well dressed middle class men & women. Like the ancient Silk Road, the modern global economy will always have a place where talent could make a go of it. And while anyone from any race may succeed, those with the innate talent to actually do so will be mostly from Aryan or East Asian genetic lines that evolved over the course of the last 10,000 years in yeoman farming cultures. The economies that do best will be those that neither ascribe talent where it does not exist, nor block talent where it is from its aspirations. We can expect to see more successes like Tiger Woods or sen Obama, but most of the successes in the global market economy will be from Aryan, East Asian gene pools, or some hybrid. The sexy attributes we see now in these women we've seen before in the matriarchies of the Silk Road. Its perhaps instructive to consider that the 'Tantric' Taoist texts were composed when Kucha was a great Taoist center. If men shave faces to look like boys, then why cant women shave cunts to look like girls? Nobody pretends that men with shaven faces are actually boys. Unless, I guess, you are a right wing politician. And if clean shaven faces are nicer to kiss, then why not also clean shaven cunts? Since I'm already 68, I'll never find out, but we may see some reports on this question from those who've tried it. We all know what Buddhas look like, little smiling bald headed pot bellied dudes. But at the temples at Sibushi, 12 miles north of Kucha, the Bodhisattavahs all have long black curly hair, thin waists and broad shoulders, and finger pearls worn over the neck down to their exposed navels. Kucha's idea of a Buddhist saint is a stud muffin. And damn they were rich. The reason the Silk Road ends at the Jade Gate was that that was where Jade came into China, the one thing the Chinese wanted from the outside world. Jade from the mines north of Kucha. And like the Global Market now, they had the money to import books from the rest of the world. Kucha was like a college town, with Buddhist, Confucian, Taoist, Zororastrian, Nestorian, Manichean, etc, scholars. They also exported magicans. We know the Magi came from the East. Well, this is *that* East. And in China, the texts say that the great wizards came from the West. This is *their West*. Kucha exported magicians, astrologers, & musicians to the Chinese court, and to this day, a band from Kucha gets top billing in China. Everyone loves their dancing girls. Some who, to this day, are so western looking, with lighter hair & green eyes, they would pass on the streets of Europe without notice. (Lisa See looks like a Tocharian throwback, but I dont think she knows it.) Another point the global market may consider, or may already have in place without us knowing it, was that Kucha exported the priciest call girls to Xian. You could always tell when there was going to be a palace coup when the Kuchi left town. I too have tried to explain to topaz, tooly, the infamous 71 bigots of alt.politics what was coming down, but they are all in denial. Not that it matters if they did understand. They cant change any of it. For me, the big awakening was seeing the original Girls Gone Wild *documentary* filmed at Mardi Gras. I usta live in Nola (til I read the hydrology report & got the outta town), so I'd been to lotsa Mardi Gras events. So, I was not surprised that girls would flash their titties at the camera. But then the film crew asked, if they'd do that, would they drop their drawers for a moon shot? Well, yes they would. Well ok. If they'll do that, will they show off the bushes? Yep. Ah huh. hmm. How about bending over for a clear shot at the cunt from behind? No problem. These are not porn stars. they werent being paid. This was just a random grab off the streets! Now, more recently, they've repeated it at NOLA, Lake Tahoe, Acapulco, etc, and even filmed girls ing on the stage at Spring Break. There's been a cultural revolution, and these right wing nuts dont even know it. Course, they aint gettin laid either. === Subject: Re: probabilistic selector functions I just noticed that Fernando Revilla neglected to maintain the cross-post to sci.stat.math, so I'm reposting my reply so as to include both sci.math and sci.stat.math. > [This is a repost, correcting a minor typo, and this >> time also >> cross-posting to sci.stat.math] >> Let X be a nonempty set and let p:X->[0,1] be an >> arbitrary function. >> The function p induces a (random) subset Y of X as >> follows ... >> For each x in X, p(x) is the probability that x is in >> Y. >> Thus, p acts as a kind of probabilistic selector >> function (psf) on >> the set X. >> If p is identically 0, then Y = the empty set. >> If p is identically 1, then Y = X >> In all other cases, Y is a non-deterministic subset >> of X (that is, >> determined only by the probabilistic selector >> function p). >> I'm especially interested in the case where X is >> countably infinite. >> Thus, if X = {x_1, x_2, x_3, ... }, the function p >> can be regarded as >> a sequence p_1, p_2, p_3, ... where p_n is the >> probability that x_n is >> in Y. The set Y can then be built recursively, using >> p to decide >> membership, as follows: >> Y_0 = the empty set. >> For n>0, define Y_n by >> Y_n = Y_(n-1) union {x_n} with probability p_n, >> _n, otherwise Y_(n-1) >> Then let Y = union of the sets Y_n, for n = 0, 1, 2, >> 3, ... >> This seems like a very natural construction (and I >> intend to actually >> use it), but it seems unlikely that my concept of >> probabilistic >> selector function is actually a new concept. Thus, >> I'd like to know >> if there's any natural, alternate way to define it >> using concepts such >> as sample space, probability density function, >> probability >> distribution function, or random variable. >> quasi Firstly, I want to know if my interpretation of the (psf) coincides >with yours via a very simple example. Example: X={x_1, x_2}, p: X -> [0, 1]. Denote: p(x_1)= p_1, p(x_2)= p_2. Consider P(X)= { Y: Y subset of X }. Let us find the probability >of obtaining Y={ x_1 } by means of the (psf). Denote such a >probability by pr, then, according to my interpretation: pr(Y)=pr((x_1 is in Y) and (x_2 is not in Y ))=p_1(1-p_2). Define now the probabilistic space: E= { { }, {x_1}, {x_2}, X }, then: pr({})=(1-p_1) (1-p_2) >pr({x_1})=p_1 (1-p_2) >pr( {x_2})=p_2 (1-p_1) >pr(X)=p_1 p_2 We verify: (i) pr(Y) e [0, 1] for every Y e E. >(ii) Sum{Y e E } pr(Y)=1. So, we have the conditions for defining a probability pr: P(E)=P(P(x)) -> [0, 1] and the random sets are exactly the single elements of P(P(X)). Is this an aproach to your question ?. Yes. The elementary outcomes are subsets of X, hence, as you indicate, the sample space is just P(X), and events are just elements of P(P(X)). As your analysis shows, if X has 2 elements, a psf induces a probability measure on P(X). A similar analysis should work for any finite set X. For general X, I think a psf always induces a probability measure on P(X). Moreover, I believe the sigma algebra of measurable sets and the probability measure are uniquely determined by the psf. Even in the finite case, the psf interpretation (on X) seems simpler in some respects than the interpretation as a probability space on P(X). When X is countably infinite, I think the comparative simplicity of the psf interpretation is even more evident. Moreover, it affords a natural, constructive way to build random subsets of X. quasi === Subject: Re: probabilistic selector functions >> Let X be a nonempty set and let p:X->[0,1] be an arbitrary function. >> The function p induces a (random) subset Y of X as follows ... >> For each x in X, p(x) is the probability that x is in Y. The difficulty here is that p _may_ be used to construct such a subset >Y, but the creation of Y is an entirely different process with >apparently no impact on the structure of p itself. The selection bit >isn't a necessary part of the function, since the properties of p may >be fully considered before the selection begins. For instance, you say that p is an arbitrary function. If X is >countable, then it may be a good exercise to consider p as a sequence >of random variables. As it stands, however, we can't say much about p >other than p:X->[0,1], though it is a simultaneous presentation of a >number of sample spaces. I'm not sure what you're saying above. The probability selector function p is arbitrary. The pair (X,p) determine the random sets Y. Basically, apply p to X to get Y. Of course, p is nondeterministic. Each time p is applied, a different Y may occur, consistent with the interpretation that, for each x in X, f(x) is the probability that x is in Y. >You might have more success by beginning with p:2^X->[0,1], which >could be built to give you the probability that the randomly chosen >subset is Y. Ultimately, after all your work, this is probably what >you'd end up with anyway. If what you're saying is that, corresponding (X,p) where p is a probability selector function, there is an associated probability space (2^X,Sigma,mu) for some sigma algebra Sigma and some probability measure mu on Sigma, then sure, I agree with that. But I don't need to end up with it -- I only need to make sure such a probability space exists. The pair (X,p) can be used directly to build random sets, at least in the case where X is finite or countably infinite. As far as I can see, when X is countably infinite, if a psf is specified, it's much simpler to simply use the psf on X to analyze probabilities than to first convert to a probability space on 2^X and use the associated probability measure. >> Thus, if X = {x_1, x_2, x_3, ... }, the function p can be regarded as >> a sequence p_1, p_2, p_3, ... where p_n is the probability that x_n is >> in Y. The set Y can then be built recursively, using p to decide >> membership, as follows: >> Y_0 = the empty set. >> For n>0, define Y_n by >> Y_n = Y_(n-1) union {x_n} with probability p_n, otherwise Y_(n-1) >> Then let Y = union of the the sets Y_n, for n = 0, 1, 2, 3, ... This construction, rather than the function above, is the really >interesting part. The function is not supposed to be interesting -- it's arbitrary, but fixed and specified. >You could examine the full process by generating a sequence of >random variables {y_n} and checking the probability that >y_n > p(x_n). If the probabilities were random variables themselves, >this can get really messy. If everything is IID and nicely distributed >though, you might get some sensible properties from it. I'm not sure what you're saying above, but I claim, a psf is _always_ consistent with a probability measure on 2^X (and an induced sigma algebra). Moreover, I think the probability space is uniquely determined by the psf. Note, p need not be constant. But if p is constant, it makes for an extremely natural psf -- these can be called uniform psfs. Thus for example, choose 1,2,3, ... each with probability 1/2. What's the probability space? It's obvious that the sample points are just subsets of N, hence the sample space is P(N), but what about the probability space as a triple (sample space, sigma algebra, probability measure)? As long as such a space exists, who cares? The fact is, we can generate elements of these sets far up to any finite natural number n, and that constructive approach should be sufficient to analyze probability questions. Note -- independence is automatic. Whether a given natural number n is selected is determined only by the value of the psf applied to n, hence is not influenced by any other selections. >Ultimately, it really depends on what you want to get out of this, but >I think it all will boil down to finding p:2^X -> [0,1], the >probability measure on subsets of X. As, I mentioned above, I agree that there is a probability space on 2^X -- in fact, I conjecture that such a space always exists and is unique (subject to the requirements of consistency with the psf). >Fernando above gives one example of the process. Yes, Fernando shows how to recover the probability space from the psf (for the case where X has 2 elements). My feeling is -- as long as it can be recovered, don't bother -- stay with the psf (assuming you already have it). quasi === Subject: Re: probabilistic selector functions > [This is a repost, correcting a minor typo, and this >> time also >> cross-posting to sci.stat.math] >> Let X be a nonempty set and let p:X->[0,1] be an >> arbitrary function. >> The function p induces a (random) subset Y of X as >> follows ... >> For each x in X, p(x) is the probability that x is in >> Y. >> Thus, p acts as a kind of probabilistic selector >> function (psf) on >> the set X. >> If p is identically 0, then Y = the empty set. >> If p is identically 1, then Y = X >> In all other cases, Y is a non-deterministic subset >> of X (that is, >> determined only by the probabilistic selector >> function p). >> I'm especially interested in the case where X is >> countably infinite. >> Thus, if X = {x_1, x_2, x_3, ... }, the function p >> can be regarded as >> a sequence p_1, p_2, p_3, ... where p_n is the >> probability that x_n is >> in Y. The set Y can then be built recursively, using >> p to decide >> membership, as follows: >> Y_0 = the empty set. >> For n>0, define Y_n by >> Y_n = Y_(n-1) union {x_n} with probability p_n, >> _n, otherwise Y_(n-1) >> Then let Y = union of the sets Y_n, for n = 0, 1, 2, >> 3, ... >> This seems like a very natural construction (and I >> intend to actually >> use it), but it seems unlikely that my concept of >> probabilistic >> selector function is actually a new concept. Thus, >> I'd like to know >> if there's any natural, alternate way to define it >> using concepts such >> as sample space, probability density function, >> probability >> distribution function, or random variable. >> quasi Firstly, I want to know if my interpretation of the (psf) coincides >with yours via a very simple example. Example: X={x_1, x_2}, p: X -> [0, 1]. Denote: p(x_1)= p_1, p(x_2)= p_2. Consider P(X)= { Y: Y subset of X }. Let us find the probability >of obtaining Y={ x_1 } by means of the (psf). Denote such a >probability by pr, then, according to my interpretation: pr(Y)=pr((x_1 is in Y) and (x_2 is not in Y ))=p_1(1-p_2). Define now the probabilistic space: E= { { }, {x_1}, {x_2}, X }, then: pr({})=(1-p_1) (1-p_2) >pr({x_1})=p_1 (1-p_2) >pr( {x_2})=p_2 (1-p_1) >pr(X)=p_1 p_2 We verify: (i) pr(Y) e [0, 1] for every Y e E. >(ii) Sum{Y e E } pr(Y)=1. So, we have the conditions for defining a probability pr: P(E)=P(P(x)) -> [0, 1] and the random sets are exactly the single elements of P(P(X)). Is this an aproach to your question ?. Yes. The elementary outcomes are subsets of X, hence, as you indicate, the sample space is just P(X), and events are just elements of P(P(X)). As your analysis shows, if X has 2 elements, a psf induces a probability measure on P(X). A similar analysis should work for any finite set X. For general X, I think a psf always induces a probability measure on P(X). Moreover, I believe the sigma algebra of measurable sets and the probability measure are uniquely determined by the psf. Even in the finite case, the psf interpretation (on X) seems simpler in some respects than the interpretation as a probability space on P(X). When X is countably infinite, I think the comparative simplicity of the psf interpretation is even more evident. Moreover, it affords a natural, constructive way to build random subsets of X. quasi === Subject: Re: Which statistic to use? boundary=----=_NextPart_000_001F_01C7EC6C.614CE180 --------------------------------------------------------------------- I have two populations P1 and P2 and take samples of size n1 and n2 from each (assume large) y1 or n1 answer yes to a question, y2 of n2 answer yes to the same question. What test do I do to see if there is no difference in the way P1 and P2 answer the question? The problem seems to be similar to testing if the difference in means is significant, but I have not quite made the connection. === Subject: Extending Morera's theorem ? I was wondering about the possibility of extending Morera's theorem to various shapes. A more detailed account of my question: http://www.mymathforum.com/viewtopic.php?t=1414 . Are there any interesting results on that topic ? J. === Subject: Re: Extending Morera's theorem ? I was wondering about the possibility of extending Morera's theorem to >various shapes. A more detailed account of my question: >http://www.mymathforum.com/viewtopic.php?t=1414 . Was writing I was wondering about the possibility of extending Morera's theorem to various shapes. A more detailed account of my question: and then cut&pasting the url _really_ any easier than just cut&pasting Can Morera's theorem be generalized to any regular polygon instead of any triangle, i.e a continuous complex function f defined on an open set O such that int_G(f)=0 for every regular n-gon G in O is necessarily holomorphic ? would have been? >Are there any >interesting results on that topic ? It's true if int_S f(z) dz = 0 for all S which are translates of dilates of any piecewise-smooth simple closed curve: For eps > 0 let O_eps be the set of points of O at distance from the boundary greater than eps. Let f_eps be the convolution of f with an approximate identity supported in D(0,eps), so that f_eps is defined in O_eps. Then f_eps -> 0 uniformly on compact subsets of O, so we need only show that f_eps is holomorphic in O_eps. Fubini's theorem shows that f_eps also satisfies the hypothesis in O_eps. If f_eps is not holomorphic in O_eps then since f_eps is smooth, h_eps = partial(f)/partial(z-bar) <> 0 in O_eps, and hence there is one of our curves S such that the integral of h_eps over the interior of S is nonzero. Green's theorem shows that the integral of f_eps over S is non-zero. >J. ************************ David C. Ullrich === Subject: Sobolev space Hello everyone, I'm looking for the proof that the space V={phi in H^2(0,L) such that phi(0)=phi'(0)=0} where H^2 is the Sobolev space. Is there any Jeff === Subject: Re: Sobolev space >Hello everyone, >I'm looking for the proof that the space >V={phi in H^2(0,L) such that phi(0)=phi'(0)=0} >where H^2 is the Sobolev space. ??? Leaving out the explanation of what V is supposed I'm looking for the proof that the space V. What is it you're trying to prove about V, exactly? >Is there any >Jeff ************************ David C. Ullrich === Subject: Ctyptography & network secutity Cc: namrata_29@rediffmail.com Can u plz tell me the procedure to how to buy Cryptography and Network Security by-William stallings(3rd edition) my email is namrata_29@rediffmail.com === Subject: Re: Ctyptography & network secutity > Can u plz tell me the procedure to how to buy Cryptography and Network > Security by-William stallings(3rd edition) my email is > namrata_29@rediffmail.com Are you stupid or what? Have you never heard of bookstores, real or online? If you can't figure this out, do you really think you can figure out a technical book like that? === Subject: Re: Ctyptography & network secutity Can u plz tell me the procedure to how to buy Cryptography and Network > Security by-William stallings(3rd edition) my email is > namrata...@rediffmail.com Are you stupid or what? Have you never heard of bookstores, real > or online? If you can't figure this out, do you really think you can > figure out a technical book like that? He had high hopes, He had high hopes, He had high in the sky, apple pie hopes.... Node Turing, quit writing in from beyond the grave. === Subject: Many Solutions Manuals and Ebooks in Electronic (PDF)Format! Many Solutions Manuals and Ebooks in Electronic (PDF)Format! PS: These are part of my solutions, if the solution you want isn't on the list, do not give up, just contact with me: My email is solutionpay(at)hotmail.com( please replace the (at) with @ ) NOTE: if the solutions you want is on the list renewed, please mention in your email,thank you! Solution manual for the list: http://rapidshare.com/files/52408080/list.doc I will reply with your Email within 12 hours!! advanced engineering mathematics (8/e) by ERWIN KREYSZIG advanced engineering mathematics9/e by ERWIN KREYSZIG advanced macroeconomics Analytical Mechanics (7/e) By Grant R. Fowles, George L. Cassiday applied mathematics and modelling forchemical engineers(8/e) Applied Strength of Materials (4th Edition) by Robert MoTT Boyce Elementary Differential Equations and Boundary Value Problems by Willian E.Boyce C How to Program, 3RD Edition 2000 By Harvey M. Deitel Calculus I, II, Transidentals 10e BY George B. Thomas Calculus with Analytic Geometry Calculus, 4th edition by James Stewart Computational Techniques for Fluid Dynamics By Karkenahalli Srinivas, Clive A. J. Fletcher Computer Organization and Design: The Hardware/Software Interface93/ e) by David A. Patterson, John L. Hennessy Design of Analog CMOS Integrated Circuit by B. Razavi Digital and Analog Communication Systems by LEON W. COUCH Digital and Analog Communication Systems 5th, by Leon W. Couch, Leon W., II Couch . DISCRETE-TIME SIGNAL PROCESSING/2e by OppenheimSchafer Econometric Analysis (6/e) by willian H.GREENE Econometric Analysis ,5th Edition, by William H. Greene Electric Machinery Fundamentals 4/e By Stephen J. Chapman Electric Machinery Fundamentals, 4/e , by S. J. Chapman. Electrical Circuits (7/e) by James W. Nilsson, and Susan A. Elementary Differential Equations and Boundary Value Problems , 8thby William E. Boyce (Author), Richard C Elementary Principles of Chemical Processes Elements of Chemical Reaction Engineering By H Fogler Elements of Chemical Reaction Engineering (3rd)by H.Scott Fogler Engineering electromagnetics (6/e) by HAYT Engineering electromagnetics (7/e) by HAYT Engineering Fluid Mechanics, 7th Edition By Clayton T. Crowe, Donald F. Elger, John A. Roberson Engineering Mathematics, 4th Edition ,by John Bird Engineering Mechanics - Dynamics (11th ) by R.C.HIBBELER Engineering Mechanics - Statics (11th ) by R.C.HIBBELER Engineering Mechanics - Statics and Dynamics,11th, by Russell C Hibbeler. Engineering Mechanics, Dynamics 5th By J. L. Meriam, L. G. Kraige Engineering Mechanics: Statics By R.C. Hibbeler Engineering Mechanics: Statics ,10th ,by R.C.Hibbeler, field and wave electromagnetics (2/e) by David Cheng Fundamentals of Logic Design 5Ed by CharlesRoth Fundamentals of Chemical Reaction Engineering By Mark E. E. Davis, Robert J. J. Davis Fundamentals of Fluid Mechanics, 5th by By Bruce R. Munson, Donald, Theodore H. Okiishi, Fundamentals of Organic Chemistry, 5E Fundamentals of Thermodynamics 6ed By Richard E. Sonntag Heat Transfer: A Practical Approach Hornback's Organic Chemistry, 2nd Introduction to Electrodynamics(3/e) by David J. Griffiths Introduction to Heat Transfer 4th Edition By Frank P. Incropera, David Introduction to Solid State Physics (8 ED) by Charles.Kittel MATHEMATICAL ANALYSIS (2/e) (chapter1-9) by Tom M. Apostol Mechanical Engineering Design By Joseph Shigley, Charles Mischke, Mechanics of Materials 96/E) by R.C.Hibbeler Microeconomic Analysis, 3rd Edition, by Hal R. Varian Microeconomic Theory by Andreu Mas-Colell, Michael D. Whinston, Modern Control Engineering/ 4E by K.OGATA Modern Digital and Analog Communication Systems (3/e) Organic Chemistry, 2th by Hornback Physica Chemistry 7th.Ed. by Atkins Physical Chemistry (7/e) by Peter Atkins and Julio de Paula Physical Chemistry (7th) by P.W.Atkins Physics for Scientists and Engineers by Serway'& Jewett Probability & Statistics for Engineers & Scientists, 8th by Sharon Myers , Keying Ye, Walpole Probability and Statistics for Engineering and the Sciences 7/e JAY L.DEVORE Probability, Random Variables and Stochastic Processes,3rd, by Athanasios Papoulis Signals and Systems (2nd Edition) Thermodynamics: An Engineering Approach,5th Ed. by Cengel Thermodynamics: An Engineering Approach,6th Ed. by Cengel Thomas' Calculus (11th Edition) by George B Thomas University Physics with Modern Physics By Hugh D. Young Vector Mechanics for Engineers: Statics, 7th By Ferdinand P. Beer Visual C++ How to Program, (3rd Edition) ,by Harvey & Paul Deitel & Associates Zill's a First Course in Differential Equations with Modeling Applicants 7/e http://pdfsolution.spaces.live.com === Subject: Many Solutions Manuals and Ebooks in Electronic (PDF)Format! Many Solutions Manuals and Ebooks in Electronic (PDF)Format! PS: These are part of my solutions, if the solution you want isn't on the list, do not give up, just contact with me: My email is solutionpay(at)hotmail.com( please replace the (at) with @ ) NOTE: if the solutions you want is on the list renewed, please mention in your email,thank you! Solution manual for the list: http://rapidshare.com/files/52408080/list.doc I will reply with your Email within 12 hours!! advanced engineering mathematics (8/e) by ERWIN KREYSZIG advanced engineering mathematics9/e by ERWIN KREYSZIG advanced macroeconomics Analytical Mechanics (7/e) By Grant R. Fowles, George L. Cassiday applied mathematics and modelling forchemical engineers(8/e) Applied Strength of Materials (4th Edition) by Robert MoTT Boyce Elementary Differential Equations and Boundary Value Problems by Willian E.Boyce C How to Program, 3RD Edition 2000 By Harvey M. Deitel Calculus I, II, Transidentals 10e BY George B. Thomas Calculus with Analytic Geometry Calculus, 4th edition by James Stewart Computational Techniques for Fluid Dynamics By Karkenahalli Srinivas, Clive A. J. Fletcher Computer Organization and Design: The Hardware/Software Interface93/ e) by David A. Patterson, John L. Hennessy Design of Analog CMOS Integrated Circuit by B. Razavi Digital and Analog Communication Systems by LEON W. COUCH Digital and Analog Communication Systems 5th, by Leon W. Couch, Leon W., II Couch . DISCRETE-TIME SIGNAL PROCESSING/2e by OppenheimSchafer Econometric Analysis (6/e) by willian H.GREENE Econometric Analysis ,5th Edition, by William H. Greene Electric Machinery Fundamentals 4/e By Stephen J. Chapman Electric Machinery Fundamentals, 4/e , by S. J. Chapman. Electrical Circuits (7/e) by James W. Nilsson, and Susan A. Elementary Differential Equations and Boundary Value Problems , 8thby William E. Boyce (Author), Richard C Elementary Principles of Chemical Processes Elements of Chemical Reaction Engineering By H Fogler Elements of Chemical Reaction Engineering (3rd)by H.Scott Fogler Engineering electromagnetics (6/e) by HAYT Engineering electromagnetics (7/e) by HAYT Engineering Fluid Mechanics, 7th Edition By Clayton T. Crowe, Donald F. Elger, John A. Roberson Engineering Mathematics, 4th Edition ,by John Bird Engineering Mechanics - Dynamics (11th ) by R.C.HIBBELER Engineering Mechanics - Statics (11th ) by R.C.HIBBELER Engineering Mechanics - Statics and Dynamics,11th, by Russell C Hibbeler. Engineering Mechanics, Dynamics 5th By J. L. Meriam, L. G. Kraige Engineering Mechanics: Statics By R.C. Hibbeler Engineering Mechanics: Statics ,10th ,by R.C.Hibbeler, field and wave electromagnetics (2/e) by David Cheng Fundamentals of Logic Design 5Ed by CharlesRoth Fundamentals of Chemical Reaction Engineering By Mark E. E. Davis, Robert J. J. Davis Fundamentals of Fluid Mechanics, 5th by By Bruce R. Munson, Donald, Theodore H. Okiishi, Fundamentals of Organic Chemistry, 5E Fundamentals of Thermodynamics 6ed By Richard E. Sonntag Heat Transfer: A Practical Approach Hornback's Organic Chemistry, 2nd Introduction to Electrodynamics(3/e) by David J. Griffiths Introduction to Heat Transfer 4th Edition By Frank P. Incropera, David Introduction to Solid State Physics (8 ED) by Charles.Kittel MATHEMATICAL ANALYSIS (2/e) (chapter1-9) by Tom M. Apostol Mechanical Engineering Design By Joseph Shigley, Charles Mischke, Mechanics of Materials 96/E) by R.C.Hibbeler Microeconomic Analysis, 3rd Edition, by Hal R. Varian Microeconomic Theory by Andreu Mas-Colell, Michael D. Whinston, Modern Control Engineering/ 4E by K.OGATA Modern Digital and Analog Communication Systems (3/e) Organic Chemistry, 2th by Hornback Physica Chemistry 7th.Ed. by Atkins Physical Chemistry (7/e) by Peter Atkins and Julio de Paula Physical Chemistry (7th) by P.W.Atkins Physics for Scientists and Engineers by Serway'& Jewett Probability & Statistics for Engineers & Scientists, 8th by Sharon Myers , Keying Ye, Walpole Probability and Statistics for Engineering and the Sciences 7/e JAY L.DEVORE Probability, Random Variables and Stochastic Processes,3rd, by Athanasios Papoulis Signals and Systems (2nd Edition) Thermodynamics: An Engineering Approach,5th Ed. by Cengel Thermodynamics: An Engineering Approach,6th Ed. by Cengel Thomas' Calculus (11th Edition) by George B Thomas University Physics with Modern Physics By Hugh D. Young Vector Mechanics for Engineers: Statics, 7th By Ferdinand P. Beer Visual C++ How to Program, (3rd Edition) ,by Harvey & Paul Deitel & Associates Zill's a First Course in Differential Equations with Modeling Applicants 7/e http://pdfsolution.spaces.live.com === Subject: What's with the solution manuals? Why are there so many solution manuals being advertised and asked for? I know that it's the beginning of the fall semester, but it wasn't this bad this time last year, or any other previous year. Did something happen, like a message in the newsgroup alt.how.to.cheat.at.math, which said that you could ask for them? --- Christopher Heckman === Subject: Re: What's with the solution manuals? Why are there so many solution manuals being advertised and asked for? I know that it's the beginning of the fall semester, but it wasn't >this bad this time last year, or any other previous year. Did something happen, like a message in the newsgroup >alt.how.to.cheat.at.math, which said that you could ask for them? --- Christopher Heckman Student cheats who spend moore time trying to cheat than it would take to work the problems! === Subject: Re: What's with the solution manuals? > Why are there so many solution manuals being advertised and asked for? I know that it's the beginning of the fall semester, but it wasn't > this bad this time last year, or any other previous year. Did something happen, like a message in the newsgroup > alt.how.to.cheat.at.math, which said that you could ask for them? --- Christopher Heckman I beleive these are all from the same person - that has started a business selling them. This person is obvious scum! They don't realize the damage they cause students, publishers, and authors. Students who buy these are doing a huge dis-service to themselves as they are missing the entire point of taking classes. When did it become more about the GPA and grades than actually learning and struggling in order to develop your thought processes and problem solving ailities? Oh well - students will always look for the path of least resistance - even if that is at the cost of their own learning. Schools also don't seem to mind this because they are a business too and don't want students to flunk out. Sorry for the diatribe. ~A === Subject: Re: What's with the solution manuals? A few years ago, I noticed that my students' homework answers were sometimes looking a lot like those from solution manuals, so I stopped assigning problems from textbooks to be turned in for credit. I now pass out homework assignments on handouts, containing problems that I make up myself. In the classes I teach for the math majors, I do have them keep a journal in which they are to record the work they do on problems from the book, but I do not grade those. So I've been disappointed but not surprised to see this on sci.math. And it's probably the tip of the iceberg. --charlie === Subject: Re: What's with the solution manuals? <46d9602f$0$28852$4c368faf@roadrunner.com A few years ago, I noticed that my students' homework answers were sometimes > looking a lot like those from solution manuals, so I stopped assigning > problems from textbooks to be turned in for credit. I now pass out > homework assignments on handouts, containing problems that I make up > myself. > here is a simple workaround I have encountered a while ago as I was taking the refresher course. Professor who's teaching the course had the following strategy. He gives out the assignments, some of the answers are in the textbook, if not he provides the answers. He also provides the hints for the 'hard' problems. The day you're to submit the homework, we have a quiz, everything is closed. The quiz consists of two assignments from the homework. His reasoning is something like I don't care whether you did your homework on your own or copied the answer from somewhere, but whatever you did, you must remember what you did and reproduce it from your memory, and quickly!. Those quizes, one for each homework,(besides the semi-final and final) are the major factor in grading. He does grade the homework, but something like 10 points if you did all the assignments, minus a few points for each missing assignments, and those homework grades are not really the factor for the final grade. === Subject: Re: Prove that Right Trivialization is smooth? <46D1BB62.9090003@web.de> <46D316C5.1060405@web.de> <46D41272.7000409@web.de> <46D6DB55.6040009@web.de> <46D6DBB7.5010801@web.de >> But please also let me know your alternative to the second proof, you >> mentioned > There is an alternative to the second proof if you apply the terms of > vector bundles. But basically it is the same. > While writing the lines above I had something like this in mind: > A vector bundle V of dimension n over the smooth manifold M is globally > trivializable iff the are n global sections M -> P of the projection map typo: M -> V > V -> M which are pointwise linearly independent. > Best wishes, > J. Ok, that's clear. Sabine === Subject: Re: roots of trancedental equation <20070824100830.559$g9@newsreader.com> On Aug 29, 8:10 pm, David W. Cantrell I have strcuk in finding the root of following equation > Cotangent[Xn] = constant [Xn]. > constant can vary from 12000 to 0.0012. > Can anybody help me in this. because when i try to solve it > graphically the cotangent and straight line both shoots to > infinity. > Again i want to find the n solution. > Let me make sure that I understand what you want: > The equation cot(x) = c*x, where c is a constant, has infinitely > many real solutions. Do you want to find the Nth positive > solution for x? Shailendra replied via private email. (Unfortunately, I'm still > not entirely certain what is desired.) > If so, I should be able to help you somewhat. But be aware that > the roots of the equation cannot be stated in closed form in > terms of familiar functions. Problem: Given c > 0, solve cot(x) = c x for x. There are infinitely many real solutions. Since the negative ones > are just the negatives of the positive ones, we consider only > x > 0 henceforth. Let n be a positive integer. There is one solution (which I'll > call x_n, the nth solution) in each interval of the form > ((n - 1) pi, (n - 1/2) pi). For large n, x_n is just slightly > larger than (n - 1) pi. If one wishes to approximate solutions by an iterative method, > such as Newton's, the information above may be adequate, but > more can be said. In particular, we now consider expansions for > x_n, in three cases. Case 1: n is large This is the classic case, investigated by Euler and others. Dave > Renfro has given a list of pertinent references; see item 27 (2006 > Feb. 22) in the thread Regarding tan(x) = x at > d4a39a657745006e>. As I noted in item 28, ... in the same way that we > can get an asymptotic series for the roots of tan(x) = x, we can also > get asymptotic series for the roots of various closely related > equations, such as cot(x) = c*x ..., which is our present concern. The specific series for this case is stated as [2] in item 4 (2006 > Apr. 29) of the thread how to solve complex -valued transcendent > equation? at > thread/a54d054c3c9dd024>, but I'll restate it here. Letting q = c*(n - > 1)*pi, x_n is given by the asymptotic series q/c + 1/q - (1 + 3*c)/(3*q^3) + (3 + 20*c + 30*c^2)/(15*q^5) > - (15 + 161*c + 525*c^2 + 525*c^3)/(105*q^7) [1] > + (35 + 528*c + 2744*c^2 + 5880*c^3 + 4410*c^4)/(315*q^9) +... If q >> 1, which is, of course, true for n sufficiently large, we may > approximate x_n well using [1]. But what if we do not have > q >> 1? To handle that, we now consider two other cases. (Were the > following two cases also considered by Euler or others?) Case 2: n << 1/(c*pi) Letting p = c*(n - 1/2)*pi, x_n is given by p/(c*(1 + c)) + p^3/(3*(1 + c)^4) > - (3 - 2*c)*p^5/(15*(1 + c)^7) [2] > + (45 - 78*c + 17*c^2)*p^7/(315*(1 + c)^10) +... Case 3: n ~ 1/(c*pi) Letting r = c*(n - 3/4)*pi, x_n is given by (2*r + c)/(c*(2 + c)) + 2*(-1 + r)^2/(2 + c)^3 > + 8*(-1 + c)*(-1 + r)^3/(3*(2 + c)^5) > + 10*(-4 + c)*c*(-1 + r)^4/(3*(2 + c)^7) [3] > + 8*(24 + 56*c - 67*c^2 + 8*c^3)*(-1 + r)^5/(15*(2 + c)^9) > + 4*(-480 + 48*c + 1912*c^2 - 884*c^3 + 61*c^4)*(-1 + r)^6/ > (45*(2 + c)^11) > + 16*(1440 - 5808*c - 7264*c^2 + 12216*c^3 - 3015*c^4 + 136*c^5)*(-1 + > r)^7/(315*(2 + c)^13) +... Shailendra > In summary, to approximate x_n, decide whether n is substantially > bigger than, substantially less than, or approximately the same > as 1/(c*pi), and then use [1], [2], or [3], respectively. Above, we only considered c > 0. But we could proceed similarly > to obtain series to approximate the roots of cot(x) = c*x > for c < 0. HTH, > David W. Cantrell- Hide quoted text - - Show quoted text - === Subject: embedded submanifold without a *global defining* map Hi! As is generally known N subset M is a embedded submanifold of M (of codimension r) iff every point p in N has a neighborhood U in M such that U cap N is a level set of a submersion f: U to R^r. f is called local defining map for N (and global defining map for N if U = M) Now I want to know if there is a simple example of an emedded submanifold where it is not possible to find a *global* defining map? Sabine === Subject: Re: embedded submanifold without a *global defining* map > Hi! As is generally known N subset M is a embedded submanifold of M (of > codimension r) iff every point p in N has a neighborhood U in M > such that U cap N is a level set of a submersion f: U to R^r. Level set with respect to a single point, I assume. > f is called local defining map for N (and global defining map for N if > U = M) Now I want to know if there is a simple example of an emedded > submanifold where it is not possible to find a *global* defining map? Hint: In this case N needs to be closed. === Subject: Re: An exact simplification challenge - 39 (polylog) - Go and surpass all CASs > Hello computer algebra fans, None of the modern CASs can handle this directly. Is there a Whiz the Simplifier to come up with the > steps to squeeze (very much ;) this sum + polylog(2, (-1)^(1/5)) - polylog(2, -(-1)^(1/5)) > - polylog(2, (-1)^(2/5)) + polylog(2, -(-1)^(2/5)) > + polylog(2, (-1)^(3/5)) - polylog(2, -(-1)^(3/5)) > - polylog(2, (-1)^(4/5)) + polylog(2, -(-1)^(4/5)) ? Best wishes, Vladimir Bondarenko VM and GEMM architect > Co-founder, CEO, Mathematical Director http://www.cybertester.com/ Cyber Tester, LLChttp://maple.bug-list.org/ Maple Bugs Encyclopaediahttp://www.CAS-testing.org/ CAS Testing Apart from professor Israel's procedure I can't see another way. What is more important is that you can't base the simplification only to a combination of built-in commands of Maple or Mathematica. Just a side remark In[31]:= PolyLog[2, (-1)^(1/5)] - PolyLog[2, -(-1)^(1/5)]- PolyLog[2, (-1)^(2/5)]+ PolyLog[2, -(-1)^(2/5)]+ PolyLog[2, (-1)^( 3/5)] - PolyLog[2, -(-1)^(3/5)] - PolyLog[2, (-1)^(4/5)] + PolyLog[2, -(-1)^(4/5)]//N[#,60]&// Chop Out[31]= 1.97392088021787172376689819997523022706273988144815812528267 http://bootes.math.uqam.ca/cgi-bin/ipcgi/lookup.pl?number=1.9739208802178717 2376689819997523022706273988144815812528267&lookup_type=simple Dimitris === Subject: Re: SIGNIFICANT SIMPLIFICATION of FLT and BEAL's conjectures For the first I should apologize again for the serial of my faulty developments as above. Nowadays it seems for me clear, that Beal's conjecture for integers of gcd=1 could be solved with the help of especially retrieved equations which consists similar forms as certain retrieved equations for FLT conjecture. There is to be taken only, that FLT conjecture was solved properly from n=3,4 and next to all bigger primes... On the other way it could be seen some possible much more simple proof for FLT conjecture: Only, if there it is to consider no integer solutions for A^2 -B^2 = n(x^2 -y^2) for x;y of gcd=1 n as prime number from n=3 and A;B appropriate integers !!! How it can be done in details ? I hope my surprise will hold and be patient as I'll fight now with some highest authorities... Ro-Bin === Subject: Re: SIGNIFICANT SIMPLIFICATION of FLT and BEAL's conjectures <21541665.1188641680558.JavaMail.jakarta@nitrogen.mathforum.org For the first I should apologize again for the > serial of my faulty developments as above. > Nowadays it seems for me clear, > that Beal's conjecture for integers of gcd=1 > could be solved with the help of especially > retrieved equations which consists similar forms > as certain retrieved equations for FLT conjecture. > There is to be taken only, that FLT conjecture was > solved properly from n=3,4 and next to all bigger primes... > On the other way it could be seen some possible > much more simple proof for FLT conjecture: > Only, if there it is to consider no integer solutions > for A^2 -B^2 = n(x^2 -y^2) for x;y of gcd=1 > n as prime number from n=3 and A;B appropriate > integers !!! > How it can be done in details ? > I hope my surprise will hold and be patient > as I'll fight now with some highest authorities... Ro-Bin Yes, retrieve those equations, you nearly incomprehensible crank! And fight fight fight some highest authorities. Crank. === Subject: Re: Pattern Possibilities Pascal's Triangle would be great with divisibility rules and being able to see the application. The students would benefit from the visualization of the concept. === Subject: Probability - Cryptography The problem is... I have a 3 bit number- say x This is mapped to a 8 bit number using a function K(). We can assume that the function K() randomly maps the 3 bit number to 8 bit number and no two 3 bit number gets mapped to the same 8 bit number. Now lets name y as the first four bits of the 8 bit number. What is the probability that two 3 bit numbers (x1 and x2), generates the same 4 bit key (y) ?? -------------- A solution: z = K(x); z is 8 bit in size. We can divide 16 bit numbers into 16 bins of 4 bit numbers. bin of 0000 bin of 0001 . . . bin of 1111 P(no 2 keys are same) = P( 8 keys generated by the function K() falls in 8 different bins ). = C(16,8)/16 power 8. But i still doubt the solution is wrong!!! HELP HELP :) ... === Subject: Re: Probability - Cryptography >The problem is... I have a 3 bit number- say x This is mapped to a 8 bit number using a function K(). >We can assume that the function K() randomly maps the 3 bit number to >8 bit number and no two 3 bit number gets mapped to the same 8 bit >number. Now lets name y as the first four bits of the 8 bit number. What is the probability that two 3 bit numbers (x1 and x2), generates >the same 4 bit key (y) ?? -------------- A solution: z = K(x); z is 8 bit in size. We can divide 16 bit numbers into 16 bins of 4 bit numbers. >bin of 0000 >bin of 0001 >. >. >. bin of 1111 P(no 2 keys are same) = P( 8 keys generated by the function K() falls >in 8 different bins ). = C(16,8)/16 power 8. But i still doubt the solution is wrong!!! HELP HELP :) ... It depends on what you are asking - it seems that the solution doesn't quite match the problem. As asked, here's what I get: Each 8-bit number has an equal chance of being mapped from x1. Each of the remaining 255 8-bit numbers have an equal chance of being mapped from x2; 15 of them have the same first four bits as the number mapped from x1. The probability = 15/255 = 1/17. On the other hand, if you want to know the probability that at least one pair of mapped numbers have the same key (y) value, it's probably easier to calculate the probability that all eight numbers map to numbers with different keys, and subtract this from 1 to get the result. Let the 256 8-bit numbers be represented by 256 balls; each one is one of 16 colors based on its key value (e.g. key 0000 balls are black; key 0001 balls are red; key 0010 balls are orange). Choose one ball; this is the key of the number mapped from x0. Choose a ball for x1; the probability that it is different from x0 = 240/255. Choose a ball for x2; the probability that it is different from x0 and x1 = 224/254. Repeat for x3 through x7: P(x3) = 208/253 P(x4) = 192/252 P(x5) = 176/251 P(x6) = 160/250 P(x7) = 144/249 The final probability = 1 - (x1 * x2 * x3 * x4 * x5 * x6 * x7) = about 0.865. -- Don === Subject: Re: Probability - Cryptography <5u3jd3h3pq6krg4epam1jbvcgnisaoq7v3@4ax.com> On Sep 1, 9:26 pm, Don Del Grande The problem is... >I have a 3 bit number- say x >This is mapped to a 8 bit number using a function K(). >We can assume that the function K() randomly maps the 3 bit number to >8 bit number and no two 3 bit number gets mapped to the same 8 bit >number. >Now lets name y as the first four bits of the 8 bit number. >What is the probability that two 3 bit numbers (x1 and x2), generates >the same 4 bit key (y) ?? >-------------- >A solution: >z = K(x); z is 8 bit in size. >We can divide 16 bit numbers into 16 bins of 4 bit numbers. >bin of 0000 >bin of 0001 >. >. >. >bin of 1111 >P(no 2 keys are same) = P( 8 keys generated by the function K() falls >in 8 different bins ). > = C(16,8)/16 power 8. >But i still doubt the solution is wrong!!! >HELP HELP :) ... It depends on what you are asking - it seems that the solution doesn't > quite match the problem. As asked, here's what I get: > Each 8-bit number has an equal chance of being mapped from x1. > Each of the remaining 255 8-bit numbers have an equal chance of being > mapped from x2; 15 of them have the same first four bits as the number > mapped from x1. > The probability = 15/255 = 1/17. On the other hand, if you want to know the probability that at least > one pair of mapped numbers have the same key (y) value, it's probably > easier to calculate the probability that all eight numbers map to > numbers with different keys, and subtract this from 1 to get the > result. > Let the 256 8-bit numbers be represented by 256 balls; each one is one > of 16 colors based on its key value (e.g. key 0000 balls are black; > key 0001 balls are red; key 0010 balls are orange). Choose one ball; > this is the key of the number mapped from x0. > Choose a ball for x1; the probability that it is different from x0 = > 240/255. > Choose a ball for x2; the probability that it is different from x0 and > x1 = 224/254. > Repeat for x3 through x7: > P(x3) = 208/253 > P(x4) = 192/252 > P(x5) = 176/251 > P(x6) = 160/250 > P(x7) = 144/249 > The final probability = 1 - (x1 * x2 * x3 * x4 * x5 * x6 * x7) = about > 0.865. -- Don The second part is what i needed and that seems to be quite convincing a solution... :) === Subject: Re: Probability - Cryptography >The problem is... I have a 3 bit number- say x This is mapped to a 8 bit number using a function K(). >We can assume that the function K() randomly maps the 3 bit number to >8 bit number and no two 3 bit number gets mapped to the same 8 bit >number. Does K() always give the same output for the same input, or does the random mapping change? Now lets name y as the first four bits of the 8 bit number. What is the probability that two 3 bit numbers (x1 and x2), generates >the same 4 bit key (y) ?? Anything from zero to 1.0 depending on the details of K(). If the bits of the 3-bit number are ttt then: K(ttt) -> 0ttt1ttt -> y = 0ttt (here K(T) = 17 * T + 8) will always give different y's for different inputs. However if we have: K(ttt) -> 0101ttt0 -> y = 0101 (here K(T) = 2 * T + 80) then all ttt are mapped to the 0101 four bit key y. rossum -------------- A solution: z = K(x); z is 8 bit in size. We can divide 16 bit numbers into 16 bins of 4 bit numbers. >bin of 0000 >bin of 0001 >. >. >. bin of 1111 P(no 2 keys are same) = P( 8 keys generated by the function K() falls >in 8 different bins ). = C(16,8)/16 power 8. But i still doubt the solution is wrong!!! HELP HELP :) ... === Subject: Re: Probability - Cryptography > The problem is... I have a 3 bit number- say x This is mapped to a 8 bit number using a function K(). > We can assume that the function K() randomly maps the 3 bit number to > 8 bit number and no two 3 bit number gets mapped to the same 8 bit > number. Now lets name y as the first four bits of the 8 bit number. What is the probability that two 3 bit numbers (x1 and x2), generates > the same 4 bit key (y) ?? -------------- A solution: z = K(x); z is 8 bit in size. We can divide 16 bit numbers into 16 bins of 4 bit numbers. > bin of 0000 > bin of 0001 > . > . > . bin of 1111 P(no 2 keys are same) = P( 8 keys generated by the function K() falls > in 8 different bins ). = C(16,8)/16 power 8. But i still doubt the solution is wrong!!! HELP HELP :) ... > Could K map two different 3-bit numbers to the same 8-bit number? (No.) In your solution, yes. === Subject: Re: Probability - Cryptography <010920070632339669%anniel@nym.alias.net.invalid > The problem is... > I have a 3 bit number- say x > This is mapped to a 8 bit number using a function K(). > We can assume that the function K() randomly maps the 3 bit number to > 8 bit number and no two 3 bit number gets mapped to the same 8 bit > number. > Now lets name y as the first four bits of the 8 bit number. > What is the probability that two 3 bit numbers (x1 and x2), generates > the same 4 bit key (y) ?? > -------------- > A solution: > z = K(x); z is 8 bit in size. > We can divide 16 bit numbers into 16 bins of 4 bit numbers. > bin of 0000 > bin of 0001 > . > . > . > bin of 1111 > P(no 2 keys are same) = P( 8 keys generated by the function K() falls > in 8 different bins ). > = C(16,8)/16 power 8. > But i still doubt the solution is wrong!!! > HELP HELP :) ... Could K map two different 3-bit numbers to the same 8-bit number? (No.) > In your solution, yes. Could K map two different 3-bit numbers to the same 8-bit number? (No.) In your solution, yes. I did not get that. Probably the 16 power 8 made you think so.. Let me explain once again. 3 bit no -- K -- 8 bit no: => 4 bit no: (the first four bits) The 8bit no: is divided into 16 bins of 4 bit no:'s Bin 0000 contains numbers 0000xxxx (16 numbers)... Bin 0001 contains numbers 0001xxxx (16 numbers)... so.. in total 16 bins.. the 8 8-bit keys generated can be in any of these 16 bins... So the total sample space is '16 power 8' Now the no: of cases in which the 8 '8-bit keys' are in 8 different bins = C(16,8) P(no 2 keys are same) = P( 8 keys generated by the function K() falls in 8 different bins ). = C(16,8)/16 power 8. Does that seems to be correct!! I would love to be proved wrong... :) === Subject: Re: free groups and bounded generation <46d1d12d$0$9167$426a34cc@news.free.fr> <46d86b54$0$439$426a74cc@news.free.fr> <46d88e21$0$7759$426a74cc@news.free.fr > Hello. A discrete group G is said to be boundedly generated or of > finite width if there are elements g_1, ..., g_n of G such that > every element of G can be written as g = g_1^{N_1} .... g_n^{N_n} > for some integers N_i (not necessarily unique). > Is there an elementary proof that F_k, the free group on k generators, > is not of finite width? > I know a proof using pseudocharacters and bounded cohomology: the > Brooks pseudocharacters of a free group form an an infinite > dimensional family, which, as Grigorchuk pointed out, is not allowed > in a group of finite width. > Answering my question myself: > It's enough to show this for F_2. Now the symmetric group S_n > is generated by a 2-cycle and an n-cycle, hence is a homomorphic > image of F_2. Thus to prove that F_2 is not boundedly generated, > it suffices to show that there is no k such that S_n can be > written as a product of k cyclic groups for every n. For this > it suffices to show that if M(n) is the maximal order of > an element of S_N, then > M(n)^k << n!, > or equivalently that > k.log M(n) << n log n - n. > But it is classical (and easy to prove using cycle decompositions > in S_N) that log M(n) ~ (n log n)^{1/2}, so the result follows. >> Well, here is an argument of a similar type. Let p be a prime, and let >> K be the kernel of an epimorphism from F_2 to an elementary abelian >> group of order p^2. >> Then K is free of rank p^2+1, so K maps onto an elementary abelian >> group of order p^(p^2+1) with kernel L, say. >> So, F_2/L is of exponent p^2 and order p^(p^2+3), but if F_2 was a >> product of k cyclic groups, then it would have order at most p^(2k) - >> so just choose p large enough to make this impossible. >> Derek Holt. > from you, which is why I posted the question here (Hamish Short > also gave some encouragement for this course of action). > How well known to geometric/combinatorial group theorists is > the proof of this fact? > BTW the Landau estimate I cited uses the prime number theorem. > It can be replaced by the much coarser estimate log M(n) < n/e > which is a a simple consequence of G.M.<= A.M and bounding > the order of a permutation by the product of its cycle lengths. Continuing with your method of proof, does the result > not also follow from the fact the commutator > subgroup of F_2 is free on infinitely many generators? If F_2 were of > bounded variation this would force the commutator subgroup to be > finitely generated in particular. Might this in fact be the > obvious proof? I don't think this works directly, because the hypothesis of being a product of k cyclic groups is not inherited by subgroups of G. It is inherited by quotients of G, which is why your proof and my alternative proof work. On the other hand, the fact that F_2' is not finitely generated is somehow the reason why my proof is working, because it has the consequence that you can find finite quotients in which the derived group has arbitrarily large rank, and then you can use counting arguments. Derek Holt. === Subject: Re: The dimension of fixed space of a matrix I'm wondering if there is an easy way for knowing the dimension of the >fixed subspace of a matrix, when it act on a vector space. Here, by >the fixed subspace, what I mean is the subspace W such that Mx = x for >all x in W where M is the matrix in question. It is also the kernel >of the map (I-M), where I is the identity. (maybe there is a formal reduce matrix of M-I there is a way of know if the dimension of ker(M-I) is != 0 {x: Mx=x}!={0} => 1 is eigenvalue of M so if you prove that M has not an eigenvalue == 1 => {x: Mx=x}=={0} === Subject: Re: Math mnemonics >On Aug 31, 11:04 am, Mike Terry >> Anyone know any good math mnemonics? Here is one I got from the >> internet and it helps me remember the quadratic formula: Once there >> was a negative boy. He couldn't decide whether or not to go to a >> radical party. He was a square boy, so he missed out on 4 awesome >> chics. The entire party was over at 2am. dkw >> Smelly Armpits Cause Termites. >> (A school friend of mine made this up, and seemed to be inordinately proud >> of his achievement, but I'm nominating it for the most useless maths >> mnemonic award :-) > Here is a list of math mnemonics from my website. But most of the time it is easier to derive the thing than to remember the mnemonic. Joachim. M___________________________________________________________________________ Pi: Pi = 3.141592653589793238462643383279.................. Now I will a rhyme construct By chosen words the young instruct. Cunningly devised endeavor, Con it and remember ever. Widths of circle here you see. Sketched out in strange obscurity. Sir, I send a rhyme excelling In sacred truth and rigid spelling Numerical sprites elucidate for me the lexicon's full weight. If nature gain, who can complain tho' Doc Johnson fulminate. Sir, I bear a rhyme excelling In mystic force and magic spelling; Celestial sprites elucidate All my own striving can't relate. A.C. Orr, in: Literary Digest, vol. 32 (1906), p. 84 Now I, even I, would celebrate in rhymes inept, the great immortal Syracusan rivall'd nevermore who in his wondrous lore passed on before left men his guidance how to circles mensurate. Americans can spell rivall'd as rivaled, which works a lot better. How I want a drink, alcoholic of course, after the heavy chapters involving quantum mechanics. Xdat0911:pi Xdat0916:pi The next 9 digits are given by : All of thy geometry, Herr Planck, is fairly hard. - Sir James Jeans How I need a drink, alcoholic of course, after the least valuable discovery anybody important has or had anywhere made. A shortened version: How I need a drink, alcoholic of course, after the summer. (It is assumed that you know the first digit). I wish I could determine pi Eureka! cried the great inventor Christmas pudding, Christmas pie Is the problem's very centre. May I have a large container of coffee? Cream and sugar? How I wish I could recollect Of circle round The exact relation Archimede derived. Here is a mnemonic (from that terrific magazine, Omni, somewhere in the late 70s or early 80s) to calculate the circumference of a circle. Not only that, but it helps you memorise Pi to five decimals. Best of all, it's a limerick If you cross a circle with a line Which hits the centre and runs from spine to spine And the line's length is d The circumference will be d times 3.14159 See, I have a rhyme assisting My fevered brain its tasks resisting http://users.aol.com/s6sj7gt/mikerav.htm Poe, E.: Near A Raven The poem below, which bears an uncanny similarity to a certain famous poem by Edgar Allen Poe, is my latest and most difficult attempt at constrained writing. Constrained writing is the art of constructing a work of prose or poetry that obeys some artificially-imposed constraint. For example, there are two published novels from which the letter 'e' is absent - Gadsby, by Ernest Vincent Wright (1938), and La Disparition by George Perec (still in print, and even available in a very recent English translation (A Void, translated by Gilbert Adair) that also obeys the constraint!). Your mission, should you decide to accept it, is to figure out the constraint imposed on this poem. The answer is given after the end, so if you want to try to figure it out, just look at the beginning of the poem. Poe, E. Near A Raven Midnights so dreary, tired and weary. Silently pondering volumes extolling all by-now obsolete lore. During my rather long nap - the weirdest tap! An ominous vibrating sound disturbing my chamber's antedoor. This, I whispered quietly, I ignore. Perfectly, the intellect remembers: the ghostly fires, a glittering ember. Inflamed by lightning's outbursts, windows cast penumbras upon this floor. Sorrowful, as one mistreated, unhappy thoughts I heeded: That inimitable lesson in elegance - Lenore - Is delighting, exciting...nevermore. Ominously, curtains parted (my serenity outsmarted), And fear overcame my being - the fear of forevermore. Fearful foreboding abided, selfish sentiment confided, As I said, Methinks mysterious traveler knocks afore. A man is visiting, of age threescore. Taking little time, briskly addressing something: Sir, (robustly) Tell what source originates clamorous noise afore? Disturbing sleep unkindly, is it you a-tapping, so slyly? Why, devil incarnate!-- Here completely unveiled I my antedoor-- Just darkness, I ascertained - nothing more. While surrounded by darkness then, I persevered to clearly comprehend. I perceived the weirdest dream...of everlasting nevermores. Quite, quite, quick nocturnal doubts fled - such relief! - as my intellect said, (Desiring, imagining still) that perchance the apparition was uttering a whispered Lenore. This only, as evermore. Silently, I reinforced, remaining anxious, quite scared, afraid, While intrusive tap did then come thrice - O, so stronger than sounded afore. Surely (said silently) it was the banging, clanging window lattice. Glancing out, I quaked, upset by horrors hereinbefore, Perceiving: a nevermore. Completely disturbed, I said, Utter, please, what prevails ahead. Repose, relief, cessation, or but more dreary 'nevermores'? The bird intruded thence - O, irritation ever since! - Then sat on Pallas' pallid bust, watching me (I sat not, therefore), And stated nevermores. Bemused by raven's dissonance, my soul exclaimed, I seek intelligence; Explain thy purpose, or soon cease intoning forlorn 'nevermores'! Nevermores, winged corvus proclaimed - thusly was a raven named? Actually maintain a surname, upon Pluvious seashore? I heard an oppressive nevermore. My sentiments extremely pained, to perceive an utterance so plain, Most interested, mystified, a meaning I hoped for. Surely, said the raven's watcher, separate discourse is wiser. Therefore, liberation I'll obtain, retreating heretofore - Eliminating all the 'nevermores' . Still, the detestable raven just remained, unmoving, on sculptured bust. Always saying never (by a red chamber's door). A poor, tender heartache maven - a sorrowful bird - a raven! O, I wished thoroughly, forthwith, that he'd fly heretofore. Still sitting, he recited nevermores. The raven's dirge induced alarm - nevermore quite wearisome. I meditated: Might its utterances summarize of a calamity before? O, a sadness was manifest - a sorrowful cry of unrest; O, I thought sincerely, it's a melancholy great - furthermore, Removing doubt, this explains 'nevermores' . Seizing just that moment to sit - closely, carefully, advancing beside it, Sinking down, intrigued, where velvet cushion lay afore. A creature, midnight-black, watched there - it studied my soul, unawares. Wherefore, explanations my insight entreated for. Silently, I pondered the nevermores. Disentangle, nefarious bird! Disengage - I am disturbed! Intently its eye burned, raising the cry within my core. That delectable Lenore - whose velvet pillow this was, heretofore, Departed thence, unsettling my consciousness therefore. She's returning - that maiden - aye, nevermore. Since, to me, that thought was madness, I renounced continuing sadness. Continuing on, I soundly, adamantly forswore: Wretch, (addressing blackbird only) fly swiftly - emancipate me! Respite, respite, detestable raven - and discharge me, I implore! A ghostly answer of: nevermore. 'Tis a prophet? Wraith? Strange devil? Or the ultimate evil? Answer, tempter-sent creature!, I inquired, like before. Forlorn, though firmly undaunted, with 'nevermores' quite indoctrinated, Is everything depressing, generating great sorrow evermore? I am subdued!, I then swore. In answer, the raven turned - relentless distress it spurned. Comfort, surcease, quiet, silence! - pleaded I for. Will my (abusive raven!) sorrows persist unabated? Nevermore Lenore respondeth?, adamantly I encored. The appeal was ignored. O, satanic inferno's denizen -- go!, I said boldly, standing then. Take henceforth loathsome nevermores - O, to an ugly Plutonian shore! Let nary one expression, O bird, remain still here, replacing mirth. Promptly leave and retreat!, I resolutely swore. Blackbird's riposte: nevermore. So he sitteth, observing always, perching ominously on these doorways. Squatting on the stony bust so untroubled, O therefore. Suffering stark raven's conversings, so I am condemned, subserving, To a nightmare cursed, containing miseries galore. Thus henceforth, I'll rise (from a darkness, a grave) -- nevermore! -- Original: E. Poe -- Redone by measuring circles. Solution: Despite the rather difficult constraint (to be revealed shortly), observe how this revised version of The Raven duplicates the story, tone, and rhyme scheme of the original fairly closely (including the internal rhymes in the first and third line of each stanza). The only major concession to the form is that the original has six lines per stanza, with the fourth and fifth lines usually being very similar. Due to the nature of the constraint I imposed (revealed in the next paragraph), this would have been nearly impossible to do. Therefore, this version eliminates the similar line in each stanza. Give up? Hint: Start at the very beginning (with the word 'Poe') and write next to each word the number of letters it contains. Put a decimal point after the first digit. Look at the first few digits (or more if, like me, you know the first several hundred by heart). Are you impressed yet? Even given the rather difficult constraint, I was able to match the original very closely in spots. The very first line, although its meter is wrong, is surprisingly close. Others which are very close, even to the point of using many of the same words, are stanza 4 line 5, stanza 6 line 3, stanza 7 line 4, and stanza 15, line 1. Note the use of the term blackbird a couple of times. Though not, strictly speaking, correct (a raven is a black bird, not a blackbird), the term is particularly appropriate. It is a subtle reference to George Perec's La Disparition, which contains another written-with-constraints version of The Raven - in this case the constraint being write it in French without using the letter 'e'. In the English translation of La Disparition by Gilbert Adair, the poem is faithfully translated into English, also without using letter 'e'. The English version of the poem is titled (wait for it...) Black Bird! The poem encodes the first 740 decimals of pi. The encoding rule is this: a word of N letters represents the digit N if N<9, the digit 0 if N=10, and two adjacent digits if N>10 (e.g., a 12-letter word represents the digit '1' followed by '2'). A much less well-known example is this nice poem by Joseph Shipley (1960): But a time I spent wandering in bloomy night; Yon tower, tinkling chimewise, loftily opportune. Out, up, and together came sudden to Sunday rite, The one solemnly off to correct plenilune. I believe that Near a Raven establishes the world record for length of a pi mnemonic. I would be glad to hear of other wordy attempts, either in prose or poetry. Perhaps someone would like to attempt a short story or a novel?! I have just finished composing a short story that sets a new world record for the length of a pi mnemonic: 3835 decimals! Check it out, at http://users.aol.com/s6sj7gt/cadenza.htm You may recognize the first section, a pi-digits version of Edgar Allen takes off from there, in a somewhat science-fictiony vein. It occurred to me that the technique used in the The Raven version for representing 0, using 10-letter words, is a trifle inelegant; ideally, one should use zero-letter words. Alas, these are in short supply in written English and the best examples, numbers written in Arabic numerals, have a tendency not to come up in poetry. Nonetheless, taking advantage of a different commonly-used symbol, I've just completed the following (a translation of Sappho's Hymn to Aphrodite): Now I pray, O queen Aphrodite on ornate chair, Sly, death-shunning thunderer-progeny, Devastate not my own emotions with aching or sorrow; Come the way formerly you, my plaints detecting, Heard & in hurrying downward left A begetter's mansion. A golden cabriolet You harnessed; posthaste did finches impel 't & Wings vibrated by & enveloped Midgard Arrived speedily. O milady, holy & eterne in splendor, Smiled ye & inquired wherefore lamenting resounds, Whence my distress, & For what, signally, I'm heart-mad. Whom am I t' ensnare & seduce? Whoever currently troubles ye, O poet? Rebuffer & offering-dumper shall I set to pursuing ye now, & Giving thence many gifties; & transform now-unloving maid Into adorer (& unwilling wooer, maybe). & Speed likewise to me now, I entreat; my heart set again Woelessly free, & whatever I so heartily wish achieved p.d.q., Fulfill that thing, & be Psappho's ally. For PI, we have in France : Que j'aime a faire apprendre un nombre utile aux sages Immortel Archimede, artiste, ingenieur Qui de ton jugement peut priser la valeur ? Pour moi ton probleme eut de pareils avantages. 1. Que j'aime a faire apprendre un nombre utile aux sages. 2. Glorieux Archimede, artiste ingenieux ! 3. Toi, de qui Syracuse, aime encore la gloire, 4. Soit ton nom conserve par de savants grimoires. 5. Jadis, mysterieux, un probleme existait. 6. Tout l'admirable procede (l'oeuvre etonnante !) 7. Que Pythagore decouvrit aux anciens Grecs : 8. O quadrature ! Vieux tourment du philosophe ! Sibylline rondeur ! 9. Trop longtemps vous avez defie Pythagore et ses imitateurs ! 10. Comment integrer l'espace plan circulaire ? 11. Thales tu tomberas ! Platon tu desesperes ! 12. Apparait Archimede : 13. Archimede inscrira dedans un hexagone : 14. Appreciera son aire fonction du rayon ; 15. Pas trop ne s'y tiendra ! 16. Dedoublera chaque element anterieur, 17. Toujours de l'orbe calculee approchera ; 18. Laquelle limite donne l'arc, 19. La longueur de cet inquietant cercle, 20. Ennemi trop rebelle ! 21. Professeur, enseignez son probleme avec zele ... You can change lines 11 et 12 to 11'. Former un triangle auquel il equivaudra ? 12'. Nouvelle invention : and lines 18 and 19 to 18'. Definira limite ; enfin, l'arc, 19'. le limiteur de cet inquietant cercle In Dutch: Mag 't kind 't paard roskammen en voeren? In German: Wie? O! Dies pi Machst ernstlich so vielen viele M.9fh! Lernt immerhin, J.9fnglinge, leichte Verselein, Wie so sum Beispiel dies d.9frfte zu merken sein. Dir, O Held, o alter Philosoph, du RiesengenieQ Wie viele Tausende bewundern Geister Himmlisch wie du und g.9attlich! Noch reiner in Aeonen Wird das uns strahlen, Wie im lichten Morgenrot Spanish: Con 1 palo y 5 ladrillos se pueden hacer mil cosas Bretons: Piv a zebr a-walc'h dimerc'her? Ne lavaro netra, tud Breizh! Method in Portuguese to memorize pi to 8 digits. Just count the number of letters for each word in this sentence, it's a digit of PI (starts at 3, you know where the dot goes): sem o fogo .88 noite, escurid.8bo na cidade pobre sem = 3 letters o = 1 letter fogo = 4 letters .88 = 1 letter noite = 5 letters escurid.8bo = 9 letters na = 2 letters cidade = 6 letters pobre = 5 letters What it means is pretty meaningless: Without the fire at night, darkness in the poor city. Obviously this only works in Portuguese. M__________________________________________________________________________ 1/pi Les trois journ.8ees de 1830 ont renvers.8ee 89 M__________________________________________________________________________ e: To destroy a building we detonate a quantity of hydrogen bombs. (count the letters of each word) We require a mnemonic to remember e whenever we scribble math. In seeking a mnemonic, we composed a sentence of sensible words. A french riddle to remember the digits of e : Tu aideras a rappeler ta quantite a beaucoup de docteurs amis (You will help to remember your quantity to many friend doctors) I have found them in the last issue (October 1998) of Pour la science (french edition of Scientific American). M__________________________________________________________________________ Reading the following, It would help to know Korean counting system: Korean Counting System Number 1 2 3 4 5 6 7 8 9 Korean hana dul set net daseot yeoseot ilgop yeodeol ahop Sino-K il i sam sa o yuk chil pal gu And for zero, there is no Korean word for that, but there are two Sino-Korean* reading: yeong and gong *Sino-Korean: Reading of Chinese letters in Korean fashion. Isn't it fairly nice that there are two readings for every number? I think Korean counting is a ideal system to make mnemonics! Note. Since Korean is non-European language, it is hard to give an one-to-one literal translation. And sentences for mnemonics are usually very skewed, therefore it is impossible to give an literal translation. (However, native speaker of Korean will understand every proper meanings and silly nuances immediately...) Root 3: I think this is the best one I've ever heard. There is a mnemonic to memorize a value of root 3 in Korea: han chi se du go o go in ne 1. 7 3 2 0 5 0 1 4 This sounds like 'hana chil set dul gong o gong il net', (especially when you ignore the last consonants or vowel!) meaning '1 7 3 2 0 5 0 1 4' in Korean counting. What this sentence means is quite meaningless: (Root 3) is coming after counting one chi* (of whatever) *chi: Korean traditional measuring unit for length. After counting one chi (of whatever), root 3 will come to you. :) Root 2: This one is fairly good, though digits aren't many. wan ne wan ne dul il se 1. 4 1 4 2 1 3 For sure, this sounds like 'hana net hana net dul il set'. which means '1 4 1 4 2 1 3' in Korean counting. This sentence means: Coming! Coming! (something coming is) two! After chanting this, the result is 'coming' of the root 'two'. :) If I got more of these stuffs, I would send it, too. P.S: Was it interesting? Perhaps it is boring for someone who knows nothing about Korean... But I hope you enjoy this one. PPS: I hope to recieve your short answer. Is my English O.K.? This one is my nearly first attempt to write an E-mail in English... M__________________________________________________________________________ My father learned this on in Hong Kong and I can't believe it hasn't made it's way here sooner. The mnemonic doesn't hold in English, but it's only needed for the placement of the functions which is easily remembered. (This MUST be viewed in a non-proportional font): ----------------- | | | SIN-----COS | | / | | / | | / | | TAN--1--COT | | | / | | | | / | | | |/ | | | SEC CSC | | | ----------------- (SIN TAN SEC on left, CO-functions on right, 1 in the middle) Using this chart (I just look at it in my head) you can remember the following things: Across the 1: 1/SIN=CSC or 1/CSC=SIN 1/TAN=COT or 1/COT=TAN 1/SEC=COS or 1/COS=SEC Down any triangle: SIN^2+COS^2=1 TAN^2+1 =SEC^2 1+COT^2=CSC^2 Up any triangle: SEC^2-1 =TAN^2 or 1+TAN^2=SEC^2 CSC^2-1 =COT^2 or CSC^2-COT^2=1 1-SIN^2=COS^2 or 1-COS^2=SIN^2 A function and its two nearest CLOCKWISE or COUNTERCLOCKWISE neighbors around any edge of the square: (listed starting at tan going clockwise) TAN=SIN/COS SIN=COS/COT COS=COT/CSC CSC=SEC/TAN SEC=TAN/SIN (listed starting at tan going counter-clockwise) TAN=SEC/CSC SEC=CSC/COT CSC=COT/COS COS=SIN/TAN SIN=TAN/SEC A function and its two neighbors around any edge of the square: (listed starting at tan going clockwise) TAN=SIN*SEC SIN=COS*TAN COS=COT*SIN CSC=COT*SEC SEC=TAN*CSC M_________________________________________________________________________ Here are some phrases used to remember SIN, COS, and TAN. (SIN = Opposite/Hypotenuse, COS = Adjacent/H, TAN = O/A). Soh-Kah-Toa Sine=opposite/hypotenuse, etc. Some officers add curly auburn hair to offer attraction Sydney Opera House: Costs are higher than originally anticipated. how about Oscar Had A Hit Of Acid? write the first letter of each word along with the letters SCT like : S OH (sine = opposite/hypotenuse) C AH (cosine = adjacent/hypotenuse) T OA (tangent = opposite/adjacent) Two Old Angels Skipped Over Heaven Carrying Ancient Harps Two Old Angels Skipped Over Heaven Carrying A Harp Oscar Had A Heap Of Apples - you just have to remember the sine, cosine, tangent progression on your own. Saddle Our Horses, Canter Away Happily, To Other Adventures. Silly old Henry, caught Albert Hugging/Humping two old Aunts. Oscar had a hairy old ass. (T)ommy (O)n (A) (S)hip (O)f (H)is (C)aught (A) (H)addock T = O/A S = O/H C=A/H SOHCAHTOA (sock-a-toe-a) The Cat Sat On An Orange And Howled Hard Some Old Hulks Carry A Huge Tub Of Ale Silly Old Hitler Caused Awful Headaches To Our Airmen Some Old Hag Cracked All Her Teeth On Asparagus Some Old Hairy Camels Are Hairier Than Others Are Silly Old Harry Caught A Herring Trawling Off America SOPHY, CADHY, TOAD Smiles Of Happiness Come After Having Tankards Of Ale!!! I was taught the following phrase to remember SIN, COS, and TAN relationships: The Old Arab Sat On His Camel And Hiccupped For remembering the sign of trig functions in the quadrants: All Suckers Take Calculus: in quadrants one through four S | A ---|--- T | C All=sin, cos, and tan are all posative Suckers=sine positive (others negative) Take=tangent positive (others negative) Calculus=cosine positive (others negative) I was taught it as a CAST-iron rule ^ | | | ^ positive S | A | ---+-----------> | 0 T | C | v negative taking quadrant 1 (all) covering positive X and Y Signs of trignometric functions in the four quadrants: Aunt Sally Tickles Cannibals Admiral Spock Tickles Cabbages After Saturday, Tommy Croaked Atra Shaved Timmy Closer All stoner's take crack. Perp=Perpendicular /| hyp=hypotenuese (hyp)/ | (perpendicular) base=base /___| Base Sine=Perp/hyp Cos=Base/hyp Tan=perp/base In one single rhyme it can be summarised as: Some people have curly brown hair turned permanantly black. Sin= p/h cos=b/h Tan=p/b Scruffy Old He Cats Are Hungrier Than Other Animals (Rules of Triganometry) For positive or negative signs: All Sausages Taste Cool (or, very UK this) All Trains Stop (at) Crewe All Sadists Teach Chemistry law: Some Orifices Have Curly Auburn Hair To Obscure Approach. Spite Or Homesickness Caused Adolf Hitler To Occupy Austria. M__________________________________________________________________________ I've got a mnemonic to remember SIN, COS and TAN Silly Old Hens, Cackle And Howl, Till Old Age. M__________________________________________________________________________ Another mnemonic for remembering sin, cos, tan... Some old hippy Caught another hippy Tripping on acid M__________________________________________________________________________ I don't have a better one for the roots of quadratics, but I learned the sine-cosine song for the sum and difference formulae. (I'll describe it here, but it works better if you can hear the chant.) You memorize the formulae for the sine of a sum or difference on the first line and the cosine on the second. The chant goes sine cosine cosine sine cosine cosine sign sine sine (the last three are a triplet -- done in the same time as two of the previous) then fill in the angle names alternately and the + and - signs as appropriate. (That's the purpose of the 'sign' -- to remind you that if the angles are added, then the products of trig functions are subtracted.) I also learned a cute, no-brainer method of remembering the second derivative test. You'll see the trick if you draw a smiley face with +'s for eyes and a frowning face with -'s for eyes. (I don't really like to teach this one, as I think that the students are better off understanding what the sign of the second derivative tells us about the first, and what that entails about the concavity of the function. I usually mention it during the review for the final exam, rather than the chapter test that includes the second derivative test. M___________________________________________________________________________ Weber Tracy L (tweber@cc.brynmawr.edu): Please excuse my dear aunt Sally or PEMDAS Default operator precedence () ^ * / + - I was taught a longer version at school: Brackets of my dear aunt Sally Which nicely included the fact that brackets and of were higher in precedence that * / + -. Being a bunch of nasty snivelling (sp?) ten year olds, we changed it to Bollocks of my dear aunt Sally. For our American readers, Bollocks == Gonads. Not biologically correct but who cares ? Please excuse my dear aunt Sally parentheses exponents multiplication division addition subtraction Porno Pictures Make Dad Act Silly (algebraic order of operations) Brackets Blue Order Ovaries Division Disgust Multiplitcation My Addition Anal Subtraction Sultanas It didn't win best team name in our pub quiz, but it got the biggest laugh. M__________________________________________________________________________ Quotient rule for derivatives ala Cab Calloway: Hodehi minus hideho over hoho. My brother gave me this one from his math professor. It is a mnemonic for the quotient rule, called the Heidi Ho, or Cab Calloway, mnemonic. Hi represents the numerator (high), Ho the denominator (low), and De is the derivative operator. Ho De Hi minus Hi De Ho over Ho Ho Sometimes it's called the Santa Claus mnemonic. M__________________________________________________________________________ My friend and colleague, Lynn Gruner (who teaches BC Calculus with me at Walt Whitman HS in Bethesda, MD) has altered the quotient rule song that we received some years back. Her version (sung to OLD MACDONALD'S FARM) goes like this: Lo-de-hi less hi-de-lo EIEIO Then draw the line and down below EIEIO With a dx here and a dy there Here a slope, yes there's hope, you can cope Denominator squared will go EIEIO I composed a chain rule song to the tune of Allouette, but it's too long to be of much value as a mnemonic. The point of the song certainly underscores how the chain rule works, but it's not one you'd be likely to remember. On another mathematical subject, Lynn also uses EIEIO as a mnemonic for extracting roots and when the absolute value symbols are required in the answer Even Index, Even In yielding Odd (exponents). M__________________________________________________________________________ The numerator is called hi. The demoniator is called ho. The derative is called d The derivative of the fraction is as follows- ho d(hi) minus hi d(ho) over ho ho yd(x)-xd(y)/Ysquare M__________________________________________________________________________ sin 2a = 2 * sin a * cos a -- 2sicko cos 2a = (cos a)^2 - (sin a)^2 -- coas2si2 (no hint for signal, but is obvious that is -, for cos^2 + sin^2 = 1 ...) M__________________________________________________________________________ I remember one my physics teacher taught me (I still use it... but that probably says more about me than the mnemonic) Is dc negative? Means Integrate Sine / Differentiate cos gives negative M__________________________________________________________________________ A student of mine learned a song (from her mother) that helps her remember it. It is sung to the tune of Pop Goes the Weasel X equals negative B Plus or minus square root of B squared minus four A C All over two A. M__________________________________________________________________________ When I was in Jr. High and first learning about the trig functions, I thought of Howard Cosell. Cosell is an a**hole for cos=a/h. I never got sine and cosine confused since. M__________________________________________________________________________ For those wishing to remember which is the domain and which the range: ^ y | |-----___ | _ __|~@@@@@@@ | |_| ~~@@@@@@ |____ / ~~@@@@@@@ |____| / |-----/ | +-------------------> x Home on the Range (Acknowledgements to whoever drew this on a men's room wall in the U of Chicago mathematics department many years ago, which is where I saw it. Few graffiti one sees in such places are so useful!) M__________________________________________________________________________ May I submit the following of my own devising? MATRICES: Multiply Appropriate Two Row Into Column, Evaluate Sum MOM'S ACE BRA: Matrices Only Multiply Should A's Columns Equal B's Rows... Actually M__________________________________________________________________________ In the early morning, astronomers spiritualized nonmathematicians. Counting the letters of each word gives you the first seven prime numbers. -- Joachim Verhagen WWW http://www.xs4all.nl/~jcdverha/ (Science Jokes) === Subject: Re: Math mnemonics <13dgm1pb4vqfoc4@corp.supernews.com> On Sep 1, 3:38 am, Joachim Verhagen On Aug 31, 11:04 am, Mike Terry >> Anyone know any good math mnemonics? Here is one I got from the >> internet and it helps me remember the quadratic formula: Once there >> was a negative boy. He couldn't decide whether or not to go to a >> radical party. He was a square boy, so he missed out on 4 awesome >> chics. The entire party was over at 2am. dkw >> Smelly Armpits Cause Termites. >> (A school friend of mine made this up, and seemed to be inordinately proud >> of his achievement, but I'm nominating it for the most useless maths >> mnemonic award :-) Here is a list of math mnemonics from my website. But most of the time it is > easier to derive the thing than to remember the mnemonic. Joachim. M ? > Pi: Pi = 3.141592653589793238462643383279.................. > Now I will a rhyme construct > By chosen words the young instruct. > Cunningly devised endeavor, > Con it and remember ever. > Widths of circle here you see. > Sketched out in strange obscurity. Sir, I send a rhyme excelling > In sacred truth and rigid spelling > Numerical sprites elucidate > for me the lexicon's full weight. > If nature gain, who can complain > tho' Doc Johnson fulminate. Sir, I bear a rhyme excelling > In mystic force and magic spelling; > Celestial sprites elucidate > All my own striving can't relate. > A.C. Orr, in: Literary Digest, vol. 32 (1906), p. 84 > Now I, even I, would celebrate in rhymes inept, > the great immortal Syracusan rivall'd nevermore > who in his wondrous lore passed on before > left men his guidance how to circles mensurate. Americans can spell rivall'd as rivaled, which works a lot better. How I want a drink, alcoholic of course, > after the heavy chapters involving quantum mechanics. Xdat0911:pi Xdat0916:pi The next 9 digits are given by : > All of thy geometry, Herr Planck, is fairly hard. > - Sir James Jeans > How I need a drink, alcoholic of course, after the least valuable > discovery anybody important has or had anywhere made. > A shortened version: > How I need a drink, alcoholic of course, after the summer. (It is assumed that you know the first digit). I wish I could determine pi > Eureka! cried the great inventor > Christmas pudding, Christmas pie > Is the problem's very centre. May I have a large container of coffee? > Cream and sugar? > How I wish I could recollect > Of circle round > The exact relation > Archimede derived. > Here is a mnemonic (from that terrific magazine, Omni, somewhere in the > late 70s or early 80s) to calculate the circumference of a circle. Not only > that, but it helps you memorise Pi to five decimals. Best of all, it's a > limerick If you cross a circle with a line > Which hits the centre and runs from spine to spine > And the line's length is d > The circumference will be d times 3.14159 > See, I have a rhyme assisting > My fevered brain its tasks resisting > The poem below, which bears an uncanny similarity to a certain famous poem > by Edgar Allen Poe, is my latest and most difficult attempt at constrained > writing. Constrained writing is the art of constructing a work of prose or > poetry that obeys some artificially-imposed constraint. For example, there > are two published novels from which the letter 'e' is absent - Gadsby, by > Ernest Vincent Wright (1938), and La Disparition by George Perec (still in > print, and even available in a very recent English translation (A Void, > translated by Gilbert Adair) that also obeys the constraint!). Your mission, should you decide to accept it, is to figure out the > constraint imposed on this poem. The answer is given after the end, so if > you want to try to figure it out, just look at the beginning of the poem. Poe, E. > Near A Raven Midnights so dreary, tired and weary. Silently pondering volumes extolling > all by-now obsolete lore. During my rather long nap - the weirdest tap! > An ominous vibrating sound disturbing my chamber's antedoor. > This, I whispered quietly, I ignore. Perfectly, the intellect remembers: the ghostly fires, a glittering ember. > Inflamed by lightning's outbursts, windows cast penumbras upon this floor. > Sorrowful, as one mistreated, unhappy thoughts I heeded: > That inimitable lesson in elegance - Lenore - > Is delighting, exciting...nevermore. Ominously, curtains parted (my serenity outsmarted), And fear overcame my > being - the fear of forevermore. Fearful foreboding abided, selfish > sentiment confided, As I said, Methinks mysterious traveler knocks afore. > A man is visiting, of age threescore. Taking little time, briskly addressing something: Sir, (robustly) Tell > what source originates clamorous noise afore? Disturbing sleep unkindly, > is it you a-tapping, so slyly? Why, devil incarnate!-- Here completely > unveiled I my antedoor-- Just darkness, I ascertained - nothing more. While surrounded by darkness then, I persevered to clearly comprehend. > I perceived the weirdest dream...of everlasting nevermores. Quite, > quite, quick nocturnal doubts fled - such relief! - as my intellect said, > (Desiring, imagining still) that perchance the apparition was uttering a > whispered Lenore. > This only, as evermore. Silently, I reinforced, remaining anxious, quite scared, afraid, > While intrusive tap did then come thrice - O, so stronger than sounded > afore. Surely (said silently) it was the banging, clanging window > lattice. > Glancing out, I quaked, upset by horrors hereinbefore, > Perceiving: a nevermore. Completely disturbed, I said, Utter, please, what prevails ahead. > Repose, relief, cessation, or but more dreary 'nevermores'? The bird > intruded thence - O, irritation ever since! - > Then sat on Pallas' pallid bust, watching me (I sat not, therefore), > And stated nevermores. Bemused by raven's dissonance, my soul exclaimed, I seek intelligence; > Explain thy purpose, or soon cease intoning forlorn 'nevermores'! > Nevermores, winged corvus proclaimed - thusly was a raven named? > Actually maintain a surname, upon Pluvious seashore? > I heard an oppressive nevermore. My sentiments extremely pained, to perceive an utterance so plain, > Most interested, mystified, a meaning I hoped for. Surely, said the > raven's watcher, separate discourse is wiser. > Therefore, liberation I'll obtain, retreating heretofore - > Eliminating all the 'nevermores' . Still, the detestable raven just remained, unmoving, on sculptured bust. > Always saying never (by a red chamber's door). A poor, tender > heartache maven - a sorrowful bird - a raven! > O, I wished thoroughly, forthwith, that he'd fly heretofore. > Still sitting, he recited nevermores. The raven's dirge induced alarm - nevermore quite wearisome. > I meditated: Might its utterances summarize of a calamity before? O, a > sadness was manifest - a sorrowful cry of unrest; > O, I thought sincerely, it's a melancholy great - furthermore, > Removing doubt, this explains 'nevermores' . Seizing just that moment to sit - closely, carefully, advancing beside it, > Sinking down, intrigued, where velvet cushion lay afore. A creature, > midnight-black, watched there - it studied my soul, unawares. > Wherefore, explanations my insight entreated for. > Silently, I pondered the nevermores. Disentangle, nefarious bird! Disengage - I am disturbed! > Intently its eye burned, raising the cry within my core. That > delectable Lenore - whose velvet pillow this was, heretofore, > Departed thence, unsettling my consciousness therefore. > She's returning - that maiden - aye, nevermore. Since, to me, that thought was madness, I renounced continuing sadness. > Continuing on, I soundly, adamantly forswore: Wretch, (addressing > blackbird only) fly swiftly - emancipate me! Respite, respite, detestable raven - and discharge me, I implore! > A ghostly answer of: nevermore. 'Tis a prophet? Wraith? Strange devil? Or the ultimate evil? > Answer, tempter-sent creature!, I inquired, like before. Forlorn, > though firmly undaunted, with 'nevermores' quite indoctrinated, > Is everything depressing, generating great sorrow evermore? > I am subdued!, I then swore. In answer, the raven turned - relentless distress it spurned. > Comfort, surcease, quiet, silence! - pleaded I for. Will my (abusive > raven!) sorrows persist unabated? > Nevermore Lenore respondeth?, adamantly I encored. > The appeal was ignored. O, satanic inferno's denizen -- go!, I said boldly, standing then. Take henceforth loathsome nevermores - O, to an ugly Plutonian shore! > Let nary one expression, O bird, remain still here, replacing mirth. Promptly leave and retreat!, I resolutely swore. > Blackbird's riposte: nevermore. So he sitteth, observing always, perching ominously on these doorways. > Squatting on the stony bust so untroubled, O therefore. Suffering stark > raven's conversings, so I am condemned, subserving, > To a nightmare cursed, containing miseries galore. > Thus henceforth, I'll rise (from a darkness, a grave) -- nevermore! read more ?- Hide quoted text - - Show quoted text -... Very creative! === Subject: Re: Math mnemonics > Anyone know any good math mnemonics? How I wish I could calculate pi. --- Christopher Heckman === Subject: Re: Math mnemonics >> Anyone know any good math mnemonics? How I wish I could calculate pi. --- Christopher Heckman > There is a French mnemonic for 30 decimals of pi which I remembered vaguely and was able to find using Google: Que j'aime .88 faire apprendre un nombre utile aux sages Immortel Archim.8fde, artiste, ing.8enieur, Qui de ton jugement peut priser la valeur ? Pour moi ton probl.8fme eut de pareils avantages. This was found at the link given below. < http://fr.wikisource.org/wiki/Trente_d%C3%A9cimales_de_%CF%80 > David Bernier === Subject: Re: Math mnemonics > Anyone know any good math mnemonics? Here is one I got from the > internet and it helps me remember the quadratic formula: Once there > was a negative boy. He couldn't decide whether or not to go to a > radical party. He was a square boy, so he missed out on 4 awesome > chics. The entire party was over at 2am. dkw > Some like mnemonics when dealing with conics. Others know none but your one is fun. Rainer Rosenthal r.rosenthal@web.de === Subject: Re: Math mnemonics I had heard rumors in the past that mathematicians are > a boring lot. This thread seems to prove it. The point is that you shouldn't use mnemonics for such simple things, > especially when deducing them is as instructive as in this case. > But I agree that there are formulae that you should memorize. And it > doesn't mean that you don't understand them. You simply can't reinvent > the wheel every time. Kiuhnm Sorry, but math is only one of my many interests and since I don't use algebra and calculus very much every day, it helps to recall such formulae, classifications, rules, etc. The less involved you are in math, the more you might want to use mnemonics I would say. I also suggest that you already use a lot of mnemonics, but perhaps don't recognize them as such, because you mind makes the associations so quickly that the process is lost on your conscious mind, but they are still there whether a shape, a picture, an experience or whatever. Many of those might only work well for you, but there are many that seem to offer almost universal usefulness. === Subject: 11.- R^+ prime coding functions. Amongst the R^+ coding functions, it will be interesting to select those given by f_m : [m, m+1] -> R (m=0, 1, 2, ...), satisfying: ( i ) f_m (x) = a_m (x-m ) + B_m ( B_0 =0, B_m= Sum { j = 0 to m-1 } ( a_j ), for every m e N. ( Affine functions ). ( ii ) 0 < a_i < a_( i + 1 ) for every i e N. We call any of these functions R^+ prime coding functions . Easily proved, R^+ prime coding functions identify prime numbers by means of vortex points. Next step wiil be to create the conditions for characterizing Goldbach Conjecture using the essential region concept. Fernando. P.S. For previous comments see: http://mathforum.org/kb/thread.jspa?threadID=1615410&tstart=75 === Subject: Latitude / longitude distance and bearing. I have two locations, call them 'a' and 'b' . a) Altitude of a and b (call them alt_a and alt_b). b) Latitude of b and b (call them lat_a and lat_b) c) Longitude of a and b (call them long_a and long_b) 'a' and 'b' are fairly close together (10 - 20 km) and in line of sight distance. (Two mountain peaks). I want to find 1) The straight line distances from a to b. (*Not* the distance along the circumference of the earth, which I can get from the Haversine formula) 2) The bearing of 'a' when viewed from 'b'. 3) The vertical angle - i.e how many degress above the horizon is 'a' when viewed from 'b'. (alt_a > alt_b). If the distances were sufficiently large, the location with the higher altitude could be below the horizon when viewed from the one with lower altitude, but in this case, the distances are small. so the location with the higher altitude is well above the horizon of the location with the lower altitude. I am willing to assume the earth is spherical. The distances involved are not huge (a few tens of km), and are in Europe (Latitude is North, Longitude is East). I asked this on 'Dr. Math' and someone suggested I worked in spherical coordinates (rho, theta, phi) then transfered to rectangular. I've done that and found the points x_a, y_a and z_a using rho_a=EARTH_RADIUS+alt_a; theta_a=long_a; phi_a=M_PI/2.0-lat_a; Transfered to cartesian coordines x_a= rho_a*cos(theta_a)*sin(phi_a); y_a = rho_a*sin(theta_a)*sin(phi_a); z_a = rho_a*cos(phi_a); so I get the points x_a, y_a and z_a relative to the point 0,0,0 which is the centre of the earth. I did likewise for location b, to get x_b, y_b and z_b. Then I computed dx=x_a-x_b dy=y_a-y_b dz=z_a-z_b The radial distance between a and b, which is one of the 3 parameters I need, is r=sqrt(dx*dx + dy*dy + dz*dz); But I'm stuck as how to find the other two parameters - the bearing the angle above the horizon. I'm aware of this page: http://www.movable-type.co.uk/scripts/latlong.html which has formula for the bearing between two locations, but there is nothing there about altitude, which I suspect might mean the forumula are not valid. Any thoughts? -- Dave (from the UK) It is always of the form: month-year@althorne.org Hitting reply will work for a few months only - later set it manually. http://chessdb.sourceforge.net/ - a Free open-source Chess Database === Subject: Re: Latitude / longitude distance and bearing. >I have two locations, call them 'a' and 'b' . > a) Altitude of a and b (call them alt_a and alt_b). > b) Latitude of b and b (call them lat_a and lat_b) > c) Longitude of a and b (call them long_a and long_b) 'a' and 'b' are > fairly close together (10 - 20 km) and in line of sight distance. (Two > mountain peaks). > I want to find 1) The straight line distances from a to b. (*Not* the > distance along the circumference of the earth, which I can get from the > Haversine formula) > Consider land surveying. Latitude and longitude are often projected to plane rectangular coordinate systems. These plane rectangular coordinate systems can be the size of a state or the size of a country. UTM is a plane rectangular coordinate system to cover large areas of the globe. If the coordinate area is long North and South then often a Transverse Mercator projection is used. Now the distance from point A to point B is a horizontal distance when projected to the plane rectangular coordinate system. But one choice of radius could be used in the projection parameters (and this might be found in different parameters used by different states for their state-plane-coordinate-systems). And there could be a choice of latitude to project from. Now with the horizontal distance and the difference in elevation of course a slope distance is possible. Here is a user link to 'Geodetic/UTM-Grid Utility': http://www.kbhscape.com/gps.htm === Subject: Re: Latitude / longitude distance and bearing. >I have two locations, call them 'a' and 'b' . a) Altitude of a and b (call them alt_a and alt_b). >b) Latitude of b and b (call them lat_a and lat_b) >c) Longitude of a and b (call them long_a and long_b) >'a' and 'b' are fairly close together (10 - 20 km) and in line of sight >distance. (Two mountain peaks). I want to find 1) The straight line distances from a to b. (*Not* the distance along >the circumference of the earth, which I can get from the Haversine formula) 2) The bearing of 'a' when viewed from 'b'. 3) The vertical angle - i.e how many degress above the horizon is 'a' >when viewed from 'b'. (alt_a > alt_b). Would this work for (2): (a) Rotate Earth through the poles until 'b' is at longitude zero; (b) Rotate Earth through points on what is now the equator at longitudes +90 and -90 until 'b' is now at the north pole. (Point 'a' is rotated on a circle parallel to the one containing longitude zero.) Since 'a' has rotated over the top of the Earth, what was a northernly direction from 'b' to 'a' is now southernly; the actual bearing equals the number of degrees the new longitude of 'b' is from longitude 180. (If that's not quite right, you can always use the method I use for satellite aiming; use (a) and (b) above, but then push Earth South a distance equal to its radius, so 'b' is now at the origin of rectangular coordinates; assuming Earth is a sphere of radius R, you know the X, Y, and Z coordinates of 'a', so the tangent of the bearing equals Y/X (assume X is the direction towards lat 0 lng 0, Y is the direction towards lat 0 lng +90, and Z is the direction towards lat +90). Actually, you don't even have to to (c), since all it does is change the two points' Z-coordinates.) -- Don === Subject: Re: Latitude / longitude distance and bearing. >I have two locations, call them 'a' and 'b' . > a) Altitude of a and b (call them alt_a and alt_b). > b) Latitude of b and b (call them lat_a and lat_b) > c) Longitude of a and b (call them long_a and long_b) > 'a' and 'b' are fairly close together (10 - 20 km) and in line of sight > distance. (Two mountain peaks). > I want to find > 1) The straight line distances from a to b. (*Not* the distance along the > circumference of the earth, which I can get from the Haversine formula) > 2) The bearing of 'a' when viewed from 'b'. > 3) The vertical angle - i.e how many degress above the horizon is 'a' when > viewed from 'b'. (alt_a > alt_b). Take a look at INVERS3D/FORWRD3D at http://www.ngs.noaa.gov/PC_PROD/Inv_Fwd/ There is also FORTRAN source code. Also of interest is the porigram COMPSYS21 available at http://www.naco.faa.gov/index.asp?xml=naco/online/compsys === Subject: Re: Latitude / longitude distance and bearing. > I have two locations, call them 'a' and 'b' . a) Altitude of a and b (call them alt_a and alt_b). > b) Latitude of b and b (call them lat_a and lat_b) > c) Longitude of a and b (call them long_a and long_b) > 'a' and 'b' are fairly close together (10 - 20 km) and in line of sight > distance. (Two mountain peaks). I want to find 1) The straight line distances from a to b. (*Not* the distance along > the circumference of the earth, which I can get from the Haversine formula) > 2) The bearing of 'a' when viewed from 'b'. The Web page you refer to below mentions two kinds of bearings: (1) The initial bearing (at 'b') for an arc of a great-circle from 'b' to 'a'. (2) The rhumb line bearing, where a rhumb line or loxodrome is a path of constant bearing . The rhumb line route in general is longer than the arc of great circle route. Of the two, I think #1 is easier to compute than the rhumb line bearing. > 3) The vertical angle - i.e how many degress above the horizon is 'a' > when viewed from 'b'. (alt_a > alt_b). So I guess for the horizon you mean the plane perpendicular to a plumb line ... > If the distances were sufficiently large, the location with the higher > altitude could be below the horizon when viewed from the one with lower > altitude, but in this case, the distances are small. so the location > with the higher altitude is well above the horizon of the location with > the lower altitude. I am willing to assume the earth is spherical. The distances involved > are not huge (a few tens of km), and are in Europe (Latitude is North, > Longitude is East). I asked this on 'Dr. Math' and someone suggested I worked in spherical > coordinates (rho, theta, phi) then transfered to rectangular. I've done that and found the points x_a, y_a and z_a using rho_a=EARTH_RADIUS+alt_a; > theta_a=long_a; > phi_a=M_PI/2.0-lat_a; Transfered to cartesian coordines x_a= rho_a*cos(theta_a)*sin(phi_a); > y_a = rho_a*sin(theta_a)*sin(phi_a); > z_a = rho_a*cos(phi_a); so I get the points x_a, y_a and z_a relative to the point 0,0,0 which > is the centre of the earth. I did likewise for location b, to get x_b, y_b and z_b. Then I computed dx=x_a-x_b > dy=y_a-y_b > dz=z_a-z_b > The radial distance between a and b, which is one of the 3 parameters I > need, is r=sqrt(dx*dx + dy*dy + dz*dz); But I'm stuck as how to find the other two parameters - the bearing the > angle above the horizon. I'm aware of this page: http://www.movable-type.co.uk/scripts/latlong.html which has formula for the bearing between two locations, but there is > nothing there about altitude, which I suspect might mean the forumula > are not valid. If the altitude values are included, and the bearing of 'a' when viewed from 'b' is measured as the crow flies or would fly, I believe the altitudes don't matter and the initial bearing for an arc of a great-circle from b0 to a0 can be used, where a0 (resp. b0) has the same latitude/longitude as a (resp. b) but altitude 0... For the the elevation, consider the points a, b and O, the center of the earth. The lengths of the three sides of triangle abO can be computed. Then I think the elevation, from my assumption about the horizon, would be the measure of the angle of the triangle at 'b' minus 90 degrees. David Bernier === Subject: Re: Latitude / longitude distance and bearing. > I have two locations, call them 'a' and 'b' . >> a) Altitude of a and b (call them alt_a and alt_b). >> b) Latitude of b and b (call them lat_a and lat_b) >> c) Longitude of a and b (call them long_a and long_b) >> 'a' and 'b' are fairly close together (10 - 20 km) and in line of >> sight distance. (Two mountain peaks). >> I want to find >> 1) The straight line distances from a to b. (*Not* the distance along >> the circumference of the earth, which I can get from the Haversine >> formula) >> 2) The bearing of 'a' when viewed from 'b'. The Web page you refer to below mentions two kinds of > bearings: (1) The initial bearing (at 'b') for an arc of a great-circle from 'b' > to 'a'. (2) The rhumb line bearing, where a rhumb line or loxodrome is a path > of constant bearing . The rhumb line route in general is longer > than > the arc of great circle route. Of the two, I think #1 is easier to compute than the rhumb line bearing. But the distance I want is I believe shorter than even the arc of the great circle, as that is (I believe) the distance you would travel if you drove a car from a to b, rather than tunnel through the earth which would give a shorter distance. I believe the distance r = sqrt(dx*dz + dy*dy + dz*dz) is the correct distance - i.e. the distance the crow would fly. >> 3) The vertical angle - i.e how many degress above the horizon is 'a' >> when viewed from 'b'. (alt_a > alt_b). So I guess for the horizon you mean the plane perpendicular > to a plumb line ... If I interpret what you say correctly, then you mean 90 deg away from vertical, i.e. horizontal. That is indeen what I mean by horizon. > If the altitude values are included, and the > bearing of 'a' when viewed from 'b' is measured as the crow flies or would > fly, I believe the altitudes don't matter and > the initial bearing for an arc of a great-circle from b0 to a0 can be used, > where a0 (resp. b0) has the same latitude/longitude as a (resp. b) but > altitude 0... > For the the elevation, consider the points a, b and O, the center of the > earth. The lengths of the three sides of triangle abO can be computed. Yes, I think I can do that. I know the xyz coordinates of all points. > Then I think the elevation, from my assumption about the horizon, > would be the measure of the angle of the triangle at 'b' minus 90 degrees. That is interesting. I'll look into that and calculate that. I have done this for a couple of places a and b and get an elevation angle of about 30 degrees. Someone else gets about 80 degrees - clearly a huge difference. I don't know what method he is using. I've done it like this. 1) Calculated the radial distance r from r = sqrt(dx*dz + dy*dy + dz*dz) (we agress on that one.) 2) Assumed a right-angled with a hypotenuse of the length r, which is known from above. 3) The vertical side of the triangle is assumed to be alt_a - alt_b, which is the difference in altitudes of the two mountains. 4) The unknown horizontal side of the triangle (call it horz) is then found from: r^2 = horz^2 + (alt_a - alt_b)^2 so horz = sqrt(r^2 - (alt_a - alt_b)^2) 5) The elevation angle alpha is then alpha = atan( (alt_a-alt_b)/ horz); Comments on this method are welcome. -- Dave (from the UK) It is always of the form: month-year@althorne.org Hitting reply will work for a few months only - later set it manually. http://chessdb.sourceforge.net/ - a Free open-source Chess Database === Subject: Tommy is an embarassment to whatever educational system attempted to teach him English <15641467.1188503057290.JavaMail.jakarta@nitrogen.mathforum.org> Alas, the poor Dutch, having TOMMY among them (snicker). I do think tommy is *not* Dutch. ... > So don't embarass the Dutch by identifying with them. He doesn't. > -- > dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 > home: bovenover 215, 1025 jn amsterdam, nederland;http://www.cwi.nl/~dik/ By He doesn't, do you mean Tommy doesn't embarass the Dutch, or Tommy doesn't identify with them? Okay, Dutch may be ambiguous. But Tommy says above he speaks Dutch and implies that he's from Belgium (alas for Belgium). In another thread, Tommy says: and if you ever visit belgium again , let me know :-) I imagine Tommy skulking around Belgium, confusing and confounding all of those people in Belgium he encounters. Poor, poor Belgium. Well, I think Tommy is some sloppy American. And I can say that, since I'm American. Okay, let me not be ambiguous, since Canadians and people in Latin America don't like the United States co-opting the word American (ooo, those evil imperialistic United-States-ians!). I think Tommy is some sloppy person from the United States, and I can say that since I'm from the United States. Tommy should GO BACK TO SCHOOL FOR ENGLISH! (note my allcaps for emphasis). So then maybe Tommy can learn English AND learn to use English (happy, Joshua Cranmer?), and then Tommy can USE English properly. === Subject: Re: pi as unit real number replacing unity > On Sep 1, 1:57 am, Mark Nudelman > On Aug 31, 9:40 am, Narasimham >> If hypothetically the yardstick of unit real > numbers counting is >> changed to include (0, pi, 2pi, 3pi,... ) with > its A.P. common >> difference of the irrational number pi as basis > instead of the present >> (0,1,2,3,... ) with common difference rational > unity 1, what >> simplifications or changes could be effected in > all of Real Analysis? >> Narasimham > Asked this as pi is _ratio_ of the most natural > figure,the circle. > By definition it is non-dimensional and might > have been a natural > number choice for a unit of rotation rather than > translation. In > this system,sin(0) = sin(1) = 0, cos(1)= -1 > If I'm understanding your system, cos(1) = -1/pi, > not -1. > --Mark electrostatic/magnetic > theory and elsewhere with uncomfortable pi related > coefficients could > get tidied up. > Possibly. There is a distinction between abstract counting, however, which employs dimensionless real integers--and measure, which represents the difference in size among counted quantities. The former lives in ordered relations, the same counting line in which you substitute pi for the integer 1. Why pi, though? Why not sqrt(2)? In fact, any positive non-zero number will work, won't it? Now, you are taking the constant pi as a geometric ratio and then saying that by definition it is non- dimensional. Do you realize that this is the same insight by which we get to complex analysis? That is, the derivation of the Euler Identity e^ix=cosx + isinx, when x=pi, is in logarithmic terms ln(-1)=ipi. Engineers find it easier to work in the complex plane because they are not concerned with counting, but with measure. The advantage of the two-dimensional analysis is that more room to calculate, in which pi IS a unit of rotation rather than translation (rotation through the complex plane)allows one to get real results in desired continuous functions while ignoring imaginary results. One would need to know more about how you propose to make real analysis simpler than complex analysis for measure problems. What advantage? By the way, Hans Schwerdtfeger in Geometry of Complex Numbers (Dover,1979)has a nice section on the analytic geometry of circles. Tom === Subject: Re: pi as unit real number replacing unity <20182375.1188647495954.JavaMail.jakarta@nitrogen.mathforum.org > On Sep 1, 1:57 am, Mark Nudelman > On Aug 31, 9:40 am, Narasimham >> If hypothetically the yardstick of unit real > numbers counting is >> changed to include (0, pi, 2pi, 3pi,... ) with > its A.P. common >> difference of the irrational number pi as basis > instead of the present >> (0,1,2,3,... ) with common difference rational > unity 1, what >> simplifications or changes could be effected in > all of Real Analysis? >> Narasimham > Asked this as pi is _ratio_ of the most natural > figure,the circle. > By definition it is non-dimensional and might > have been a natural > number choice for a unit of rotation rather than > translation. In > this system,sin(0) = sin(1) = 0, cos(1)= -1 > If I'm understanding your system, cos(1) = -1/pi, > not -1. > --Mark > electrostatic/magnetic > theory and elsewhere with uncomfortable pi related > coefficients could > get tidied up. Possibly. There is a distinction between abstract > counting, however, which employs dimensionless real > integers--and measure, which represents the > difference in size among counted quantities. The > former lives in ordered relations, the same counting > line in which you substitute pi for the integer 1. > Why pi, though? Why not sqrt(2)? In fact, any positive > non-zero number will work, won't it? Now, you are taking the constant pi as a geometric ratio > and then saying that by definition it is non- > dimensional. Do you realize that this is the same > insight by which we get to complex analysis? That is, > the derivation of the Euler Identity e^ix=cosx + isinx, > when x=pi, is in logarithmic terms ln(-1)=ipi. Engineers find it easier to work in the complex plane > because they are not concerned with counting, but > with measure. The advantage of the two-dimensional > analysis is that more room to calculate, in which > pi IS a unit of rotation rather than translation > (rotation through the complex plane)allows one to > get real results in desired continuous functions while > ignoring imaginary results. One would > need to know more about how you propose to make real > analysis simpler than complex analysis for measure > problems. What advantage? electrical technology complex currents,voltages and impedances, phase lead/lags of RLC circuits,servo transfer functions etc.), but mentioned Real Analysis only notionally. By the way, Hans Schwerdtfeger in Geometry of Complex > Numbers (Dover,1979)has a nice section on the analytic > geometry of circles. 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Website : http://www.shopbb.com MSN and E-mail: shopbb@hotmail.com Yahoo ID:mallinchina@yahoo.com.cn Michael === === === Subject: inverse substitution Suppose I have an expression and I substitute another expression in, is there a way to find the inverse of this? Specifically what I have is something like F(x(t),t)*x''(t) But I want to find what expression gave this expression when x(t) was substituted in for x. There is probably many ways to find this Parent expression but I'm looking for the most natural one(what ever that means). Any ideas? Jon === Subject: Re: inverse substitution > Suppose I have an expression and I substitute another expression in, is > there a way to find the inverse of this? Suppose I have two functions f and g. I then take the composition of the functions h(x) = f(g(x)). Let's first assume that we know f and know that f is invertible. I can recover g by calculating f^-1(h(x)) = f^-1(f(g(x))) = g(x). Or, if I know g and know that it is invertible, I can recover f by calculating h(g^-1(x)) = f(g(g^-1(x))) = f(x). > Specifically what I have is something like F(x(t),t)*x''(t) This will be your h(t) = f(x(t)). If you know that x(t) is invertible, you may be able to write h(x^-1(t)) = f(x(x^-1(t))) = f(t). Is this the parent expression you're looking for? === Subject: Re: Pi in non-euclidiean spaces Just to drive home the point that Pi is a constant ... a geometer living in a non-Euclidean space in which circles looked pretty much like the ones we see would likely be aware of the constant Pi. In such a space, the smaller the circumference, the more closely the ratio of circumference and diameter would be to Pi. So, Pi would show up as a limit. Come to think of it ... I guess the jury is still out on the shape of the space we live in, and yet we know about Pi. --charlie === Subject: Re: Pi in non-euclidiean spaces > So...we should treat the pi in G_uv = 8pi*T_uv as a variable that is a > function of the geometry? No! That 8 pi was determined via correspondence to Newtonian gravitation, and is the value here on earth (very weak fields). Equivalently, it is merely a conversion factor between units. You used units in which G=1, but one can use units with 8piG=1 and avoid the question altogether (well, I guess one could ask should we treat that 1 as a function of geometry? but that is rather silly). As I said before, pi is a symbol referring to a mathematical quantity defined as 3.14159.... The ratio of a circle's circumference to its diameter is different, and does indeed depend on the geometry. Tom Roberts === Subject: Re: Pi in non-euclidiean spaces >> So...we should treat the pi in G_uv = 8pi*T_uv as a variable that is a >> function of the geometry? No! That 8 pi was determined via correspondence to Newtonian >gravitation, and is the value here on earth (very weak fields). >Equivalently, it is merely a conversion factor between units. You used >units in which G=1, but one can use units with 8piG=1 and avoid the >question altogether (well, I guess one could ask should we treat that >1 as a function of geometry? but that is rather silly). As I said before, pi is a symbol referring to a mathematical quantity >defined as 3.14159.... The ratio of a circle's circumference to its >diameter is different, and does indeed depend on the geometry. Sarcasm, Tom. >Tom Roberts === Subject: Re: Pi in non-euclidiean spaces >> [If] you keep poking the center of the rubbery sheet it means the >> circumference will be SMALLER than the diameter. This IS an interesting concept! Especially given the theory of a > spherical universe (see my other post). The end result is that given > a spherical geometry of space, like your conical one, mathematical Pi > unlike the common assumption in science would NOT be the true value of > the ratio of a circumference to the diameter of a circle. pi is a symbol that refers to a defined mathematical constant equal to 3.14159.... pi is the ratio of a circle's circumference to its diameter ONLY in Euclidean geometry. There are LOTS of non-Euclidean geometries in which that ratio is not pi. Do not confuse these two. Tom Roberts === Subject: Re: Pi in non-euclidiean spaces > So you should really talk about the ratio, not pi. > No, the OP had it right and everyone here got it wrong. > Pi IS the ratio of the circumference of a circle to its diameter - > that's how the Greeks defined it, that's what they meant by it. This > is obvious as pi predates the discovery of the irrational numbers. > If you want to separate the number pi from pi then it's you who > needs to make the distinction, not the OP. > Pi takes on separate values in non-Euclidean geometries. Oh, well if the *Greeks* defined it that way, then there's nothing we > can do about it. The definition is fixed forever. You are free to define it anyway you like, just not impose your definitions over those who defined it first (unless qualified by some statement). > The Greeks also defined, for example, sqrt(2) as the length of the > diagonal of a unit square. Does the sqrt function therefore also change > in different geometries? Does sqrt(8) sometimes not equal 2*sqrt(2)? No, they must've defined the diagonal of a unit square as sqrt(2) because pythagorean theorem requires sqrt a priori. > --Mark === Subject: Re: Pi in non-euclidiean spaces > Observing the rays of WW2 is a time-machine. Observing the reflected > rays of WW2 (via stored video for example) is not a time-machine. I was about to argue with you, but I think you are right! I was > misled by the popular idea of a time-machine where one goes back and > changes the past etc. But obviously that idea is incorrect. The past > is fixed once it passes out of the present. Therefore, the best one > can do is to just OBSERVE the past, but cannot change it. Hence if > one were to accept the notion that the entire universe is a large > hypersphere there exists the possibility that the rays of any > particular time are still traveling on along the sphere. Hence > eventually all past events may circle around the spherical universe > and could be read as visions from the past. In that sense the entire > universe would be a time-machine. I believe Kip Thorne (don't quote me on that) discovered the (general) solutions to the Einstein-Hilbert field equations allowing causality- preserving time-travel as previously described. If you want to travel back into time and interact with the past you can use a wormhole or you could orbit an infinitely long cylinder or rotating blackhole - the (suitable) orbit not only returns you to the same point in space, but in time too. Quantum Physics offers you the possibility to teleport into parallel universes that look just like the past except with you there to observe it and interact with it. But, science is never wrong in the present only in the past. > The necessity for the universe being spherical has to do with the > edge problem. By the flatland analogy, one would have to ask what a > flatlander would find if he traveled as far as possible in his > universe? One would have to imagine some massive God-like clamps at > the edge of Flatland. Clearly such a solution is not very elegant. > A much more elegant possibility would be to make flatland actually > sphereland! If the Sphere were large enough, flatlanders would not be > able to detect the spherical geometry with their instruments (such as > sum of angles of a triangle). My calculation shows the universe to be a hypersphere about 500 > million light years in diameter. Without anything to back it up, what am I supposed to make of that? === Subject: Re: Pi in non-euclidiean spaces according to Greitzer and Coxeter (Copyr. 20cce), Menelaus actually proved the theorem for the spherical trigon, or Archimedes did that, as if the planar version was well-known, but no citation. note that tangents of a sphere map to greatcircles, and tangential segments to arcs of them. see trivial exercise to derive Heron's formula for area of trigon from Brahmagupta's theorem for the tetragon.... well, anyway, the formula for the tetragon (abcd) is symmetrical, A^2 = (s-a)(s-b)(s-c)(s-d), s is half of a+b+c+d; I'd've said, tetragon (ABCD), but the labels for the sides are not opposite the vertices. fortunately, the peer-review occurs after the publication, such as it is! --n~nerfman~n! http://larouchepub.com/pr/2007/070730conyers_impeach_dick.html 14 Italian Senators Call for Cheney Impeachment Aug. 1, 2007 (EIRNS)- The Lyndon LaRouche Political Action Committee (LPAC) issued the following release today. Fourteen members of the Italian Senate have signed a call to the Members of Congress to support Rep. Kucinich's House Resolution 333 for the Impeachment of Dick Cheney. http://larouchepub.com/pr/2007/070801italian_senators_call.html === Subject: Re: Poor teaching of econ <46cdb987.6203293@news.telus.net> <46d07264$0$31919$4c368faf@roadrunner.com> <46d0b87f.1988497@news.telus.net> <46d24e13$0$16512$4c368faf@roadrunner.com> <46d32764$0$15370$4c368faf@roadrunner.com> <46d46144.10216759@news.telus.net> <46d49edb$0$32547$4c368faf@roadrunner.com> <46d550ee$0$19568$4c368faf@roadrunner.com> <46d63d06$0$11085$4c368faf@roadrunner.com> <46d78cd5$0$28798$4c368faf@roadrunner.com> <46d84c3e$0$18966$4c368faf@roadrunner.com> On Aug 31, 1:13 pm, professorchaos > Research by psychologists has shown > that economics students are the most amoral on campus, even beating > out law students. >> Any cites to such studies? > Rob posted one. I'm sure Google can find others. Quite the contrary. Rob's post said nothing about amorality. It showed > that in the prisoner's dilemma that economic students were less likely to > cooperate. It said nothing about amorality and there is nothing I saw in > the paper that indicates amorality to me. You would have to think Except for the fact that the human biological faculty for morality as we know it very possibly evolved due to selection pressures based on iterated prisoners' dilemmas. > cartels, and pact of silence made by two murders trying to escape justice > is moral to read amorality into the findings that economic That's a base, ignorant description of the prisoner's dilemma. > students tend to cooperate less in the prisoner's dilemma. Did you > actaully read the paper? I know Roy did not because I can't remember a > single reference to law students. statement on morality. I will say it again. I am sure Roy, Rob, and you > may find the findings indicate amorality but that is purely opinion. You > have the right to your opinion and I can not prove you wrong but it is not > science. Yeah, sure, for someone who has no understanding of human morality and human nature. === Subject: Re: Poor teaching of econ How do you define it, observe it, measure > it? How do you scientifically distinguish > between moral, immoral, and amoral? Among these psychologists, by any chance, was > the redoubtable Alan Sokal? The only Alan Sokal I've heard of is a _physicist_ and left-wing debunker of post-modernist nonsense. >> Economists know very well they are lying for >> the purpose of deceiving journalists and voters, >> not other economists who are also in on the deceit. Which would explain, for instance, the > ramblings of the 'eminent economist' > ubersocialist Paul Krugman, in his NY Times > column, which is 99% horse? Krugman? A socialist? LOL! > I don't know... it's unclear whether he > deliberately lies, as you suggest, or he's > genuinely thick... my guess is both... LOL! Yeah, he was really thick when he correctly adduced the cause of the California energy crisis (viz, power generators cutting supply to create huge spikes in spot prices) or when he critiques Bush's Iraq disaster. Mark === Subject: Re: Poor teaching of econ > .... a real psychologist doing real research > would have to define amoral and be able to measure it. >> No, stupid, he wouldn't. I just had to see that in print again. > Mark > It is rather funny isn't it? Sounds like a line from a Pee Wee Herman movie. === Subject: Re: Poor teaching of econ >> How do you define it, observe it, measure >> it? How do you scientifically distinguish >> between moral, immoral, and amoral? By reference to accepted norms. > Whose accepted norms? Yours? Muslim norms? Jewish norms? Buddhist norms? You see the problem. I would still like an answer from you or Rob as why failure to cooperate in the prisoner's dilemma game is amoral. I would still like an answer to what behaviors you take offense to and why rather than everyone knows it is amoral. If you want to argue amoral then lets have a philosophical discussion. What behavior is amoral and why. Is lack of cooperation amoral? I have already given reasons why it is not always amoral eg. price fixing, cartels, cooperating to murder people because of their birth. So what behavior is amoral? Why is it amoral? Do you think because economics students cooperated less it means less willingness to help their fellow man? Do you think that giving less to charity means that people do less for others? As for charity many arguing that many charitable organizations put too much in the paychecks of administrators and too little into helping people. So would failure to donate money to the food bank but instead donating your time to distributing food to the homeless be amoral? The point I am trying to make here is you haven't defined what is amoral about the findings. You point to a set of findings and say it is amoral and everyone knows it. What part? Why is that amoral? > Economists know very well they are lying for > the purpose of deceiving journalists and voters, > not other economists who are also in on the deceit. >> Which would explain, for instance, the >> ramblings of the 'eminent economist' >> ubersocialist Paul Krugman, in his NY Times >> column, which is 99% horse? Krugman strikes me as one of the less dishonest ones. > Why because you agree with him more? Krugman is so tainted with political spin in his column he forgets about economics all together. Krugman has violated the unwritten standard of neutrality in research That being said he has done some great work as a professional economist but Paul Krugman the columnist rarely allows Paul Krugman the economist outstanding and professional he has an interest style of writing where he sets up a proposal then slams into the ground and rebuilds it him or what ever the Democrat leaning bosses over the NY times tell him to write and tries to use his title as authority. > -- Roy L === Subject: Re: Poor teaching of econ How do you define it, observe it, measure > it? How do you scientifically distinguish > between moral, immoral, and amoral? >> By reference to accepted norms. Whose accepted norms? Yours? Muslim norms? Jewish norms? Buddhist norms? > You see the problem. No, actually, there is no problem, because the claim that there's _no universal norms_ rooted in a bedrock, general, universal human nature is a crock. I would still like an answer from you or Rob as why failure to cooperate > in the prisoner's dilemma game is amoral. I would still like an answer to > what behaviors you take offense to and why rather than everyone knows it > is amoral. If you want to argue amoral then lets have a philosophical Certainly not everyone knows it's amoral. Everyone with a _good understanding_ of these things, however, does realize that the only explanation that anyone ever came up with for the biological evolution of human morality---in particular, why human are one of the few species marked by non-kin altruism---is that iterated prisoner's dilemmas. > discussion. What behavior is amoral and why. Is lack of cooperation > amoral? I have already given reasons why it is not always amoral eg. price > fixing, cartels, cooperating to murder people because of their birth. So what behavior is amoral? Why is it amoral? Do you think because > economics students cooperated less it means less willingness to help their > fellow man? Do you think that giving less to charity means that people do > less for others? Absolutely. spin in his column he forgets about economics all together. Sure. > Krugman has violated the unwritten standard of neutrality in research and LOL! The ole myth of pure positivism in economics. Uh huh. Sure. Economists came up with nonsense with real business cycle theory only because they're positive scientists, not (largely) a bunch of normative hacks working on behalf of the powerful. And how is it that Martin Feldstein, President of NBER, didn't violate this standard when he argued (incorrectly, as it turned out---but data never stops these handmaidens to the powerful, does it?) that Clinton's 1993 income tax hike would create a recession? > That being said he has done some great work as a professional economist > but Paul Krugman the columnist rarely allows Paul Krugman the economist > outstanding and professional he has an interest style of writing where he > sets up a proposal then slams into the ground and rebuilds it correctly. > ever the Democrat leaning bosses over the NY times tell him to write and > tries to use his title as authority. Uh huh. Sure. Krugman's point that power generators had an incentive to cut supply to drive spot electricity prices out the roof during the California energy crisis had no theory or evidence behind it, only partisan animus, and the reverse is true of whatever genius economists came up with the deregulatory program to begin with. LOL! > -- Roy L === Subject: Re: Poor teaching of econ >> That is the whole point. YOU CAN NOT SCIENTIFICALLY PROVE ONE GROUP IS >> MORE MORAL THAN ANOTHER. Oh but you certainly can, Bosco. If you remain within a sovereignty or > culture you can absolutely have a clear definition of most of what is > moral or not. Not a scientific one that can tested and proven. That is the point. Anyone can argue at any time that the same observation is moral when your culture said was amoral. You can not prove them wrong. A scientific study can not prove something is moral or amoral only the effect happens or does not. === Subject: Column Echelon Form If I transpose a matrix that is in row echelon form will the result always be a matrix that is in column echelon form. === Subject: Re: Column Echelon Form > If I transpose a matrix that is in row echelon form will the result > always be a matrix that is in column echelon form. > Matrix M in row-echelon form: 5 * * * * 0 3 * * * 0 0 0 9 * 0 0 0 0 4 M transpose: 5 0 0 0 * 3 0 0 * * 0 0 * * 9 0 * * * 4 I don't know what column echelon form is, but assuming that it implies a form of: a * * * 0 b * * 0 0 * * 0 0 c * 0 0 0 d The answer is 'no'. === Subject: Re: integral zeta > To tommy1729: >> If you insist that primitives are uniquely > determined >> simply by the >> concept of just set C=0, you are going to run > into >> some problems. >> For example, let f(x )= e^x - x. >> Let's integrate f(x) two different ways .... >> method (1) [standard Calc 1 approach]: >> int f(x) dx = e^x - x^2/2 + C >> Setting C=0 yields e^x - x^2/2 >> method (2) [using power series]: >> e^x = 1 + x + x^2/2 + x^3/6 + x^4/24 + ... >> f(x) = e^x - x = 1 + x^2/2 + x^3/6 + x^4/24 >> + > ... >> int f(x) dx = (x + x^3/6 + x^4/24 + x^5/120 + >> ... >> ... ) + C >> Setting C=0 yields x + x^3/6 + x^4/24 + x^5/120 >> + >> 0 + ... >> which equals e^x - x^2/2 - 1. >> So which one is the unique primitive? >> quasi >>intresting argument. :-) >>first note : i have already defined integral >> zeta > by a series. >>although perhaps there might be discussion about >> the > analytic continuation or riemann surface .... >>but anyways integral zeta is already defined... First, it _had not_ been defined at the point >> where > you started insulting people for not knowing what >> you > meant. Second, that series does not converge >> except > for Re(z) > 1, and it has many _different_ > continuations > to larger regions - hence that series does _not_ > specify where the zeroes in the plane are - where >> the > zeroes in the plane are depends on what particular > continuations we're talking about. Saying that >> there > might be discussion about analytic continuation > is progress, but it shows you still have no idea > what you're talking about - the question of > non-uniqueness of analytic continuation is crucial > here. in your argument, perhaps a good way to clarify >> is > this >>f(0) = INTEGRAL f(0)dx if possible by changing C. >>so f(x) = exp(x) - x >>f(0) = 1 = integral f(0) >>therefore the integral is method(1). >>another reason for avoiding series is the taylor > expansion of exp(x^2) at 0 ... >>you know what happens there dont you ? >>a bit off topic perhaps but can you give nice > examples of an integral which can take 3 or more > values ... >>just for fun :-) >>tommy1729 > ************************ David C. Ullrich >>ok , so you FINALLY accepted the series. >> Huh? What does it mean to accept a series? >>the continuation is arguable yes. >>i admit that. >>but there are zero's that are in common with any >> possible continuation ; critical ones. >>correct me if im wrong about that >>( would surprise me ; the wrong , not the correction >> ) >>( critical is not the same here as usual ; not >> referring to a line but the zero' s that are in >> common to all continuations ) >>i never claimed to be an expert on continuation >> though ... >> In fact you know nothing whatever about it, but that >> doesn't stop you from making statements about it. >> I'll give you a hint, so you can realize exactly >> how absurd you're being here: >> Hint: What you're claiming is this: If f is a >> function >> defined in a certain region and g is defined in the >> same region by g = f + 2 pi i then f and g have >> certain zeroes in common. your making this up david , i never said that. take for example the zeta function if we use the alternating form wich defines the zeta function from R= [0,inf] and call that A(z) >and the entire analytic continuation of zeta simply called zeta(z) then zeta(z) and A(z) have zero's in common the critical ones. and that is true, wheiter you want that or not. Certainly that's true. That has nothing to do with anything I said. The question was about the zeroes of the _integral_ of the zeta function, not about zeroes of the zeta function. Someday if you ever learn anything about complex analysis you'll realize what a fool you're making of yourself here. As has been explained many times, there's a big difference between the zeta function and the integral of the zeta function here: The zeta function does have a unique analytic continuation, while its integral does not. Various branches of the integral of zeta differ by multiples of 2 pi i. >>i might even learn something here about it ... >>although probably not from my critics ... >> Probably not. Before I answer your questions you >> should >> answer mine: >> (i) Exactly what was incorrect about the things >> I've said about the zeta function here? >> (ii) Exactly what was wrong with my demonstration >> that your set theory is inconsistent? >> Hint: The answer to both questions is There was >> nothing wrong with that, sorry. If you give >> any other answer to either question you will >> continue to be a laughingstock. bogus david , i already explained (i)... a functions needs it zero's. an analytic continuation can add zero's but it cant remove them. and there is no series without a zero in C*. a function needs it zero's even without analytic continuation. and thats what i have been telling here >and nobody ( who understands continuation ) disputes that apart from you ... Really? Then why haven't we seen anyone agree with you in this thread? Not that the question of whether anyone agrees with you really proves anything, but I'm just curious what makes you think that nobody disagrees with you. >> Assuming you give the correct answer to questions >> (i) and (ii) you should then answer a new question: i did yes so : >> (iii) So now, given that the things I've said were >> correct and you replied with a long string of >> insults i did not reply with a long string of insults , you confuse me with you projecting again. , do you _seriously_ expect me to simply >> try to help you learn some elementary complex >> analysis? you havent learned me anything , instead you made false claims that i was wrong ... >>anyways if you ( FINALLY ! ) accept my series , we >> might finally get some sensible posts in this topic >> ... >>continuation is debatable ... >>and as i said who knows someone might learn me >> something about it that i didnt know before ... >>on the other hand , that would be the first time >> here on the forum ... >>tommy1729 >> ************************ >> David C. Ullrich tommy1729 ************************ David C. Ullrich === Subject: Re: Surrogate factoring, periodic behavior >> Having completed better analysis on surrogate factoring I found the >> equations that explain a periodic behavior at least one person has >> noted in posts, where for a given k and n, if you find a prime factor >> p of your target T with that n, then you will find other solutions by >> adding multiples of p to n. >> Two of the equations determining that behavior are >> Cw = n + (k + 2xr_1*p_1)( k + 2xr_2*p_2) - ((k + 2xr_1*p_1)( k + >> 2xr_2*p_2) - 2k^2)/T >> What is C? >> w is defined below as a function of k,x,p_2,T >> What is p_1 ? p_2 ? r _1 ? >> where does x come from ? >> n and k are guesses Yes, I did leave a lot of variables unexplained. I'm analyzing when what I call surrogate factoring works to factor a > target T, where T = p_1*p_2 but that means you have to factor the target first into p_1, p_2 ??? where those are primes, so the p's above are those prime factors. Further equation definitions are r_1 = (p_1)^{-1} mod p_2 and r_2 = (p_2)^{-1} mod p_1. how is taking the inverse rational ? To understand where those come from you need to look over the detailed > page found at my Extreme Mathematics group: > But the main point of this thread is that you have two equations that > decide whether or not surrogate factoring will work against a target T > for a particular k and n. > and >> w = k + 2xr_2*p_2 mod T >> where if the second equation is true for a given n, then you will have >> a solution to the surrogate factoring equations at that n, but that is >> an only if. >> so it could or could not be a solution? If and only if BOTH equations can be satisfied--and all variables I > should mention are integers--can you have a solution and, if both are > satisfied then yes, surrogate factoring will give an answer. so one still guesses at a factor, but indirectly and has to choose more variables, sounds very ineffecient. So they are the decision relations. > There C doesn't matter but is just some non-zero integer, >> as w just needs to be any factor of the right side >> so C is any integer, and w is factored from where ? n + (k + 2xr_1*p_1)( k + 2xr_2*p_2) - ((k + 2xr_1*p_1)( k + 2xr_2*p_2) > - 2k^2)/T but this requires that you have factored your target first into p_1, etc. which is an integer because ((k + 2xr_1*p_1)( k + 2xr_2*p_2) - 2k^2) must have T as a factor. So you have like n+z, where z = (k + 2xr_1*p_1)( k + 2xr_2*p_2) - ((k + 2xr_1*p_1)( k + 2xr_2*p_2) > - 2k^2)/T what is z ? did it replace C ? to make it look simpler and you factor n+z and if for ANY of its > factors w you have that w = k + 2xr_2*p_2 mod T then you will have a surrogate factorization there. but factoring n + z can be as difficult as the target T in larger numbers, how do you propost to do that? >>--which is an >> integer I should note as the T must divide through--for which the >> second condition is met. >> what do you mean by devide through ? ((k + 2xr_1*p_1)( k + 2xr_2*p_2) - 2k^2) has T as a factor. >> That is the primary decision relation that determines if a surrogate >> factorization can work or not. >> which equation? I was thinking more of w = k + 2xr_2*p_2 mod T as THE decision relation, but of course, you need them both to know > what w is. > Remember the surrogate factorization involves factoring a target >> composite T by solving >> (x+k)^2 = y^2 + 2k^2 + nT >> where the primary question has been, how do you pick k and n? >> where did y come from? you guess n and k, but where does x come from? >> T is given to you as the number to factor. x and y are solutions found by factoring 2k^2 + nT. but one guesses k and n, therefore x and y are guesses, and what is the equation for relating x,y to k,n ? For instance, if you have 4f_1*f_2 = 2k^2 + nT What does f_1 mean ? then x = f_1 + f_2 - k, and y = f_1 - f_2. So you only need to know k, n and T, as everything else depends on > them. I like to pick f_1 and f_2 near integers so that 2*f_1 and 2*f_2 are > integers, so they are near in that they may be rationals that are > fractions with a denominator of 2. >> If they are picked correctly then some solution for x and y will also >> be a solution for >> x^2 = y^2 mod p >> where does p come from ? >> where p is a prime factor of T. p is a prime factor of the target composite T. > James Harris >> I can help further if you can provide some more information on the >> variables. >> Dr Simonies PhD Math I have done so and any help would be appreciated. Surrogate factoring works but the question has been, how do you pick k > and n? My detailed analysis is about answering that question and this thread > gives two key relations that decide when, and if, surrogate factoring > will non-trivially factor a target composite T, with a given k and n. > James Harris > === Subject: Re: Surrogate factoring, periodic behavior > Having completed better analysis on surrogate factoring I found the >> equations that explain a periodic behavior at least one person has >> noted in posts, where for a given k and n, if you find a prime factor >> p of your target T with that n, then you will find other solutions by >> adding multiples of p to n. >> Two of the equations determining that behavior are >> Cw = n + (k + 2xr_1*p_1)( k + 2xr_2*p_2) - ((k + 2xr_1*p_1)( k + >> 2xr_2*p_2) - 2k^2)/T >> What is C? >> w is defined below as a function of k,x,p_2,T >> What is p_1 ? p_2 ? r _1 ? >> where does x come from ? >> n and k are guesses > Yes, I did leave a lot of variables unexplained. > I'm analyzing when what I call surrogate factoring works to factor a > target T, where > T = p_1*p_2 but that means you have to factor the target first into p_1, p_2 ??? > No. In trying to figure out when surrogate factoring works and when it doesn't I'm analyzing assuming that the target T is a composite with two prime factor p_1 and p_2. The main question is how to pick k and n, so I'm trying to see how they are dependent on the prime factors of T. If it turned out that you cannot do a practical search for a working k and n without first knowing the underlying prime factors then the idea would be defunct. > where those are primes, so the p's above are those prime factors. > Further equation definitions are > r_1 = (p_1)^{-1} mod p_2 > and > r_2 = (p_2)^{-1} mod p_1. how is taking the inverse rational ? > That is the modular inverse, so it is an integer. If you don't know what a modular inverse is then you should do a web search on the topic or pick up a book on modular arithmetic, but I'll give you something quick here as I think it might help others who might be confused on this point. It is also called clock arithmetic, as for instance, taking an integer mod 5, you only have for positive integers, 0, 1, 2, 3 and 4 available. The modular inverse of 2 mod 5 is 3 because 2*3 = 6, which is 1 mod 5. So 2^{-1} mod 5 = 3. > To understand where those come from you need to look over the detailed > page found at my Extreme Mathematics group: > But the main point of this thread is that you have two equations that > decide whether or not surrogate factoring will work against a target T > for a particular k and n. >> and >> w = k + 2xr_2*p_2 mod T >> where if the second equation is true for a given n, then you will have >> a solution to the surrogate factoring equations at that n, but that is >> an only if. >> so it could or could not be a solution? > If and only if BOTH equations can be satisfied--and all variables I > should mention are integers--can you have a solution and, if both are > satisfied then yes, surrogate factoring will give an answer. so one still guesses at a factor, but indirectly and has to choose more > variables, sounds very ineffecient. > Sounds like doesn't interest me. The equations given ARE the decision equations for surrogate factoring, so it is irrelevant how they sound to any particular person as the mathematical reality is an absolute. Does that make sense? They ARE the decision equations whether we like them or not. There is no choice in the matter. > So they are the decision relations. >> There C doesn't matter but is just some non-zero integer, >> as w just needs to be any factor of the right side >> so C is any integer, and w is factored from where ? > n + (k + 2xr_1*p_1)( k + 2xr_2*p_2) - ((k + 2xr_1*p_1)( k + 2xr_2*p_2) > - 2k^2)/T but this requires that you have factored your target first into p_1, etc. > Yeah, if you want to actually check that relation, and see what the numbers are. But I'm analyzing what it means, as I work out the underlying theory that governs surrogate factoring. > which is an integer because > ((k + 2xr_1*p_1)( k + 2xr_2*p_2) - 2k^2) > must have T as a factor. > So you have like n+z, where > z = (k + 2xr_1*p_1)( k + 2xr_2*p_2) - ((k + 2xr_1*p_1)( k + 2xr_2*p_2) > - 2k^2)/T what is z ? did it replace C ? > I just added z on the fly. Sounds like you're way lost on this subject, so I'm going to stop here. James Harris === Subject: Re: Surrogate factoring, periodic behavior > Having completed better analysis on surrogate factoring I found the > equations that explain a periodic behavior at least one person has > noted in posts, where for a given k and n, if you find a prime > factor > p of your target T with that n, then you will find other solutions > by > adding multiples of p to n. > Two of the equations determining that behavior are > Cw = n + (k + 2xr_1*p_1)( k + 2xr_2*p_2) - ((k + 2xr_1*p_1)( k + > 2xr_2*p_2) - 2k^2)/T > What is C? > w is defined below as a function of k,x,p_2,T > What is p_1 ? p_2 ? r _1 ? > where does x come from ? > n and k are guesses >> Yes, I did leave a lot of variables unexplained. >> I'm analyzing when what I call surrogate factoring works to factor a >> target T, where >> T = p_1*p_2 >> but that means you have to factor the target first into p_1, p_2 ??? No. In trying to figure out when surrogate factoring works and when > it doesn't I'm analyzing assuming that the target T is a composite > with two prime factor p_1 and p_2. They are what you are solving for. The main question is how to pick k and n, so I'm trying to see how > they are dependent on the prime factors of T. you can back calculate it, given T and both primes, calculate the set or number of n,k pairs that work then determine if there is a relationship between n,k If it turned out that you cannot do a practical search for a working k > and n without first knowing the underlying prime factors then the idea > would be defunct. agreed > where those are primes, so the p's above are those prime factors. >> Further equation definitions are >> r_1 = (p_1)^{-1} mod p_2 >> and >> r_2 = (p_2)^{-1} mod p_1. >> how is taking the inverse rational ? That is the modular inverse, so it is an integer. If you don't know what a modular inverse is then you should do a web > search on the topic or pick up a book on modular arithmetic, but I'll > give you something quick here as I think it might help others who > might be confused on this point. It is also called clock arithmetic, as for instance, taking an integer > mod 5, you only have for positive integers, 0, 1, 2, 3 and 4 > available. The modular inverse of 2 mod 5 is 3 because 2*3 = 6, which is 1 mod 5. So 2^{-1} mod 5 = 3. by doing this you snip off part of the number, so you could be missing 50% of possable solutions, as it could be on either side. > To understand where those come from you need to look over the detailed >> page found at my Extreme Mathematics group: >> But the main point of this thread is that you have two equations that >> decide whether or not surrogate factoring will work against a target T >> for a particular k and n. > and > w = k + 2xr_2*p_2 mod T > where if the second equation is true for a given n, then you will > have > a solution to the surrogate factoring equations at that n, but that > is > an only if. > so it could or could not be a solution? >> If and only if BOTH equations can be satisfied--and all variables I >> should mention are integers--can you have a solution and, if both are >> satisfied then yes, surrogate factoring will give an answer. >> so one still guesses at a factor, but indirectly and has to choose more >> variables, sounds very ineffecient. Sounds like doesn't interest me. if you add more varables, you add more dimentions, complexity increases exponentially try a DO loop with x, then x,y then x,y,k then x,y,k,n where each goes between 1 and 10,000 how many calculation are there for each case? The equations given ARE the decision equations for surrogate > factoring, so it is irrelevant how they sound to any particular person > as the mathematical reality is an absolute. but the equations are not directly realted, only related by guessing n,k therfore cannot be absolute >Does that make sense? you have missed the point. They ARE the decision equations whether we like them or not. if you have to add more variables, more dimensions to make your equations work, it gets slower and slower, less efficient than a direct search. There is no choice in the matter. of course there is, one can always modify them, you do it all the time > So they are the decision relations. > There C doesn't matter but is just some non-zero integer, > as w just needs to be any factor of the right side > so C is any integer, and w is factored from where ? >> n + (k + 2xr_1*p_1)( k + 2xr_2*p_2) - ((k + 2xr_1*p_1)( k + 2xr_2*p_2) >> - 2k^2)/T >> but this requires that you have factored your target first into p_1, etc. Yeah, if you want to actually check that relation, and see what the > numbers are. but that means your equation above is meaningless unlessyou can derrive it from T = p_1*p_2 But I'm analyzing what it means, as I work out the underlying theory > that governs surrogate factoring. > which is an integer because >> ((k + 2xr_1*p_1)( k + 2xr_2*p_2) - 2k^2) >> must have T as a factor. >> So you have like n+z, where >> z = (k + 2xr_1*p_1)( k + 2xr_2*p_2) - ((k + 2xr_1*p_1)( k + 2xr_2*p_2) >> - 2k^2)/T >> what is z ? did it replace C ? I just added z on the fly. more complexity and confustion Sounds like you're way lost on this subject, so I'm going to stop > here. yea, seems like you have some more work to do on it for a while. Don't take it personally, but try derriving that equation directly from T = p_1*p_2 , I don't think you can. If you can then it will work, if you cannot then it will not work or you are not too good in math. > James Harris > === Subject: PDF to TeX? Can I take a pdf and turn it into TeX? i.e. I have a math paper in pdf format and I would like to see the TeX of it...I have WinEdt and was wondering if there's a command to do this? James === Subject: Re: PDF to TeX? > Can I take a pdf and turn it into TeX? i.e. I have a math paper in pdf format and I would like to see the TeX of it...I have WinEdt and was wondering if there's a command to do this? > James if you have a paper in pdf format, contact the author. chances are he or she used LaTeX (or whatever flavor of TeX), and then converted the DVI file to pdf. You don't create pdf files from the scratch (well, you can, in principle, using pdf pro, but noone really does that). === Subject: Re: PDF to TeX? > You don't create pdf files from the scratch (well, you can, in > principle, using pdf pro, but noone really does that). Real men write PostScript by hand. This is the God-honest truth. -- Aatu Koskensilta (aatu.koskensilta@xortec.fi) Wovon man nicht sprechen kann, daruber muss man schweigen - Ludwig Wittgenstein, Tractatus Logico-Philosophicus === Subject: Re: PDF to TeX? <87642u1fxv.fsf@huxley.huxley.fi> On Sep 1, 12:57 pm, Aatu Koskensilta occasionally I do write some embedded postscript, inside pstricks (in LaTeX). I always feel quite miserable after that, for at least a couple of days. === Subject: Re: PDF to TeX? > Can I take a pdf and turn it into TeX? i.e. I have a math paper > in pdf format and I would like to see the TeX of it...I have > WinEdt and was wondering if there's a command to do this? This question is about TeX and therefore you should have posted it at the comp.text.tex newsgroup, not here. But before posting it there, you should read the FAQ. 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I assume that every initial segment of the first column (including the complete first column) corresponds to (is in bijection with) a natural number. > If a bijection exists, > then appending (in the manner of Cantor) one element to each partner > of the bijection, then the bijection persists. > Obvious. As each partner in the bijection is the set of natural numbers. > That is incorrect. Each partner on the one side is a number of natural > numbers and on the other side each partner is a natural number. I > tried to express that by the variables {1,2,3,...,n} <--> n. Again, you lost me here. The partners where both the set of natural > numbers. The partners include {1,2,3,...}. That is not a natural number. > But this leads to omega > + 1 being in bijection with the set of natural numbers. > Not at all. Why do you think so? What you actually *do* when you append > a 1 to each row is changing each element of the set {1,2,3,...} to its > successor, so you change it to {2,3,4,...}. You do not add something to > the set the column is bijected with. > In fact I do not add something to the set the column is bijected witd, > but I do neither add something to the column. The initial segments on > the left hand side change from > 1, 11, 111, ..., 111... to > 11, 111, ..., 111..., 111...1. There is no last row, so where does the 111...1 come from? There are omega initial segments of the first *column*. Adding one 1 to every initial segment supplies 11, 111, ..., 111..., 111...1, the last one having ordinal omega + 1. > If they rermain in bijection with the sequences in the rows, then the > set {2, 3, 4, ...} has ordinal omega + 1. It is based on your assumption that there is a last row. There is none, > so now what? No. There is no last row. But every initial segment of the first column is said to have a partner in the set of sequences in the rows. > You said it already yourself: Starting with (1) M, the rows of M > remain (except the first line), while in (2) M we get omega + 1 > columns. Your points (3) an d (4) are uninteresting. > Still I maintain, why is that an inconsistency? Note that here we are > talking about indices! > We have a bijection between natural numbers and ordinal numbers of > sets of natural numbers. Oh. I did not know that. As far as I know, in this part we were talking > about matrices and of bijections between lines and columns. You switch > point of view from one to another without consistency. The natural numbers are represented by the sequences in the rows. The ordinal numbers are represented by the initial segments of the first column. > The set of second indexes of M' (which is containing a completed > infinity) cannot be the same as the set of second indexes of M (which > is not containing a completed infinity). > Note that M' violates your writing above that the rows represent natural > numbers written in unary notation! So either go one way or the other, do > not mix them. > M' is mere an example of a possible trijection. But it violates your view that the rows represent natural numbers. So > when you go to M' you should lose the view that each row represents a > natural number. Of course. I did never state the opposite. > But let us see. When defined as indices, your M looks like: > a_ij is defined for every j in N and every i <= j > and your M' looks like (I assume here replacing the first line, I > disremember which it was, but it makes no difference): > a_ij is defined for every j in N and whenever i = 1 or i <= j > where is the difference between sets of second indices? > So M and M' have the same set of second indices. > That means there is no difference in the set of numbers represented by > the sequences of 1's in the rows of M and M'. That means that there is no difference in the *size* of those sets of > numbers. > The set of natural > numbers has the same set of second indices as that set with an > infinite number added? I said *replaced*. But let's see whether I do understand you: > a natural number n has the set of second indices {1, 2, 3, ..., n} > a set of natural numbers {n1, ..., nk} has the set of second indices > U{l = 1, ..., k} {1, 2, 3, ..., l} = {1, 2, 3, ..., k}. The set of > natural numbers has as second indices {1, 2, 3, ...} = N. If we add > that infinite number 111..., we have that that number has the set > of indices {1, 2, 3, ...} = N. So, yes, the sets of second indices > is the same. Initially you were of opposite opinion. > I do not see why that should be a problem. If you add a sequence which is larger than any finite sequence, then you do not add any index? That hints to the fact that you add nothing. The infinite sequence does not provably existt, because there is no indication (no piece of circumstantial evidence) that you have done anything at all. > I must say, I am not really surprised. (The problem is that a set of > finite natural numbers cannot be complete, i.e., its ordinal number > cannot exist as a number which is in trichotomy with the elements of > the set and which is different from omega + 1.) Again the negation of the axiom of infinity. There is no problem once > you are able to distinguish between natural numbers and ordinal numbers. > Properly speaking, the first ordinal number is 0, not 1. So each > ordinal number is the order number of the ordered set of all preceding > ordinal numbers. And once you see that, there is no problem at all. Wrong. Repeat twice adding a 1 to all partners of the bijection. Then you see the problem again. === Subject: Re: Two results of set geometry <46d63c3d$0$19339$afc38c87@news.optusnet.com.au> But in order to shorten the discussion: It is impossible to > define or construct a bijection between the set of constructible reals > and N. Again you are guilty of abuse of terminology. Using common mathematical > terminology, it is possible to construct a bijection between N and the > response to your garbage. I did not see it. (By the way, do I have the point?) But if you can, then define it and take the diagonal number which then is defined too. > But you mean finitely defined. State so > when you mean that. And be aware that that notion holds a lot of > problems. > Perhaps there are problems in matheology but not in mathematics. Any number which can be defined, i.e., which can be addressed as an individuum, is a finitely definable number. (Becausen non-finite definitions are not definitions.) > It is sufficient when you show an *injection* between the paths and N. Every separation requires a node. There cannot be more separated paths than nodes. The bijection between nodes and natural numbers is obvious. So what do you not understand? === Subject: Re: Mathematics: art or science? <1917518.1188595023780.JavaMail.jakarta@nitrogen.mathforum.org > The mathematical canon of knowledge, on the other > hand, > never discards a theorem. > This theorem is the first to be discarded. (Such > claims belong to > matheology at most, they are foreign to sciences and > arts.) > If you think you have a case, support it with an > example. Did I write too much in one go? Here is a shorter version: One counter- > example is the theorem for which Legendre presented six strict > proofs: The parallel postulate is not an axiom but can be proven from > Euclid's other axioms. > Actually, using Playfair's Axiom and not Euclid's 5th. > In any case, the parallel postulate is still true in > Euclidean geometry--no theorem of Euclid has been > rescinded. One can invent any manner of systems of > axioms; the self consistent results deduced therefrom > are added to the canon of mathematical knowledge. I > hope I was clear in identifying the term knowledge > with theorem. Legendre's are as good as Euclid's. Legendre proved (or rather collected some proofs) of the theorem that the fifth postulate can be proven from the rest of Euclid's axioms. According to current mathematics this theorem is wrong. It has been abolished. This makes your theorem that mathematics only adds theorems also being wrong and to be abolished. It is simply a matter of taste and fashion what one wants to understand by a strict proof. It is rather ridiculous to believe that the current formalizations or the acceptance of actual infinity will be the end of the story. === Subject: Re: Mathematics: art or science? > On 31 Aug., 23:16, T.H. Ray The mathematical canon of knowledge, on the > other > hand, > never discards a theorem. >> This theorem is the first to be discarded. > (Such > claims belong to > matheology at most, they are foreign to > sciences and > arts.) > If you think you have a case, support it with an > example. > Did I write too much in one go? Here is a shorter > version: One counter- > example is the theorem for which Legendre presented > six strict > proofs: The parallel postulate is not an axiom but > can be proven from > Euclid's other axioms. > Actually, using Playfair's Axiom and not Euclid's > 5th. > In any case, the parallel postulate is still true > in > Euclidean geometry--no theorem of Euclid has been > rescinded. One can invent any manner of systems of > axioms; the self consistent results deduced > therefrom > are added to the canon of mathematical knowledge. > I > hope I was clear in identifying the term > knowledge > with theorem. Legendre's are as good as > Euclid's. Legendre proved (or rather collected some proofs) of > the theorem that > the fifth postulate can be proven from the rest of > Euclid's axioms. > According to current mathematics this theorem is > wrong. It has been > abolished. This makes your theorem that mathematics > only adds > theorems also being wrong and to be abolished. It is > simply a matter > of taste and fashion what one wants to understand by > a strict proof. > It is rather ridiculous to believe that the current > formalizations > or the acceptance of actual infinity will be the end > of the story. Your curiously nonstandard idea of what constitutes a theorem renders your argument impotent in the context of how mathematics is actually done. As I said, and which is not controversial, any consistent result from any self consistent system of axioms is true. Legendre's failure simply supports the longstanding fact that the fifth postulate is independent of the other postulates of Euclidean geometry. Success would have simply reduced the number of axioms, and not have substitutions for the Fifth Postulate, beginning with Playfair and extending to non-Euclidean geometry, leads So far as actual infinity goes, it is neither a theorem nor an axiom. So really, what is your point? If it is merely that mathematicians argue over proof theory from generation to generation, I only say, So what? The objective standards of proof have not changed. The judgment still has to be consistent with the axioms chosen, without contradiction. Tom === Subject: Re: Mathematics: art or science? > As I said, and which is not controversial, any consistent result > from any self consistent system of axioms is true. Really? So it is true that, say, Peano arithmetic is inconsistent? -- Aatu Koskensilta (aatu.koskensilta@xortec.fi) Wovon man nicht sprechen kann, daruber muss man schweigen - Ludwig Wittgenstein, Tractatus Logico-Philosophicus === Subject: Re: Mathematics: art or science? As I said, and which is not controversial, any > consistent result > from any self consistent system of axioms is true. Really? So it is true that, say, Peano arithmetic is > inconsistent? -- > Aatu Koskensilta (aatu.koskensilta@xortec.fi) Wovon man nicht sprechen kann, daruber muss man > schweigen > - Ludwig Wittgenstein, Tractatus > s Logico-Philosophicus As I said, and which is not controversial, any > consistent result > from any self consistent system of axioms is true. Really? So it is true that, say, Peano arithmetic is > inconsistent? -- > Aatu Koskensilta (aatu.koskensilta@xortec.fi) Wovon man nicht sprechen kann, daruber muss man > schweigen > - Ludwig Wittgenstein, Tractatus > s Logico-Philosophicus Why would you say that? The axioms of Peano (I prefer to say Dedekind-Peano) are certainly self- consistent. If I venture to try and interpret what you mean--that (as Godel proved) no system of axioms is strong enough to prove its own consistency--such does not obviate anything that I said. Tom === Subject: Re: Mathematics: art or science? > Why would you say that? The axioms of Peano (I > prefer to say Dedekind-Peano) are certainly self- > consistent. As I said, and which is not controversial, any consistent result from any self consistent system of axioms is true. The theory PA + PA is inconsistent is consistent. Does it follow that it is true that PA is inconsistent? -- Aatu Koskensilta (aatu.koskensilta@xortec.fi) Wovon man nicht sprechen kann, daruber muss man schweigen - Ludwig Wittgenstein, Tractatus Logico-Philosophicus === Subject: Re: Mathematics: art or science? Why would you say that? The axioms of Peano (I > prefer to say Dedekind-Peano) are certainly self- > consistent. > As I said, and which is not controversial, any > y consistent result from > any self consistent system of axioms is true. The theory PA + PA is inconsistent is consistent. > Does it follow > that it is true that PA is inconsistent? -- > Aatu Koskensilta (aatu.koskensilta@xortec.fi) Wovon man nicht sprechen kann, daruber muss man > schweigen > - Ludwig Wittgenstein, Tractatus > s Logico-Philosophicus You're not even reading my whole post. No point in trying to have a dialogue on those terms. Clever editing is no substitute for sound argument. But just to be a good sport, and I promise you this will be my last reply if you cut me short again: That a system of axioms is not strong enough to prove its own consistency (Godel) does not render untrue the results deduced from that system. So, to your question: The theory PA + 'PA is inconsistent' is consistent. Does it follow that it is true that PA is inconsistent? It follows, metamathematically. Which is why Godel's Theorem is sometimes characterized by truth is stronger than proof. Proofs of theorems, however, are not affected thereby. We don't know of a stronger system of axioms than Dedekind-Peano. Philosophy of mathematics is to mathematics as book review is to book. Tom === Subject: Re: Mathematics: art or science? <23698964.1188588087624.JavaMail.jakarta@nitrogen.mathforum.org > On Aug 31, 2:56 am, T.H. Ray That mathematics is a liberal art is not debatable. > And yet here we are debating it! Go figure. You may think you're debating. I am only reciting facts. These facts are only facts in the eye of their beholders. > After all, to some, even the claim of creationism vs. > evolution is a debate. Quite unfortunately for you, even evolution is not settled. You're just a dogmatic, T.H. Ray. Face it. It's hard to let uncertainity and doubt enter into your life, isn't it? Han de Bruijn === Subject: Re: Mathematics: art or science? > On 31 aug, 21:20, T.H. Ray On Aug 31, 2:56 am, T.H. Ray That mathematics is a liberal art is not > debatable. > And yet here we are debating it! Go figure. > You may think you're debating. I am only reciting > facts. These facts are only facts in the eye of their > beholders. After all, to some, even the claim of creationism > vs. > evolution is a debate. Quite unfortunately for you, even evolution is not > settled. You're just a dogmatic, T.H. Ray. Face it. It's hard > to let > uncertainity and doubt enter into your life, isn't > it? Han de Bruijn > Actually, not at all. I am uncertain about a great number of things. Of those things I have studied and reached a rational conclusion, however, I am certain. It would, after all, be irrational to say that I am uncertain of my certainty. I know for certain, for example, that the theory of common ancestry that explains the fact of evolution is a true scientific theory validated by overwhelmingly compelling results. I know for certain that even should the theory be falsified, the fact of evolution would remain. I know for certain that the art of mathematics shares the properties and characteristics of every other liberal art. If you think not--please provide a counterexample. You may be an irrational postmodernist who denies the very existence of facts and truth. For that discussion, I have no time at all. Tom === Subject: Re: Mathematics: art or science? <23698964.1188588087624.JavaMail.jakarta@nitrogen.mathf orum.org>, > On Aug 31, 2:56 am, T.H. Ray After all, to some, even the claim of creationism vs. > evolution is a debate. My first rule of debate is when there are two well defined positions, they are both wrong. -- Michael Press === Subject: Re: Mathematics: art or science? > <23698964.1188588087624.JavaMail.jakarta@nitrogen.mathf > orum.org>, On Aug 31, 2:56 am, T.H. Ray > That mathematics is a liberal art is not debatable. > And yet here we are debating it! Go figure. >> You may think you're debating. I am only reciting facts. >> After all, to some, even the claim of creationism vs. >> evolution is a debate. My first rule of debate is when there are two > well defined positions, they are both wrong. This thread reminds me of the curious question: Is the question as to whether some matter is a matter of fact (or else a matter of opinion) a matter of fact (or else a matter of opinion)? Does the answer depend on the matter in question? === Subject: Re: Mathematics: art or science? > <23698964.1188588087624.JavaMail.jakarta@nitrogen.math > f > orum.org>, On Aug 31, 2:56 am, T.H. Ray > That mathematics is a liberal art is not > debatable. > And yet here we are debating it! Go figure. >> You may think you're debating. I am only reciting > facts. >> After all, to some, even the claim of creationism > vs. >> evolution is a debate. My first rule of debate is when there are two > well defined positions, they are both wrong. This thread reminds me of the curious question: Is the question as to whether some matter is a matter > of fact (or else a > matter of opinion) > a matter of fact (or else a matter of opinion)? Does > the answer depend > on the matter in question? > Opinions and positions in a debate assume that some facts, characteristics, properties of the object are in question--and that rhetoric will reveal a finer- grained view of the object in order to--if not settle the question--at least to focus it more clearly. I am all in favor of Joseph Joubert's advice that It is better to debate a question without settling it, than to settle a question without debating it. There is no question, however, that mathematics is a liberal art. This is not a position or an opinion of mine. Mathematics shares all the properties and characteristics of every other liberal art, and only some of the properties and characteristics of physical science. I exclude the soft social sciences because the question of whether these belong to art or science IS debatable. It may even be debatable into which category computer science falls--and on that I would be willing to take a position and participate in debate. By every objective standard, though, mathematics is a liberal art. Tom === Subject: Re: Mathematics: art or science? <29848239.1188383860675.JavaMail.jakarta@nitrogen.mathf orum.org>, > The sciences are driven by a process of > falsification. That is, new results that some theory > cannot incorporate, guarantee a continual pruning of > the scientific canon of knowledge. For example, the > phlogiston theory of combustion was discarded when > results showed that combustion is merely rapid oxidation. > Another example is the abandonment of the ether theory of > wave propagation, in favor of general relativity. Phlogiston became an untenable theory when it became evident that it cannot be formalized as an exact differential. -- Michael Press === Subject: Re: Mathematics: art or science? > <29848239.1188383860675.JavaMail.jakarta@nitrogen.math > f > orum.org>, The sciences are driven by a process of > falsification. That is, new results that some > theory > cannot incorporate, guarantee a continual pruning > of > the scientific canon of knowledge. For example, > the > phlogiston theory of combustion was discarded when > results showed that combustion is merely rapid > oxidation. > Another example is the abandonment of the ether > theory of > wave propagation, in favor of general relativity. Phlogiston became an untenable theory when > it became evident that it cannot be formalized > as an exact differential. -- > Michael Press Yes. Its most obvious flaw is empirical. Metallic combustion (rusted iron, e.g.) was said to have positive properties, because it appeared to add mass. Negative phlogiston was said to inhabit fire, as it appeared to subtract mass from combustibles such as wood. That the positive and negative properties of phlogiston theory are contradictory did not seem to bother anyone until Lavoisier came along and set things right. You raise a critically important point. That is, the closed judgment that characterizes a mathematically complete theory is certain knowledge, when consistent with experimental results. The art of mathematical theory is primary to the scientifically objective explanation of observed results. Tom === Subject: Re: Finding shortest path into unweighted undirected graph mensanator, I'm interested in your neighboor algoritm of creating graphs? This is what I will need someday. By now path seems short with random (max 4) links between nodes - the longest path I've discovered is about 15-20 nodes in a set of 10000 nodes. Would you explain it a bit more in depth? This problem caught my eye instantly. I'll see your other data later. === Subject: Re: Finding shortest path into unweighted undirected graph Just a note: all tests published by me are run on Pentium 4 3GHz, 512MB memory. I'll try a Perl version of the same BFS script and see if there are differences. === Subject: JSH: What is surrogate factoring? Once more. IN arguing about research I call surrogate factoring, I bump into this weird thing where posters seem to be lost on what is actually going on, so I thought I'd start a thread informing, yet again, what surrogate factoring is. Years ago, while thinking about RSA encryption, I wondered to myself if instead of directly attacking a large number that you wanted to factor, you might instead factor some other number and in that way factor the target. I termed the concept: surrogate factoring. So, to repeat, years ago, as in about four years ago I think it was, I was just kind of wondering about factoring because I was thinking about RSA encryption, and I wondered if you might go after a large composite that was otherwise hard to factor, by instead factoring some other number. To me a good name for the concept was surrogate factoring, so it was called surrogate factoring. Now years later I have finally settled in my own mind that mathematically the concept reduces to considering x^2 = y^2 mod T and k = 2x mod T and equations that result from those two basic congruences, where T is the target, which took me about three years to figure out. With those two relations I found that my surrogate to factor is given by deriving (x+k)^2 = y^2 + 2k^2 + nT as then the surrogate S, is S = 2k^2 + nT and the big question is, how do you pick k and n? For those of you who wonder how it works from there, it's trivial algebra that if you let 4f_1*f_2 = 2k^2 + nT then x+y = 2f_1 - k and x-y = 2f_2 - k so once you factor the surrogate S, you just loop through solutions for x+y and x-y, by going through the various possible values for f_1 and f_2, and check the gcd with T. So, to recap, about four years ago I was wondering whether or not you could go after an RSA sized number to try and factor it by instead factoring another number. For years I tried various approaches and last year I boiled down the idea to two congruence relations, which lead through some simple algebra to a way to factor the target T, by factoring the surrogate S. So I had an idea, and after four years I have the math that implements the idea. That is the pure math aspect of it all where a person just pursues a mathematical problem for the hell of it, you might say, while, of course, I had practical reasons for picking the factoring problem. Now then, from the realm of mathematical curiosity to a world changing idea requires that surrogate factoring be a way to actually factor a large composite faster than the other known methods, which is where the arguing comes in with people who want to be certain that no one believes it can be, or who are getting on my case for declaring it is, and then not delivering by factoring some large number. But that is secondary, as it is a practical matter that can move stock markets and scare people because if surrogate factoring makes factoring easy, then a lot of industries around the world would be impacted. But what real mathematician cares about practical crap anyway? So there is the pure math of being curious about this way to factor. And to the extent that math people act more like business people who care about the practical side than math people who would care about the curiosity side, I point out a contradiction! Maybe they are not math people after all, eh? As there is the practical and political reality of possibly changing the world with a simple concept. Understand surrogate factoring now? Oh yeah, so recently I came up with a detailed analysis of when and why surrogate factoring works, which has some very complicated looking equations in it, so it is a massive puzzle. A MASSIVE puzzle. Some have done experiments where they claim that surrogate factoring works worse than random! And the world hangs in the balance on the answer, or maybe not, if it's just a crap idea, but for some reason, supposedly brilliant mathematicians have not settled the question so that the stock markets can rest easy. And your fate may depend on the answer, so the math world cannot keep looking, so Google and Yahoo! search results move accordingly, as if this concept is viable, then it ends the modern math world as it currently operates. But, on the other hand, it is also just a 'pure math' idea in a lot of ways. Two ways of looking at it, and entire economies can be destroyed if people do not do the right thing here, and guess wrong. James Harris === Subject: Re: JSH: What is surrogate factoring? Once more. > Years ago, while thinking about RSA encryption, I wondered to myself > if instead of directly attacking a large number that you wanted to > factor, you might instead factor some other number and in that way > factor the target. So factoring 1024 helps when factoring 234576345712341234789346857? I somehow doubt that... > With those two relations I found that my surrogate to factor is given > by deriving (x+k)^2 = y^2 + 2k^2 + nT as then the surrogate S, is S = 2k^2 + nT and the big question is, how do you pick k and n? Easy, pick k = 9 and n = 0. > For those of you who wonder how it works from there, it's trivial > algebra that if you let 4f_1*f_2 = 2k^2 + nT then x+y = 2f_1 - k and x-y = 2f_2 - k so once you factor the surrogate S, you just loop through solutions > for x+y and x-y, by going through the various possible values for f_1 > and f_2, and check the gcd with T. In my example, no factor of the surrogate is a factor of T (gcd is 1). I have just found a counterexample that breaks your method, so it doesn't work. > That is the pure math aspect of it all where a person just pursues a > mathematical problem for the hell of it, you might say, while, of > course, I had practical reasons for picking the factoring problem. You think it will make you a big shot if you solve it. But you haven't, so everything is still hypothetical > But what real mathematician cares about practical crap anyway? Anyone who wants to get funding for research? > Understand surrogate factoring now? No, it doesn't seem to work. > And the world hangs in the balance on the answer, or maybe not, if > it's just a crap idea, but for some reason, supposedly brilliant > mathematicians have not settled the question so that the stock markets > can rest easy. I would say that most of the world does not really care about factoring. Most high-class encryption uses more mathematically difficult methods. P=NP matters more (i.e., tractably cracking encryption methods). > Two ways of looking at it, and entire economies can be destroyed if > people do not do the right thing here, and guess wrong. If factoring is 'broken', the world will focus more on elliptic-curve cryptography and over more advanced methods. === Subject: Re: What is surrogate factoring? Once more. No, not once more. Again and again, failing every time. You can't factor anything. === Subject: Re: Sinc integrals > Let sinc(x) = sin(pi * x) / (pi * x) > I'm looking for a solution to: > integrate[-r, r] sinc(x) * sinc(x / r) dx > (This is a generalization of the Lanczos filter, and I am looking for a > normalization constant such that the filter function integrates to 1) > How do you arrive to it? According to Mathematica 5.2, your integral above equals ((1 + r)*Si(pi*(1 + r)) - (1 - r)*Si(pi*(1 - r)))/pi where Si denotes the sine integral, as discussed at > . In a later message, you said The first integral is clearly too tricky to evaluate in my program. But note that the link above gives information (such as series) which might allow you to adequately approximate your first integral in your program. Also, various approximation formulas could be given. For example, if r is large, then your integral is approximately 1 - 2 sin(pi r) / (pi^3 r^2) More accurate approximations for large r could given, if you're interested. David === Subject: Re: Sinc integrals <20070831173248.358$1z@newsreader.com> <20070901124320.670$69@newsreader.com > Let sinc(x) = sin(pi * x) / (pi * x) > I'm looking for a solution to: > integrate[-r, r] sinc(x) * sinc(x / r) dx > (This is a generalization of the Lanczos filter, and I am looking for a > normalization constant such that the filter function integrates to 1) > How do you arrive to it? > According to Mathematica 5.2, your integral above equals > ((1 + r)*Si(pi*(1 + r)) - (1 - r)*Si(pi*(1 - r)))/pi > where Si denotes the sine integral, as discussed at > . In a later message, you said The first integral is clearly too tricky to > evaluate in my program. But note that the link above gives information > (such as series) which might allow you to adequately approximate your first > integral in your program. Also, various approximation formulas could be given. For example, if r is > large, then your integral is approximately 1 - 2 sin(pi r) / (pi^3 r^2) More accurate approximations for large r could given, if you're interested. You could also precompute some values, store them in a table, and interpolate. === Subject: Re: Sinc integrals > You could use Mathematica to do the integral here: > I am also interested on how to derive the solution to: >integrate[-oo, oo] sinc(x) dx The easiest way, I think, is to use a bit of Laplace transform theory > as is done here: > -- Kalle Rutanen http://kaba.hilvi.org === <46cdb987.6203293@news.telus.net> <46d07264$0$31919$4c368faf@roadrunner.com> <46d0b87f.1988497@news.telus.net OK, I'll bite. Try biting this: This is _not_ a wager. It's an offer of a free market free trade: I'll pay $200 for the first letter from an outspoken market economist from Hoover, Heritage, Am. Enterprise, the Chicago School, Cato, von Mises, etc., who answers this question: Does free speech precede each and every free trade. Just get all this on hardcopy: 1. letterhead of GOP think tank 2. the question 3. an answer -- it can be _any_ text whatsoever. 4. the name of the outspoken market economist 5. the signature of the outspoken market economist Scan the letter and email it to BretCahill@aol.com with a mailing address. You'll get a M. O. for $200 in one week. Bret Cahill === (What is a octonion: http://en.wikipedia.org/wiki/Octonions) This relation is of course NOT general, but I think, that it will apply under certain conditions, which I will specify later: I define an 'S-octonion' like this: S = c*(t-to) + (x-x0)*j + (y-y0)*k + (z-z0)*l + i*(E-E0)/(h*c) + ij*(px-px0)/(h*c) + ik*(py-py0)/(h*c) + il*(pz-pz0)/(h*c) Where the constants h and c are Plancks constant and the speed of light. t, x, y, z, E, px, py, pz are just the usual 'stuff' from physics. So is m, simply a mass, and vx = (x-x0)/(t-t0) and so on with vy and vz. It's known that: E-E0 = 1/(t-t0) pn-pn0 = 1/(n-n0), n = x, y, z Finally I define gamma = gamma(vx, vy, vz) = 1/sqrt(1-(vx/c)^2-(vy/c)^2-(vz/c)^2) When we assume that: (1): E-E0 = gamma*m*c^2 pn-pn0 = gamma*m*vn The octonion can be written like this: S = c*(t-to) + (x-x0)*j + (y-y0)*k + (z-z0)*l + i*(gamma*m*c)/h + ij*gamma*m*vx/(h*c) + ik*gamma*m*vy/(h*c) + il*gamma*m*vz/(h*c) If I just call t-t0 for dt and so on with x, y and z: S = c*dt + dx*j + dy*k + dz*l + i*gamma*m*c/h + ij*gamma*m*vx/(h*c) + ik*gamma*m*vy/(h*c) + il*gamma*m*vz/(h*c) = c*dt + dx*j + dy*k + dz*l + i*gamma*m*c/h + ij*gamma*m*vx/(h*c) + ik*gamma*m*vy/(h*c) + il*gamma*m*vz/(h*c) What I would like to show, is that under the specified conditions (1), then S CAN be rewritten to be a multiplication of an ordinary complex number and a quaternion, like this S = (dt+i*gamma*m*c/h) * (c+j*vx+k*vy+l*vz) So S = R + i*P = R + i*h*K (This actually means, that we go down from 8 dimensions to only 6 dimensions: S -> (A+i*B)*(C+j*D+k*E+l*F) ) The R-quaternion is given by R = c*(t-to) + (x-x0)*j + (y-y0)*k + (z-z0)*l and the P-quaternion is given by P = h*gamma*m/c * (c+j*vx+k*vy+l*vz) = h * ((E-E0) + j*(px-px0) + k*(py-py0) + l*(pz-pz0))/c and K = ((E-E0) + j*(px-px0) + k*(py-py0) + l*(pz-pz0))/c Ok, a bit confusing (or a lot?), but I'm working on a new and more mathematical formulation of the problem, without all the 'stuff' from physics. I would just like to tell what I'm really thinking about first... Rgds, PC === Subject: JSH: Contradictory behavior, issue of math fraud I have pure math research that I say is important, while mathematicians have in various ways denied that, even when I had backup, albeit brief, from mathematicians who published some of my So I say my work is important, yet mathematicians say, in various ways, so that it can be a symbolic say, that it is not, which leaves me with a quandary, as it's my word against theirs. So I went to the factoring problem. If as I say mathematicians routinely lie about math, and I do come up with a viable factoring approach then it stands to reason that they would CONTINUE to lie, but other people might use the research anyway. But then again, I might simply be unable to come up with a viable approach to the factoring problem. However, if I come up with an approach then if it is NOT viable then mathematicians, supposedly brilliant, should be able to settle it, and simply proclaim me as just being the crackpot who has nothing--and prove it. Otherwise they leave the world at the wrong end of the whip where BILLIONS of dollars US, as in yes, BILLIONS of dollars could swing in hours on what is the truth, and that is the lever. Archimedes said, give me a lever long enough and a solid place to stand and I can move the world. We live in a world that has learned to dismiss ideas, and believes that genius can be controlled. The death of modern mathematics as a viable discipline so that science depends on the discoveries of past mathematicians is about attempts at controlling creativity squeezing the life out of the modern research world. But these people are about politics, so they work to convince, and if they get something wrong then entire economies can fall.j The entire planet of humanity can believe the world is flat and be wrong. Belief can be just a way for you to get yourself killed. And LOTS of people believing the same thing can be just a way for you to get yourselves all killed. What did the people of Hiroshima and Nagasaki believe? Did that matter? So for you there is the question on which your life savings can depend--the potential to lose everything you have worked your entire life for, literally, overnight, because some people you do not even know, lied. Lose everything. No retirement. No golden years looking back but working harder than ever knowing that everything you did before was lost because you trusted the wrong people. Or there is nothing here and I'm just a loudmouth on Usenet babbling nonsense, and you can trust those math people you don't even know to keep you safe, and keep your retirement safe, and keep your family safe. Or force mathematicians to settle the question: Does surrogate factoring work or not? If not, what is the mathematical analysis that proves it does not? Or sit and wait, and stay at the wrong end of the whip and see how long you get yanked around. James Harris === Subject: Re: JSH: Contradictory behavior, issue of math fraud > So I went to the factoring problem. And never solved it. > If as I say mathematicians routinely lie about math, and I do come up > with a viable factoring approach then it stands to reason that they > would CONTINUE to lie, but other people might use the research anyway. That is irrelevant, since you will never come up with a viable factoring approach faster than the known ones. > But then again, I might simply be unable to come up with a viable > approach to the factoring problem. You *will* be unable to come up with a viable approach to the factoring problem faster than the known ones. > Archimedes said, give me a lever long enough and a solid place to > stand and I can move the world. That same Archimedes created a method of computing pi and he actually did compute pi with great accuracy. Why don't you follow his lead and actually find a faster way of factoring numbers, instead of just babbling about it. > Or there is nothing here and I'm just a loudmouth on Usenet babbling > nonsense, Nice and accurate self-description, James! Jose Carlos Santos === Subject: Re: JSH: Contradictory behavior, issue of math fraud <5jtmbnF17r3tU1@mid.individual.net > So I went to the factoring problem. And never solved it. > Maybe not, but what is your proof? Or do you want people to trust you? And don't say if I had it I'd use it, as why? Why would I bother if I think the math world is corrupt? What might I do instead? > If as I say mathematicians routinely lie about math, and I do come up > with a viable factoring approach then it stands to reason that they > would CONTINUE to lie, but other people might use the research anyway. That is irrelevant, since you will never come up with a viable factoring > approach faster than the known ones. > And you have a crystal ball? Where is the mathematical analysis? You're sounding no better than a fortuneteller, got anything else? If my retirement dollars depend on the answer, what are you giving me so that I can feel safe? > But then again, I might simply be unable to come up with a viable > approach to the factoring problem. You *will* be unable to come up with a viable approach to the factoring > problem faster than the known ones. > And if I do, will you personally vouch for the money lost for those who lose their savings? Are you ready to say here and now that you will give every dollar you own to make up as best you can for those who lose money, if you are wrong? > Archimedes said, give me a lever long enough and a solid place to > stand and I can move the world. That same Archimedes created a method of computing pi and he actually > did compute pi with great accuracy. Why don't you follow his lead and > actually find a faster way of factoring numbers, instead of just > babbling about it. > How do you know that I'm not just setting the stage to do just that? It is a long weekend you know, here in the US. Do you want to stake your entire worth on the answer? Put up everything you own against the question. Promise to give every penny you have to those who lose money if you're wrong. > Or there is nothing here and I'm just a loudmouth on Usenet babbling > nonsense, Nice and accurate self-description, James! > Jose Carlos Santos If so, then there is nothing to stop you from pledging every dime you own to those who lose money if somehow, someway you got it wrong. James Harris === Subject: Re: JSH: Contradictory behavior, issue of math fraud <5jtmbnF17r3tU1@mid.individual.net > So I went to the factoring problem. > And never solved it. Maybe not, but what is your proof? I believe the burden of proof is on you. > Or do you want people to trust you? And don't say if I had it I'd use it, as why? Why would I bother if I think the math world is corrupt? Good point, but then why do you bother to post here in the first place? --- J K Haugland http://home.no.net/zamunda === Subject: Re: JSH: Contradictory behavior, issue of math fraud <5jtmbnF17r3tU1@mid.individual.net > So I went to the factoring problem. > And never solved it. > Maybe not, but what is your proof? I believe the burden of proof is on you. Not necessarily if you believe that a concept can be of interest in and of itself to people who are supposedly experts in a field. Surrogate factoring is at its heart just an idea, a what if? MY position is that modern math people routinely lie and don't actually care about math except as a tool to use to get what they want--employment for acting like mathematicians. If I prove overnight that they lie through factoring then most can claim ignorance. > Or do you want people to trust you? > And don't say if I had it I'd use it, as why? > Why would I bother if I think the math world is corrupt? Good point, but then why do you bother to post here in the first > place? --- > J K Hauglandhttp://home.no.net/zamunda Because by posting here I can present ideas to the math community worldwide. If later those ideas are shown to be viable and there is no possible way a math community that cares about mathematical research for real and has natural human curiosity could have ignored them, then I make my point that most math people today are con artists. So you see, I have to put the information in a place where math people can get to it. And I have to talk enough around it about basic human curiosity and evidence of truly valuing a subject to take away what is often called plausible deniability. That is, I have to remove all other possibilities EXCEPT math people being con artists. And that takes time and some careful maneuvering as well as multiple actions to ensure that mathematicians had every chance to do the right thing. Challenging Santos to commit every dime is part of that action, as to con artists, what really is more important than money? I challenge you as well to pledge every penny you own to anyone worldwide who loses money if surrogate factoring turns out to be what your community is saying it is not. By pledging what you own to them you can give them the knowledge that you have determined to the best of your ability that there is nothing to what I say, and are willing to accept consequences if you are wrong. As being an expert gives responsibility and part of responsibility is accepting the consequence of your actions. So it's gut check time. Put up all your money--after all, what does it mean to you anyway if math is what you care about--as a gift to anyone who loses money if you are wrong, as your personal compensation for their loss. James Harris === Subject: Re: JSH: Contradictory behavior, issue of math fraud > So I went to the factoring problem. >> And never solved it. Maybe not, but what is your proof? I gave a proof in another post, but my newsreader seems to have fallen apart in the last ten minutes, so it might not exist. Select k=9, n=0 for T = 23457634568903458768912756896234625612456734523. The largest factor your method will find is 1. That violates no constraint of your method. Therefore your method as stated doesn't work. > If as I say mathematicians routinely lie about math, and I do come up > with a viable factoring approach then it stands to reason that they > would CONTINUE to lie, but other people might use the research anyway. >> That is irrelevant, since you will never come up with a viable factoring >> approach faster than the known ones. And you have a crystal ball? No, but your past antics indicate that you do not have sufficient mathematical ability beyond anyone else working on the problem. I can say P = NP, and give some rationale, but I can never *prove* it because I do not have the sufficient mathematical abilities. > If my retirement dollars depend on the answer, what are you giving me > so that I can feel safe? A naive Bayesian classifier trained on your previous performance as data says you won't. > But then again, I might simply be unable to come up with a viable > approach to the factoring problem. >> You *will* be unable to come up with a viable approach to the factoring >> problem faster than the known ones. And if I do, will you personally vouch for the money lost for those > who lose their savings? *Who* will lose their savings? Almost all serious cryptography has passed up factoring and started using stuff like elliptic-curve. Many of the secure algorithms most people use have been shown to be breakable, but we still use them. Best examples: RC4 and MD5. === Subject: Re: JSH: Contradictory behavior, issue of math fraud <5jtmbnF17r3tU1@mid.individual.net> So I went to the factoring problem. >> And never solved it. > Maybe not, but what is your proof? I gave a proof in another post, but my newsreader seems to have fallen > apart in the last ten minutes, so it might not exist. Select k=9, n=0 for T = 23457634568903458768912756896234625612456734523. > The largest factor your method will find is 1. That violates no > constraint of your method. Therefore your method as stated doesn't work. > If as I say mathematicians routinely lie about math, and I do come up > with a viable factoring approach then it stands to reason that they > would CONTINUE to lie, but other people might use the research anyway. >> That is irrelevant, since you will never come up with a viable factoring >> approach faster than the known ones. > And you have a crystal ball? No, but your past antics indicate that you do not have sufficient > mathematical ability beyond anyone else working on the problem. I can > say P = NP, and give some rationale, but I can never *prove* it because > I do not have the sufficient mathematical abilities. > If my retirement dollars depend on the answer, what are you giving me > so that I can feel safe? A naive Bayesian classifier trained on your previous performance as data > says you won't. > But then again, I might simply be unable to come up with a viable > approach to the factoring problem. >> You *will* be unable to come up with a viable approach to the factoring >> problem faster than the known ones. > And if I do, will you personally vouch for the money lost for those > who lose their savings? *Who* will lose their savings? Almost all serious cryptography has > passed up factoring and started using stuff like elliptic-curve. Many of > the secure algorithms most people use have been shown to be breakable, > but we still use them. Best examples: RC4 and MD5. Fine. So Santos can pledge his entire life savings, every penny he owns to anyone who might lose money if he and you are wrong. Based on your analysis he is perfectly safe, right? So he should do the pledge, and anyone else of you I ask should do it as well. I want a pledge of every dime you have, so that you put enough out there that people can know where you stand, without question. James Harris === Subject: Advanced Management Accounting Solutions Manual Does anyone have a solutions manual for Kaplan, R. S., & Atkinson, A. A. (1998). Advanced Management Accounting (3rd edition). Upper Saddle River, New Jersey: Prentice Hall, Inc. ISBN 0-13-262288-2 Please let me know asap === Subject: Re: math is a physical process >> Math is the software running within the hardware of Reality. I'd like to make this quote immortal! Han de Bruijn Assholes. Go get yourselves girlfriends. Sorry blabblers like the two of you who post to alt.philosophy should do what another such character did, here watch'm: http://www.shabnameh.org/images/khabar2m.jpg But the good thing for you is that you don't have to go to Africa to get a thing like that, do you. -- chAghu dasteye khodesho nemiboreh. === Subject: Re: math is a physical process <3udlc3d29ickupj87kkddln5gj4fv7mn6t@4ax.com> <5dbb7$46cad8ce$82a1e228$32721@news1.tudelft.nl> <2limc3983vfpimvmapj1co5kknkqvgbllk@4ax.com> if not you will learn it from crackpot Porat .. Indeed. Porat is a really good demonstration of both. - M === Subject: Re: Many Solutions Manuals and Ebooks in Electronic (PDF)Format! Can you please send me the solution for Solution Manual for Electrical Circuits (7/e) by James W. Nilsson, and Susan A. Riedel,Prentice Hall at soulz9@gmail.com === Subject: Many Solutions Manuals and Ebooks in Electronic (PDF)Format! Many Solutions Manuals and Ebooks in Electronic (PDF)Format! PS: These are part of my solutions, if the solution you want isnOt on the list, do not give up, just contact with me: My email is solutionpay(at)hotmail.com( please replace the (at) with @ ) NOTE: if the solutions you want is on the list renewed,please mention in your email,thank you! Solution manual for the list:.81B I will reply with your Email within 12 hours!! accompany Boyce Elementary Differential Equations and Boundary Value Problems by Willian E.Boyce accompany Fundamentals of Fluid Mechanics, 5th by By Bruce R. Munson, Donald, Theodore H. Okiishi, advanced engineering mathematics (8/e) by ERWIN KREYSZIG advanced engineering mathematics.81i9/e.81j by ERWIN KREYSZIG advanced macroeconomics Analytical Mechanics (7/e) By Grant R. Fowles, George L. Cassiday applied mathematics and modelling forchemical engineers(8/e) Applied Strength of Materials (4th Edition) by Robert MoTT C How to Program, 3RD Edition 2000 By Harvey M. Deitel Calculus I, II, Transidentals 10e BY George B. Thomas Calculus with Analytic Geometry Calculus, 4th edition by James Stewart Classical Electrodynamics 2Ed by Jackson Computational Techniques for Fluid Dynamics By Karkenahalli Srinivas, Clive A. J. Fletcher Computer Organization and Design: The Hardware/Software Interface93/e) by David A. Patterson, John L. Hennessy Design of Analog CMOS Integrated Circuit by B. Razavi Digital and Analog Communication Systems by LEON W. COUCH Digital and Analog Communication Systems .81C5th, by Leon W. Couch, Leon W., II Couch . DISCRETE-TIME SIGNAL PROCESSING/2e by Oppenheim.81ASchafer Econometric Analysis (6/e) by willian H.GREENE Econometric Analysis ,5th Edition, by William H. Greene Electric Machinery Fundamentals 4/e By Stephen J. Chapman Electric Machinery Fundamentals, 4/e , by S. J. Chapman. Electrical Circuits (7/e) by James W. Nilsson, and Susan A. Elementary Differential Equations and Boundary Value Problems , 8th.81Cby William E. Boyce (Author), Richard C Elementary Principles of Chemical Processes Elements of Chemical Reaction Engineering By H Fogler Elements of Chemical Reaction Engineering (3rd)by H.Scott Fogler Elements of engineering electromagnetics (6/e) by N.N.RAO Engineering electromagnetics (6/e) by HAYT Engineering electromagnetics (7/e) by HAYT Engineering Fluid Mechanics, 7th Edition By Clayton T. Crowe, Donald F. Elger, John A. Roberson Engineering Mathematics, 4th Edition ,by John Bird Engineering Mechanics - Dynamics (11th ) by R.C.HIBBELER Engineering Mechanics - Statics (11th ) by R.C.HIBBELER Engineering Mechanics - Statics and Dynamics,11th, by Russell C Hibbeler. Engineering Mechanics, Dynamics 5th By J. L. Meriam, L. G. Kraige Engineering Mechanics: Statics By R.C. Hibbeler Engineering Mechanics: Statics ,10th ,by R.C.Hibbeler, field and wave electromagnetics (2/e) by David Cheng Fundamentals of Logic Design 5Ed by CharlesRoth Fundamentals of Chemical Reaction Engineering By Mark E. E. Davis, Robert J. J. Davis Fundamentals of Organic Chemistry, 5E Fundamentals of Thermodynamics 6ed By Richard E. Sonntag Introduction to Electrodynamics(3/e) by David J. Griffiths Introduction to Heat Transfer 4th Edition By Frank P. Incropera, David Introduction to Solid State Physics (8 ED) by Charles.Kittel__ MATHEMATICAL ANALYSIS (2/e) (chapter1-9) by Tom M. Apostol Mechanical Engineering Design By Joseph Shigley, Charles Mischke, Mechanics of Materials 96/E) by R.C.Hibbeler Microeconomic Analysis, 3rd Edition, by Hal R. Varian Microeconomic Theory by Andreu Mas-Colell, Michael D. Whinston, Modern Control Engineering/ 4E by K.OGATA Modern Digital and Analog Communication Systems (3/e) Modern Control Engineering Ogata 4E Organic Chemistry, 2th by Hornback Physical Chemistry (7/e) by Peter Atkins and Julio de Paula Physical Chemistry (7th) by P.W.Atkins Physics for Scientists and Engineers by Serway'& Jewett Probability & Statistics for Engineers & Scientists, 8th by Sharon Myers , Keying Ye, Walpole Probability and Statistics for Engineering and the Sciences 7/e JAY L.DEVORE Probability, Random Variables and Stochastic Processes,3rd, by Athanasios Papoulis Signals and Systems (2nd Edition) Thermodynamics: An Engineering Approach,5th Ed. by Cengel Thermodynamics: An Engineering Approach,6th Ed. by Cengel Thomas' Calculus (11th Edition) by George B Thomas University Physics with Modern Physics By Hugh D. Young Vector Mechanics for Engineers: Statics, 7th By Ferdinand P. Beer Vector Mechanics for Engineers: Dynamics, 7th By Ferdinand P. Beer Visual C++ How to Program, (3rd Edition) ,by Harvey & Paul Deitel & Associates Zill's a First Course in Differential Equations with Modeling Applicants 7/e http://pdfsolution.spaces.live.com === Subject: Solutions Guides Does anyone have solutions manuals for the following books: Byrd, C., & Chen, I. (2007). Canadian Tax Principles. Toronto: Pearson Education (2006-2007 ed.). ISBN-10: 0132325314; ISBN-13: 978013235318 (4th ed.). Toronto: Prentice Hall. Romney, M., & Steinbart, P. (2006). Accounting information systems (10th Ed.). Upper Saddle River, NJ: Pearson Education, Inc. ISBN 0-13-147591-6 === Subject: Re: Solutions Guides > Does anyone have solutions manuals for the following books: > Byrd, C., & Chen, I. (2007). Canadian Tax Principles. Toronto: Pearson > Education (2006-2007 ed.). > ISBN-10: 0132325314; ISBN-13: 978013235318 (4th ed.). Toronto: Prentice Hall. Romney, M., & Steinbart, P. (2006). Accounting information systems > (10th Ed.). Upper Saddle River, NJ: Pearson Education, Inc. ISBN > 0-13-147591-6 What a stupid question. Obviously Pearson Education has the 1st and 3rd ones, and Prentice Hall has the second one. Duh. B. -- Cheerfully resisting change since 1959. === Subject: Re: best braking technique as one approaches red light <20545240.1188582154477.JavaMail.jakarta@nitrogen.mathforum.org> |the assumption is fixed red length with some probability |p(t)dt to change in dt. |It looks like no one can actually answer this so it looks like I must |give up on the math forum as a source of answer. I hope you'll excuse my pointing out that you've jumped to conclusions here about the abilities of the people you're dealing with, more than one of whom know plenty about how to solve problems of this kind. You seem to have an odd idea of how to go about getting answers to questions on usenet. A lot of people seem to be used to the idea that the person asking the question has a minimal role. They take a consumerist attitude toward the exchange of knowledge. They think that the idea is, you pose your question to some expert, they give you a comprehensive answer to it tailored to your level of preparation, which you don't need to mention (for free, too, isn't that nice?) and then you're done. Or else they don't know how and you leave. Unless the problem is fairly cut-and-dried, this tends not to be the best way to do it. More often questions are to some extent open-ended, like this one, and we'll start with some partial answer, and then refine it with feedback from the person asking the question. For example, sometimes, at least, the kind of answer I gave is what the person actually wanted. There are also various ways to refine the answer I gave you. Someone might want to have it further explained how to maximize P(t)/t. Because of your mention of having tried some techniques, I figured you probably knew some calculus already, and would be able to figure out that maximizing P(t)/t is equivalent to finding a solution to tp(t) = P(t). You might well already know a numerical method for computing a root of that. And, surprise, that's about as much of an answer as it's possible to get. In general, there's no closed-form expression for t. This is very commonplace. If p(t) is a Gaussian, for example, P(t) is a special function, and you might as well compute t numerically. It hardly seemed worth the trouble to present you with a tutorial on this kind of thing when it seemed fairly likely from your initial message that you would know all that already. Someone might want an answer that dealt also with cases where p(t) isn't monotone increasing and then decreasing (unlike the Gaussian which you gave as an example). If you really understand the answer I gave, then you can apply the same reasoning to cases where p is piecewise monotone, and see that the solution has to be a stair-step function, where the discontinuous drops in speed come during periods where p(t) is non-increasing. To get a specific answer requires finding where to put the boundaries between these intervals, and what speeds to assume during them. Again, expecting a general-purpose closed-form solution is unrealistic. There are iterative methods for computing the solution, but it's just going to be a solution of a fairly arbitrary set of equations again. Usually some interesting approximations and special cases are possible. There are alternative assumptions one could make about how the braking works. There was the suggestion that perhaps you wanted to maximize the expected kinetic energy when the light changes instead of the expected momentum. In any case, you didn't bother to say what further you wanted, which is why you didn't get more. Keith Ramsay