mm-4609 === Subject: Re: area >area S ; enclosure >C1;125 + 60*x^2 + 512*x^3 + 30*x^4 + 540*x^6 - 243*x^8 + 60*y^2 - 1536*x*y^2 + > 60*x^2*y^2 + 1620*x^4*y^2 - 972*x^6*y^2 + 30*y^4 + 1620*x^2*y^4 - > 1458*x^4*y^4 + 540*y^6 - 972*x^2*y^6 - 243*y^8 == 0, >C2;x^2 + y^2 = 1 S=_________________________. Hint: Set up the integral for the area in polar coordinates. --Lynn === Subject: Re: Operator theory My questions are really two: 1' x : R(x), min x : R(x), ExRx, AxRx are generalized in operator > theory. I don't understand your notation at all. Perhaps you could explain more. Please, is there a standard introductory text to this field? (I looked > up the net, but it turned up references to functional analysis.) I > mean operator theory as mentioned by Tarski in his Introduction. 2' What is the standard mathematical cirriculum? Taught at, say, MIT. > I would love to see the bibliographical references, if posssible, too. Tom === Subject: Re: No McCain/Obama apologies -day 12 (taped racism) >Numerous claims are all over the internet about Obama Anti-Jewish >campaign stances. Can you link to just one that agrees with you that the term jewry is > a racial slur? æWhether Obama is an anti-semite is a completely > different argument than the one about jewry. Jewry. Jewry. Jewry. Jewry. Jewry. æ æ æ æ ... life is but a dream. Obama Camp Chairman McPeak said, American Jewry has some influence, just like -- blogs.abcnews.com/politicalpunch/2008/03/obama-mcpeak-an.html (some dream) === Subject: Re: No McCain/Obama apologies -day 12 (taped racism) > gbsn9kdgd9e@4ax.com: >Numerous claims are all over the internet about Obama Anti-Jewish >campaign stances. > Can you link to just one that agrees with you that the term jewry > is a racial slur? æWhether Obama is an anti-semite is a completely > different argument than the one about jewry. > Jewry. Jewry. Jewry. Jewry. Jewry. > æ æ æ æ ... life is but a dream. Obama Camp Chairman McPeak said, American Jewry has some influence, > just like > -- blogs.abcnews.com/politicalpunch/2008/03/obama-mcpeak-an.html (some dream) > Row your boat, troll. Get it now. My bad. McPeak is quoted using the word Jewry. Why aren't you claiming that the RJC is anti-semitic? Their rep used the word as well. Hint: It isn't a slur. === Subject: How does one treat zero values in time series? Is there an issue if a few values are sequential or if they start the series? Is there a limit to the number? === Subject: Re: How does one treat zero values in time series? > Is there an issue if a few values are sequential or if they start > the series? Is there a limit to the number? I have no idea what you're trying to ask. Perhaps an example might help? - Tim === Subject: Difference equations posting-account=O8fKzgoAAAAh8QHGtIiFpPapSw9sTgQ1 Gecko/20080311 Dealio Toolbar 3.2 Firefox/2.0.0.13,gzip(gfe),gzip(gfe) I have a question: suppose I have the difference equation x(k+1)=0.5[x^3(k) +x(k) ] where ^ is to the power. k=0,1,2,3..... then I can show easily that the equation has 3 equilibrium points at x*=0,-1 and +1 Only the one at x=0 is stable. What does equilibrium point mean in this context? I simulated this and found it is stable if -1 I have a question: suppose I have the difference equation x(k+1)=0.5[x^3(k) +x(k) ] where ^ is to the power. k=0,1,2,3..... then I can show easily that the equation has 3 equilibrium points at > x*=0,-1 and +1 Only the one at x=0 is stable. What does equilibrium point mean in > this context? I simulated this and found it is stable if -1 where x0 is the initial condition of x ie x(0). Should x(0) be less > than the equilibrium points for stability in general? K. No. Since 0 is the stable equilibrium point, x(k) should converge to 0 if x(0) is near 0. But since 1 is NOT stable, even if x(0) is very close to 1, you cannot expect x(k) to converge to 1. Similar for -1. -- G. A. Edgar http://www.math.ohio-state.edu/~edgar/ === Subject: Re: Difference equations <110420081650026549%edgar@math.ohio-state.edu.invalid > I have a question: > suppose I have the difference equation > x(k+1)=0.5[x^3(k) +x(k) ] where ^ is to the power. k=0,1,2,3..... > then I can show easily that the equation has 3 equilibrium points at > x*=0,-1 and +1 > Only the one at x=0 is stable. What does equilibrium point mean in > this context? I simulated this and found it is stable if -1 where x0 is the initial condition of x ie x(0). Should x(0) be less > than the equilibrium points for stability in general? > K. No. Since 0 is the stable equilibrium point, x(k) should converge to 0 > if x(0) is near 0. But since 1 is NOT stable, even if x(0) is very > close to 1, you cannot expect x(k) to converge to 1. Similar for -1. -- > G. A. Edgar http://www.math.ohio-state.edu/~edgar/ > Perhaps what kronecker means is this. Suppose f is a continuous function on the real line with an attracting fixed point p. The immediate basin of attraction of p is the largest open interval (a,b) containing p in which all points are attracted to p. Assuming a and b are finite, the boundary {a,b} of the immediate basin of attraction is mapped into itself by p. Thus there are four possibilities: (1) f(a) = a, f(b) = b: a and b are unstable equilibrium points. (2) f(a) = b, f(b) = a: a and b form an unstable 2-cycle. (3) f(a) = a, f(b) = a: a is an unstable equilibrium point and b maps into a. (4) f(a) = b, f(b) = b: b is an unstable equilibrium point and a maps into b. In particular, if f is nondecreasing (as in kronecker's example) the only possibility is (1), while if f is nonincreasing the only possibility is (2). Robert Israel israel@math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Ten points in a square It is a standard exercise on Pigeonhole Principle to prove: If you place 10 distinct points in a square of side 1, then at least two points will have distance no more than sqrt(2)/3 (about 0.4714). My question: This number is an upper bound for the minimum positive distance. Has anyone found the least upper bound? (It is at least 1/3, just place the points at lattice points with stepsize 1/3. With slightly more effort, one can replace 1/3 by sqrt(2)/(2*sqrt(2)+1), about 0.3694.) By the way, tens of millions of pseudorandom experiments have not exceeded 0.32. === Subject: Re: Ten points in a square > It is a standard exercise on Pigeonhole Principle to prove: If you place 10 distinct points in a square of side 1, then at least > two points will have distance no more than sqrt(2)/3 (about 0.4714). My question: This number is an upper bound for the minimum > positive distance. Has anyone found the least upper bound? (It is at least 1/3, just place the points at lattice points > with stepsize 1/3. With slightly more effort, one can replace > 1/3 by sqrt(2)/(2*sqrt(2)+1), about 0.3694.) By the way, tens of millions of pseudorandom experiments have > not exceeded 0.32. It is 0.421..., which follows from the packing of ten unit circles, proven optimal, shown at . David W. Cantrell === Subject: Re: Ten points in a square > It is a standard exercise on Pigeonhole Principle to prove: > If you place 10 distinct points in a square of side 1, then at least > two points will have distance no more than sqrt(2)/3 (about 0.4714). > My question: This number is an upper bound for the minimum > positive distance. Has anyone found the least upper bound? > (It is at least 1/3, just place the points at lattice points > with stepsize 1/3. With slightly more effort, one can replace > 1/3 by sqrt(2)/(2*sqrt(2)+1), about 0.3694.) > By the way, tens of millions of pseudorandom experiments have > not exceeded 0.32. It is 0.421..., which follows from the packing of ten unit circles, proven >optimal, shown at . It's not clear to me that the 10 circle packing configuration answers the OP's question. There's no requirement for the placed points to be any given distance away from the boundary of the square. Letting x be the answer to the OP's question, then, as far as I can see, the 10 circle packing configuration gives a _lower_ bound on x. In other words, what we now know is 0.421... <= x <= sqrt(2)/3 Unless I'm missing something. quasi === Subject: Re: Ten points in a square > It is a standard exercise on Pigeonhole Principle to prove: > If you place 10 distinct points in a square of side 1, then at least > two points will have distance no more than sqrt(2)/3 (about 0.4714). > My question: This number is an upper bound for the minimum > positive distance. Has anyone found the least upper bound? > (It is at least 1/3, just place the points at lattice points > with stepsize 1/3. With slightly more effort, one can replace > 1/3 by sqrt(2)/(2*sqrt(2)+1), about 0.3694.) > By the way, tens of millions of pseudorandom experiments have > not exceeded 0.32. It is 0.421..., which follows from the packing of ten unit circles, proven >optimal, shown at . It's not clear to me that the 10 circle packing configuration answers > the OP's question. There's no requirement for the placed points to be any given distance > away from the boundary of the square. Assuming that there's one circle abutting each edge of the square, then you can be sure that all the centres fit within a square with width 2 less, 4.747+. Then scale that down to be 1, and count the distance between points as that of 2 radii. If you could improve on this ratio, then by adding the 1-unit border back round the outside you'd be able to improve on the packing found at DC's link. Phil -- -- Microsoft voice recognition live demonstration === Subject: Re: Ten points in a square On 12 Apr 2008 02:29:17 +0300, Phil Carmody > It is a standard exercise on Pigeonhole Principle to prove: If you place 10 distinct points in a square of side 1, then at least > two points will have distance no more than sqrt(2)/3 (about 0.4714). My question: This number is an upper bound for the minimum > positive distance. Has anyone found the least upper bound? (It is at least 1/3, just place the points at lattice points > with stepsize 1/3. With slightly more effort, one can replace > 1/3 by sqrt(2)/(2*sqrt(2)+1), about 0.3694.) By the way, tens of millions of pseudorandom experiments have > not exceeded 0.32. >It is 0.421..., which follows from the packing of ten unit circles, proven >optimal, shown at . > It's not clear to me that the 10 circle packing configuration answers > the OP's question. > There's no requirement for the placed points to be any given distance > away from the boundary of the square. Assuming that there's one circle abutting each edge of the >square, then you can be sure that all the centres fit within >a square with width 2 less, 4.747+. Then scale that down to >be 1, and count the distance between points as that of 2 >radii. If you could improve on this ratio, then by adding >the 1-unit border back round the outside you'd be able to >improve on the packing found at DC's link. I don't see it. If you start with a maximal 10-circle packing configuration with all equal circles of radius r, that induces a 10-point configuration with min distance d = 2r. The converse doesn't seem to automatic, and may not be true. In other words, if you start with a 10-point configuration with min distance d, that doesn't necessarily induce a 10-circle packing configuration with all circles of radius r, where r = d/2. The issue is the outer points, which need not be d away from the boundary of the square. quasi === Subject: Re: Ten points in a square >On 12 Apr 2008 02:29:17 +0300, Phil Carmody > It is a standard exercise on Pigeonhole Principle to prove: > If you place 10 distinct points in a square of side 1, then at least > two points will have distance no more than sqrt(2)/3 (about 0.4714). > My question: This number is an upper bound for the minimum > positive distance. Has anyone found the least upper bound? > (It is at least 1/3, just place the points at lattice points > with stepsize 1/3. With slightly more effort, one can replace > 1/3 by sqrt(2)/(2*sqrt(2)+1), about 0.3694.) > By the way, tens of millions of pseudorandom experiments have > not exceeded 0.32. It is 0.421..., which follows from the packing of ten unit circles, proven >optimal, shown at . It's not clear to me that the 10 circle packing configuration answers > the OP's question. There's no requirement for the placed points to be any given distance > away from the boundary of the square. >Assuming that there's one circle abutting each edge of the >square, then you can be sure that all the centres fit within >a square with width 2 less, 4.747+. Then scale that down to >be 1, and count the distance between points as that of 2 >radii. If you could improve on this ratio, then by adding >the 1-unit border back round the outside you'd be able to >improve on the packing found at DC's link. I don't see it. If you start with a maximal 10-circle packing configuration with all >equal circles of radius r, that induces a 10-point configuration with >min distance d = 2r. The converse doesn't seem to automatic, and may not be true. In other words, if you start with a 10-point configuration with min >distance d, that doesn't necessarily induce a 10-circle packing >configuration with all circles of radius r, where r = d/2. The issue >is the outer points, which need not be d away from the boundary of >the square. Ok, I follow the argument now. It is reversible, by scaling. The disks of radius r = d/2 induced by a given 10-point configuration must be disjoint, since if they overlapped outside the square, they would necessarily also overlap inside the square, thus violating the requirements of a 10-point configuration. Since they are disjoint, they can be contracted by an appropriate factor towards the center of the square so as to yield a valid 10-circle packing configuration, which potentially could induce back the original 10-point configuration by dilation. In other words, fully reversible. Thus, I withdraw my challenge -- David's claimed lub is correct. quasi === Subject: Re: Ten points in a square >On 12 Apr 2008 02:29:17 +0300, Phil Carmody > It is a standard exercise on Pigeonhole Principle to prove: > If you place 10 distinct points in a square of side 1, then at least > two points will have distance no more than sqrt(2)/3 (about 0.4714). > My question: This number is an upper bound for the minimum > positive distance. Has anyone found the least upper bound? > (It is at least 1/3, just place the points at lattice points > with stepsize 1/3. With slightly more effort, one can replace > 1/3 by sqrt(2)/(2*sqrt(2)+1), about 0.3694.) > By the way, tens of millions of pseudorandom experiments have > not exceeded 0.32. It is 0.421..., which follows from the packing of ten unit circles, proven >optimal, shown at . It's not clear to me that the 10 circle packing configuration answers > the OP's question. There's no requirement for the placed points to be any given distance > away from the boundary of the square. >Assuming that there's one circle abutting each edge of the >square, then you can be sure that all the centres fit within >a square with width 2 less, 4.747+. Then scale that down to >be 1, and count the distance between points as that of 2 >radii. If you could improve on this ratio, then by adding >the 1-unit border back round the outside you'd be able to >improve on the packing found at DC's link. I don't see it. If you start with a maximal 10-circle packing configuration with all >equal circles of radius r, that induces a 10-point configuration with >min distance d = 2r. The converse doesn't seem to automatic, and may not be true. In other words, if you start with a 10-point configuration with min >distance d, that doesn't necessarily induce a 10-circle packing >configuration with all circles of radius r, where r = d/2. The issue >is the outer points, which need not be d away from the boundary of >the square. It's late at night here, and I may be missing your point, but it seems as if you're repeating the argument you gave earlier, and forgetting to, as Phil put it, scale down. If you start with a 10-point configuration in a unit square, with minimum separation d = 2r, then you have a packing of 10 circles into a square of side at most 1 + 2r. So if d > .4213+, then when the packing figure is scaled up, so that the circles all have radius 1, the side of the square the circles are all packed into will have side at most (1 + 2r)/r = 2 + 1/r < 6.474- - which we know to be impossible. (I'm sorry, I haven't put this very elegantly, and who knows, I may have reversed an inequal- ity sign somewhere, and it may all be nonsense.) -- Angus Rodgers Contains mild peril === Subject: Re: Ten points in a square >On 12 Apr 2008 02:29:17 +0300, Phil Carmody > It is a standard exercise on Pigeonhole Principle to prove: If you place 10 distinct points in a square of side 1, then at least > two points will have distance no more than sqrt(2)/3 (about 0.4714). My question: This number is an upper bound for the minimum > positive distance. Has anyone found the least upper bound? (It is at least 1/3, just place the points at lattice points > with stepsize 1/3. With slightly more effort, one can replace > 1/3 by sqrt(2)/(2*sqrt(2)+1), about 0.3694.) By the way, tens of millions of pseudorandom experiments have > not exceeded 0.32. >It is 0.421..., which follows from the packing of ten unit circles, proven >optimal, shown at . > It's not clear to me that the 10 circle packing configuration answers > the OP's question. > There's no requirement for the placed points to be any given distance > away from the boundary of the square. Assuming that there's one circle abutting each edge of the >square, then you can be sure that all the centres fit within >a square with width 2 less, 4.747+. Then scale that down to >be 1, and count the distance between points as that of 2 >radii. If you could improve on this ratio, then by adding >the 1-unit border back round the outside you'd be able to >improve on the packing found at DC's link. >I don't see it. >If you start with a maximal 10-circle packing configuration with all >equal circles of radius r, that induces a 10-point configuration with >min distance d = 2r. >The converse doesn't seem to automatic, and may not be true. >In other words, if you start with a 10-point configuration with min >distance d, that doesn't necessarily induce a 10-circle packing >configuration with all circles of radius r, where r = d/2. The issue >is the outer points, which need not be d away from the boundary of >the square. It's late at night here, and I may be missing your point, but >it seems as if you're repeating the argument you gave earlier, >and forgetting to, as Phil put it, scale down. If you start >with a 10-point configuration in a unit square, with minimum >separation d = 2r, then you have a packing of 10 circles into >a square of side at most 1 + 2r. So if d > .4213+, then when >the packing figure is scaled up, so that the circles all have >radius 1, the side of the square the circles are all packed >into will have side at most (1 + 2r)/r = 2 + 1/r < 6.474- - >which we know to be impossible. (I'm sorry, I haven't put this >very elegantly, and who knows, I may have reversed an inequal- >ity sign somewhere, and it may all be nonsense.) No, it looks good -- I get it now. quasi === Subject: Re: Ten points in a square >On 12 Apr 2008 02:29:17 +0300, Phil Carmody > It is a standard exercise on Pigeonhole Principle to prove: > If you place 10 distinct points in a square of side 1, then at least > two points will have distance no more than sqrt(2)/3 (about 0.4714). > My question: This number is an upper bound for the minimum > positive distance. Has anyone found the least upper bound? > (It is at least 1/3, just place the points at lattice points > with stepsize 1/3. With slightly more effort, one can replace > 1/3 by sqrt(2)/(2*sqrt(2)+1), about 0.3694.) > By the way, tens of millions of pseudorandom experiments have > not exceeded 0.32. It is 0.421..., which follows from the packing of ten unit circles, proven >optimal, shown at . It's not clear to me that the 10 circle packing configuration answers > the OP's question. There's no requirement for the placed points to be any given distance > away from the boundary of the square. >Assuming that there's one circle abutting each edge of the >square, then you can be sure that all the centres fit within >a square with width 2 less, 4.747+. Then scale that down to >be 1, and count the distance between points as that of 2 >radii. If you could improve on this ratio, then by adding >the 1-unit border back round the outside you'd be able to >improve on the packing found at DC's link. I don't see it. If you start with a maximal 10-circle packing configuration with all >equal circles of radius r, that induces a 10-point configuration with >min distance d = 2r. The converse doesn't seem to automatic, and may not be true. In other words, if you start with a 10-point configuration with min >distance d, that doesn't necessarily induce a 10-circle packing >configuration with all circles of radius r, where r = d/2. The issue >is the outer points, which need not be d away correction: which need not be d/2 away >from the boundary of the square. quasi === Subject: Re: Ten points in a square It is a standard exercise on Pigeonhole Principle to prove: If you place 10 distinct points in a square of side 1, then at least > two points will have distance no more than sqrt(2)/3 (about 0.4714). My question: This number is an upper bound for the minimum > positive distance. Has anyone found the least upper bound? (It is at least 1/3, just place the points at lattice points > with stepsize 1/3. With slightly more effort, one can replace > 1/3 by sqrt(2)/(2*sqrt(2)+1), about 0.3694.) By the way, tens of millions of pseudorandom experiments have > not exceeded 0.32. >It is 0.421..., which follows from the packing of ten unit circles, proven >optimal, shown at . It's not clear to me that the 10 circle packing configuration answers >the OP's question. It's clear to me that it doesn't. Wow, such confidence, for once! So I must be wrong ... and indeed I am! See below. :-) >There's no requirement for the placed points to be any given distance >away from the boundary of the square. Letting x be the answer to the OP's question, then, as far as I can >see, the 10 circle packing configuration gives a _lower_ bound on x. In other words, what we now know is 0.421... <= x <= sqrt(2)/3 Unless I'm missing something. I don't think so. But it might be possible to deduce an answer. Let the radii of the circles in that configuration be r, so that the required bound is 2r. Then it looks as if the centres occupy a square of side 1 - 2r, so, if the figure is magnified by the inverse of this, it would seem that the 10 centres fit into a square of unit side when the radii are r/(1 - 2r), so the separation is 2r/(1 - 2r). If I understand the diagram correctly, r = 1/(6.747+), so 2r/(1 - 2r) = 1/(1 - 2r) - 1 = .4213+ ... which is obviously (with hindsight!) just what David meant in the first place. D'oh! -- Angus Rodgers Contains mild peril === Subject: Re: Ten points in a square > It is a standard exercise on Pigeonhole Principle to prove: > If you place 10 distinct points in a square of side 1, then at least > two points will have distance no more than sqrt(2)/3 (about 0.4714). > My question: This number is an upper bound for the minimum > positive distance. Has anyone found the least upper bound? > (It is at least 1/3, just place the points at lattice points > with stepsize 1/3. With slightly more effort, one can replace > 1/3 by sqrt(2)/(2*sqrt(2)+1), about 0.3694.) > By the way, tens of millions of pseudorandom experiments have > not exceeded 0.32. It is 0.421..., which follows from the packing of ten unit circles, proven >optimal, shown at . >It's not clear to me that the 10 circle packing configuration answers >the OP's question. It's clear to me that it doesn't. Wow, such confidence, for >once! So I must be wrong ... and indeed I am! See below. :-) >There's no requirement for the placed points to be any given distance >away from the boundary of the square. >Letting x be the answer to the OP's question, then, as far as I can >see, the 10 circle packing configuration gives a _lower_ bound on x. >In other words, what we now know is > 0.421... <= x <= sqrt(2)/3 >Unless I'm missing something. I don't think so. But it might be possible to deduce an answer. Let the radii of the >circles in that configuration be r, so that the required bound is 2r. >Then it looks as if the centres occupy a square of side 1 - 2r, so, >if the figure is magnified by the inverse of this, it would seem >that the 10 centres fit into a square of unit side when the radii >are r/(1 - 2r), so the separation is 2r/(1 - 2r). If I understand the diagram correctly, r = 1/(6.747+), so 2r/(1 - 2r) >= 1/(1 - 2r) - 1 = .4213+ ... which is obviously (with hindsight!) >just what David meant in the first place. D'oh! But it still doesn't prove that .4213 ... is an upper bound since, while every packing configuration induces a 10-point configuration, the converse is not obvious, and possibly not true. Thus, all you have is a _lower_ bound on x. Hence, bolstered by your analysis, I stand (for now) by my earlier claim that what David's argument (and your amplification) actually proves is .4213 ... <= x. Thus, all we know, based on the information so far in this thread, is that .4213 ... <= x <= sqrt(2)/3 Unless I'm missing something. quasi === Subject: In Need of the Fundamental Revision of the Current Theory of Symboloic Logic posting-account=weMSdQoAAADZJGKnAqDaw4DRn4AHCKC4 See the following Web sites:- === Subject: Re: Good at mathematics... posting-account=OKTeIQkAAAAZk6JK1hK7-grwpoUDNy98 CLR 1.1.4322; .NET CLR 2.0.50727; InfoPath.1),gzip(gfe),gzip(gfe) > Hello teacher~ Those who are good at mathematics are poor at foreign languages. ------------------------------------------ > Are you agree ? In my case, yes. In high school I got staright A's in geometry while simultaneously flunking Spanish. In my experience, > Students who are good at mathematics are good at other subjects generally. Not necessarily. Mathematics can be more than the sum of it's parts. Foreign languages ? The sum of it's parts. (Note, I never got to the stage of reading Spanish literature, couldn't make my way to the station.) === Subject: Re: Good at mathematics... posting-account=z1ZA6AoAAACEgXDaRRTJFG5d4vJvYyOY SV1),gzip(gfe),gzip(gfe) > Hello teacher~ Those who are good at mathematics are poor at foreign languages. ------------------------------------------ > Are you agree ? In my case, yes. In high school I got staright A's in geometry > while simultaneously flunking Spanish. In my experience, > Students who are good at mathematics are good at other subjects generally. Not necessarily. Mathematics can be more than the sum of it's parts. Foreign languages ? The sum of it's parts. (Note, I never got to the stage of reading > Spanish literature, couldn't make my way to the station.) You are Einstein ? === Subject: Re: Good at mathematics... posting-account=OKTeIQkAAAAZk6JK1hK7-grwpoUDNy98 CLR 1.1.4322; .NET CLR 2.0.50727; InfoPath.1),gzip(gfe),gzip(gfe) > æ> Hello teacher~ Those who are good at mathematics are poor at foreign languages. ------------------------------------------ > Are you agree ? In my case, yes. In high school I got staright A's in geometry > while simultaneously flunking Spanish. In my experience, > Students who are good at mathematics are good at other subjects generally. Not necessarily. Mathematics can be more than the sum of it's parts. Foreign languages ? The sum of it's parts. (Note, I never got to the stage of reading > Spanish literature, couldn't make my way to the station.) You are Einstein ? Of course not! I'm much smarter (selectively) than Einstein. Certain things like languages require a lot of memorization (and thus work). Certain other things, like geometry, are about how you apply a relatively small amount of memorization. I happen to be very good at such application and thus good at such subjects. Being lazy, I tend not to be good at subjects requiring a lot of work. === Subject: Re: Good at mathematics... > Hello teacher~ Those who are good at mathematics are poor at foreign languages. ------------------------------------------ > Are you agree ? > No, I am not a Greek. (I do admit I am a geek.) > In my experience, > Students who are good at mathematics are good at other subjects generally. Foreign languages ? === Subject: Re: Good at mathematics... > Hello teacher~ Those who are good at mathematics are poor at foreign languages. ------------------------------------------ > Are you agree ? In my experience, > Students who are good at mathematics are good at other subjects generally. Foreign languages ? I would say that those who are good at learning mathematics have an excellent model for learning anything they like--foreign languages not excluded. Learning mathematics reinforces habits of discipline, patience, creativity and attention to detail. Bill === Subject: Re: Good at mathematics... > Hello teacher~ > Those who are good at mathematics are poor at foreign languages. > ------------------------------------------ > Are you agree ? > In my experience, > Students who are good at mathematics are good at other subjects generally. > Foreign languages ? I would say that those who are good at learning mathematics have an >excellent model for learning anything they like--foreign languages not >excluded. Learning mathematics reinforces habits of discipline, patience, >creativity and attention to detail. I agree. Success in math requires _both_ big-picture and small-picture type thinking. Without being a big picture type thinker (the director), a student never truly understands what the theory is all about. But without also being a small-picture type thinker (the worker bee, with attention to detail), the student can never actually produce rigorous proofs, or solve problems correctly. In my opinion, having both modes, big-picture and small-picture, is key to learning _any_ complex body of knowledge with lots of structure, plus lots of details -- such as a foreign language. Thus, in most cases, a student who has succeeded at math already has both modes well developed -- director mode and worker mode, and knows when to switch between them. Moreover, math itself is language-based. Thus, in my opinion, to master an area of math, it's necessary to master the underlying language (terminology, syntax, notation), and hence, a prerequisite to such mastery (besides math talent) is (1) reasonably strong language skills (2) willingness to take the language _seriously_ Thus, for students who can master math easily, in most cases, such students would have relatively little trouble mastering a foreign language, if they so desired. quasi === Subject: Re: Good at mathematics... posting-account=bSICGQkAAADSbkxAJ5uMxFegr4rp0Qig rv:1.8.1.13) Gecko/20080311 Firefox/2.0.0.13,gzip(gfe),gzip(gfe) > Thus, for students who can master math easily, in most cases, such > students would have relatively little trouble mastering a foreign > language, if they so desired. I had no problem learning endings and grammar, which I think are very mathematical skills. But I found out that's a far cry from learning to speak or understand a language. Still, it gets one to the newspaper- or journal-reading stage. - Randy === === Subject: Re: Monty Hall problem wrong? > i think people can easily understand that these are all the > possibilities. What they have trouble with is assigning the correct > probabilites to each instance. > ------------------------------------------------ > No, I think that the problem is difficult when using a logic of > probability but that the problem is obvious when it is described with > three linear equations... The problem may be made more transparent by verbal explanation. If you choose a goat, which is 2/3 of the time, Monty has to show you the other goat. === Subject: Re: Monty Hall problem wrong? > If you have 3 doors, behind one of which is a car and behind each of > the other two of which is a goat, why is your second choice still 1 in > 3, instead of 1 in 2 ? > If you pick door 1, and it's the car, and then Monty opens door 2 and > shows you a goat, and then asks you if you want to switch, why is your > chance of winning the car or winning the goat (losing the car) not 50% > at that point? What did the contestants do with all those goats? === Subject: Re: Monty Hall problem wrong? posting-account=zKSjoQoAAAC5wIsHKdIzIXzOHEFPgaXy Gecko/20080311 Firefox/2.0.0.13,gzip(gfe),gzip(gfe) > Prize in 3 > No Prize in 2 > Not a Prize in 1 If 1 is picked, 2 is shown, and 1 is changed it wins > If 1 is picked, 2 is shown and 1 is not changed it loses If 2 is picked, 1 is shown, and 2 is changed it wins > If 2 is picked, 1 is shown, and 2 is not changed it loses If 3 is picked, 2 is shown, and 3 is changed it loses > If 3 is picked, 2 is shown, and 3 not changed it wins So there are two cases out of three where changing the pick wins. And > there > is one case out of three where holding the pick wins. And that probably demonstrates a linear algebra approach to major > fields... ------------------------------------------------ ithink people can easily understand that these are all the > possibilities. What they have trouble with is assigning the correct > probabilites to each instance. ------------------------------------------------ No, I think that the problem is difficult when using a logic of probability > but that the problem is obvious when it is described with three linear > equations... Your previous post contained NO equations at all, linear or otherwise. R.G. Vickson === Subject: Re: Monty Hall problem wrong? Your previous post contained NO equations at all, linear or > otherwise. R.G. Vickson Yeah, I knew that but thought that someone that applies linear algebra to statistics or to optimization or to actuarial science...would just take it as done. Here's the best I can do on short notice: Prize of 1 in x Prize of 0 in y Prize of 0 in z Games with changing choice: z + y = 0 y + x = 1 y + z = 0 z + x = 1 x + y = 1 y + z = 0 === Subject: Probability Understanding Help posting-account=xqox8QoAAAC11v-dV9saK8ReUdSljYj5 CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) I am having trouble interpreting the chart @http://wizardofodds.com/ blackjack/appendix4.html. > If anyone could shed some light on the subject it would be appreciated. === Subject: Re: Could you please help with this proof about a sequnce, please <2149548.1207939377733.JavaMail.jakarta@nitrogen.mathforum.org>, > I'd like to have my proof checked, please: Suppose f (real valued)is continuous, periodic and non-constant on R. If its > fundamental period p is irrational, then the sequence f(n), n=1,2,3..., is > dense in f([0, p]). I already know the set A = {m*p + n | m integer, n positive integer} is dense > in R. If you know the above, you're nearly done. Let x be in [0, p]. Then m_k*p + n_k -> x for appropriate sequences m_k in Z, n_k in N, which implies f(m_k*p + n_k) -> f(x) by continuity. But f(m_k*p + n_k) = f(n_k) by periodicity. Thus every f(x) in f([0, p]) is the limit of f(n_k) for some subsequence n_k of N. > First, let's prove the following lemma: For every real x, there is a sequence x_k = m_k *p + n_k in A that converges > to x and is such that n_k is strictly increasing. Proof: > Since A is dense in R and every element of R is a limit point of R, every > real number is a limit point of A. Hence, there exists a sequence w_i= m_i * > p + n_i in A that converges to x and has its terms pairwise distinct. We > claim w_i has a L-tail where the numbers n_i are pairwise distinct. Actually, since w_i converges, it is Cauchy. Hence, there is L such that i >= > L and j >= L implies |w_i - w_j| = |(m_i - m_j) p + (n_i - n_j)| < p > If n_i = n_j, then we get > |m_i - m_j| < 1. Since m_i and m_j are integers, this implies m_i = m_j, so > that w_i = w_j. But since this contradicts the assumption that the terms w_i > are pairwise distinct, the claim is proved. Since the numbers n_i are positive integers and are pairwise distinct for i >= L, we can find a subsequence of the L-tail of w_i (so, a subsequence of > w_i) where the numbers n_i form an strictly increasing sequence. This > subsequence, as well as w_i, converges to x. By renumbering its terms, we get > a sequence x_k = m_k *p + n_k as stated in the lemma. Now, let y be any number in f([0,p]). There is an x in [0, p] with y = f(x). > According to the lemma, there's also a sequence w_k, as stated, that > converges to x. Since f is continuous, w_k -> x, and p is a period of f, it > follows that lim f(w_k) = lim f(m_k * p + n_k) = lim f(n_k) = f(x) = y. Since > f(n_k) is a subsequence of f(n) and this holds for every y of f([0,p]), we > conclude f(n) is dense in f([0,p]). I know there are better proofs based on complex numbers, but for now they are > out of my reach. Sharon === Comments, additions and corrections are welcome. > The string DASH DASH SPACE NEWLINE is a signature delimiter. > It appears before the paragraph Google groups is the source [...] > which causes Mozilla-based clients to display the rest of the text in > light gray, which is hard to read. > Same answer, block all posts from Google groups. > Post notice once a week that more are more people are joining > the Google groups boycott and some suggestions how to avoid > the boycott by using a different news server. I hate color for text and have set my system > to black and white text. I also try to rid my self > of attributes which is only needed for the cursor. In other words, all this wonderfully unneeded extra capacity, doesn't make > our lives easier, it makes our lives more annoying. Remember the good old > days before automation and you didn't have to put up with voice activated > menus, the first lousy application of AI, Artificial Idiocy? Google has many blogs about all things Google. They have branched out from web search to Google earth and then Google the moon... Anyway, I found a Google blog about Online Security, where in a post from less than a year ago they mentioned their CAPTCHA system : I read a few posts there by Niels Provos, a math./stats. PhD in the Google Anti-Malware Team . of many things to work on, and maybe not the most interesting. After all, Usenet existed before Google, and obviously could very well exist without it. I guess I'll be checking the Google blogs from time to time since I found a few interesting things. David Bernier === >Comments, additions and corrections are welcome. NNTP news servers > Most ISP include a news server with the account > http://www.teranews.com (one time $3.95 set up cost, worth it) News Readers > SeaMonkey > Forte Agent (excellent, inexpensive) > Thunderbird (in developement) > http://www.mozilla.com/en-US/thunderbird > Gnus (for emacs) > for Mac Users: MT-Newswatcher, hogwash, thoth (not supported) News souces, web and otherwise and references to news sites > http://www.readfreenews.net > http://en.wikipedia.org/wiki/List_of_news_clients > http://dmoz.org/Computers/Usenet/Public_News_Servers > http://www.alt.free.newsservers.net > http://freenews.maxbaud.net NewsProxy (proxy news source, may be complicated) > http://bearware.info/NewsProxy/newsproxy.html commercial news servers > Giganews http://www.giganews.com ($8/month, worth it) > Supernews http://www.supernews.com > Newsfeeds http://www.newsfeeds.com > Usenetserve http://www.usenetserver.com > Easynews http://www.easynews.com > Altopia https://www.altopia.com > Newsguy https://www.newsguy.com seen before. I'm on the point of installing newsproxy to filter out groups. It probably seems like asking someone to do my work for me, but as more of an occasional than thorough reader it would probably take me some time to do. === groups. It probably seems like asking someone to do my work for me, but as > more of an occasional than thorough reader it would probably take me some > time to do. > 'paypal', etc, which I'm doing because of time limitatons filtering out all Google groups posts, you can mark all the Google group posts and in that way find the significant Google group posters. After that, then the full block can occure. I suggest you post notice that you too are about to join the Google groups blocade boycott and before you do, offer opportunity for readers to request that they individually not be blocked. What I have upon the say so of others is. Pubkeybreaker jankrihau@hotmail.com Derek Holt israel@math.ubc.ca If you find others, let me know. ---- === posting-account=yxbZkgkAAABQBvyYeebYQ-PAvi0uT3tG Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) > offer > opportunity for readers to request that they individually not be blocked. > What I have upon the say so of others is. Pubkeybreaker Derek Holt <1207526811_38690@news.usenet.com> posting-account=tQA_9wkAAAC8kqTdBlJnXYniA-oBKt-8 1.1.4322; InfoPath.2),gzip(gfe),gzip(gfe) 4099- Polack is a slur even in Poland. æRight Kent? But my impression is that Jewry is not in and of itself a slur. > In the past there was even advocacy about freeing Soviet Jewry. > It did not seem like a slur. Kentislawa Willenski's pseudo intellectualism > where his need for a Polska to English dictionary > passes as erudition is absurd. Political Correctness is an ULTRALIBERAL thing anyway. Variations on a word that means black from LATIN ORIGINS > have taken on a societal context as a slur. æThat is a done deal. Variations on language that is shorthand for > Jewish diaspora, Jewry have not yet > become inherantly seen as a slur, but the > political correctness drift may eventually > make that the case. > Aptly put. If so, news reports of abuse of the word by higher-ups > would abound. As they have. > There are no news reports. æ You're wrong. Again. You're lying. æAgain. æYou've cited *one* news report about a complaint. æ Then they are lying ?? > The word jewry was used by the complainer. æNot the person he was > complaining about. Wrong. IT was used by McPeak. > æMcPeak said, American Jewry has some influence... > æ æ -- blogs.abcnews.com/politicalpunch/2008/03/obama-mcpeak-an.html You're lying. æStill. æ Wrong. > The word jewry was used by Brook, the > complainer. æHe was complaining about McPeak's statement about the Jewish > vote in New York City and Florida. It was used by McPeak, himself. > Just a quote of someone from something called > the RJC, a Republican group. æTheir rep used the word. So did McPeak. (says the news) Care to redirect ?? If the news says, then you should quote the news that says it. I've done so above. Not you, nor anyone else trumps ABC news. > In any case, jewry isn't a slur. æIt's used by Jews to describe > populations of Jews.- Its a term that appears on Hate Websites. So it is a slur === Subject: Re: No McCain/Obama apologies -day 12 (ugly racism) > 4099- > Polack is a slur even in Poland. æRight Kent? > But my impression is that Jewry is not in and of itself a > slur. In the past there was even advocacy about freeing Soviet > Jewry. It did not seem like a slur. > Kentislawa Willenski's pseudo intellectualism > where his need for a Polska to English dictionary > passes as erudition is absurd. > Political Correctness is an ULTRALIBERAL thing anyway. > Variations on a word that means black from LATIN ORIGINS > have taken on a societal context as a slur. æThat is a done > deal. > Variations on language that is shorthand for > Jewish diaspora, Jewry have not yet > become inherantly seen as a slur, but the > political correctness drift may eventually > make that the case. > Aptly put. If so, news reports of abuse of the word by > higher-ups would abound. As they have. > There are no news reports. æ > You're wrong. Again. > You're lying. æAgain. æYou've cited *one* news report about a > complaint. æ Then they are lying ?? No, I'll accept their report as accurate. You're citing one report and expanding it to multiple reports. In any case, jewry isn't a slur. æIt's used by Jews to describe > populations of Jews.- Its a term that appears on Hate Websites. So it is a slur I'll repeat my question, which you've never answered: If Hate Websites use the words ice cream, will stop buying Ben and Jerry's? Why would you conclude that Hate Websites get to determine what names Jews find acceptable? === Subject: math -- elements of Z_p[x] which permute Z_p The following is easily proved: If p is prime, then for every function F: Z_p --> Z_p, there exists a unique polynomial f in Z_p[x], with deg(f) < p, such that, regarding f as a function from Z_p to Z_p, we have F = f. In particular, every element of the permutation group S_p is uniquely represented by a polynomial in Z_p[x] with degree < p. The simplest examples are the linear polynomials, which form a subgroup (under composition) of order p^2 - p. With that as background, here's a conjecture ... Conjecture: If p is prime, p > 2, there does not exist f in Z_p[x], with deg(f) = p - 1, which permutes Z_p. Remarks: While I've verified the conjecture for p = 3, 5, 7, 11, I don't have a lot of confidence that it holds for all primes p > 2. I would estimate my degree of belief as only about 60-40, based on what I know at this point. quasi === Subject: Re: math -- elements of Z_p[x] which permute Z_p >The following is easily proved: If p is prime, then for every function F: Z_p --> Z_p, there exists a >unique polynomial f in Z_p[x], with deg(f) < p, such that, regarding f >as a function from Z_p to Z_p, we have F = f. In particular, every element of the permutation group S_p is uniquely >represented by a polynomial in Z_p[x] with degree < p. The simplest examples are the linear polynomials, which form a >subgroup (under composition) of order p^2 - p. With that as background, here's a conjecture ... Conjecture: If p is prime, p > 2, there does not exist f in Z_p[x], with deg(f) = >p - 1, which permutes Z_p. Remarks: While I've verified the conjecture for p = 3, 5, 7, 11, I don't have a >lot of confidence that it holds for all primes p > 2. I would estimate >my degree of belief as only about 60-40, based on what I know at this >point. Ok, the conjecture is true -- I can prove it. I'll leave it as a challenge problem for whoever wants to try it. quasi === Subject: Re: math -- elements of Z_p[x] which permute Z_p posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/20080325 Fedora/2.0.0.13-1.fc8 Firefox/2.0.0.13,gzip(gfe),gzip(gfe) >The following is easily proved: If p is prime, then for every function F: Z_p --> Z_p, there exists a >unique polynomial f in Z_p[x], with deg(f) < p, such that, regarding f >as a function from Z_p to Z_p, we have F = f. In particular, every element of the permutation group S_p is uniquely >represented by a polynomial in Z_p[x] with degree < p. The simplest examples are the linear polynomials, which form a >subgroup (under composition) of order p^2 - p. With that as background, here's a conjecture ... Conjecture: If p is prime, p > 2, there does not exist f in Z_p[x], with deg(f) = >p - 1, which permutes Z_p. Remarks: While I've verified the conjecture for p = 3, 5, 7, 11, I don't have a >lot of confidence that it holds for all primes p > 2. I would estimate >my degree of belief as only about 60-40, based on what I know at this >point. Ok, the conjecture is true -- I can prove it. I'll leave it as a challenge problem for whoever wants to try it. Suppose there is an f in Z_p[X] of degree p-1 such that f(x) = x for all x in Z_p. Then, lifting the coefficients to Z, one sees that there is a polynomial g in Z[X] of degree p-1 such that p divides the difference g(x) - x for all x in Z. Since p > 2, this means, in fact, that there exists a non-zero polynomial h in Z[X] of degree p-1 such that it takes values divisible by p on all integers. Let h(X) = sum_{0<=iThe following is easily proved: >If p is prime, then for every function F: Z_p --> Z_p, there exists a >unique polynomial f in Z_p[x], with deg(f) < p, such that, regarding f >as a function from Z_p to Z_p, we have F = f. >In particular, every element of the permutation group S_p is uniquely >represented by a polynomial in Z_p[x] with degree < p. >The simplest examples are the linear polynomials, which form a >subgroup (under composition) of order p^2 - p. >With that as background, here's a conjecture ... >Conjecture: >If p is prime, p > 2, there does not exist f in Z_p[x], with deg(f) = >p - 1, which permutes Z_p. >Remarks: >While I've verified the conjecture for p = 3, 5, 7, 11, I don't have a >lot of confidence that it holds for all primes p > 2. I would estimate >my degree of belief as only about 60-40, based on what I know at this >point. > Ok, the conjecture is true -- I can prove it. > I'll leave it as a challenge problem for whoever wants to try it. Suppose there is an f in Z_p[X] of degree p-1 >such that f(x) = x for all x in Z_p. But f is not required to be the identity map on Z_p, it only has to permute Z_p. Did you miss that? I haven't yet looked at the rest of your proof -- I first just wanted to fmake sure that the problem you worked on is the correct problem. quasi === Subject: Re: math -- elements of Z_p[x] which permute Z_p <1if004lcvih5476c92uvl6uub9uc8q3g6f@4ax.com> posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/20080325 Fedora/2.0.0.13-1.fc8 Firefox/2.0.0.13,gzip(gfe),gzip(gfe) >The following is easily proved: >If p is prime, then for every function F: Z p --> Z p, there exists a >unique polynomial f in Z p[x], with deg(f) < p, such that, regarding f >as a function from Z p to Z p, we have F = f. >In particular, every element of the permutation group S p is uniquely >represented by a polynomial in Z p[x] with degree < p. >The simplest examples are the linear polynomials, which form a >subgroup (under composition) of order p^2 - p. >With that as background, here's a conjecture ... >Conjecture: >If p is prime, p > 2, there does not exist f in Z p[x], with deg(f) = >p - 1, which permutes Z p. >Remarks: >While I've verified the conjecture for p = 3, 5, 7, 11, I don't have a >lot of confidence that it holds for all primes p > 2. I would estimate >my degree of belief as only about 60-40, based on what I know at this >point. > Ok, the conjecture is true -- I can prove it. > I'll leave it as a challenge problem for whoever wants to try it. Suppose there is an f in Z p[X] of degree p-1 >such that f(x) = x for all x in Z p. But f is not required to be the identity map on Z p, it only has to > permute Z p. Did you miss that? I haven't yet looked at the rest of your proof -- I first just wanted > to fmake sure that the problem you worked on is the correct problem. Ah. I forgot that. If f is a degree (p-1) polynomial such that it permutes the elements of Z p, then the p-th composition of f with itself, g = f o f o ... o f is a polynomial of degree p(p-1) which leaves every element of Z p fixed. Now every such polynomial can be `reduced' in a straightforward way to produce another polynomial h of degree at exactly p-1 which fixes every element of Z p. This is the polynomial which leads to a contradiction in my previous post. -- m === Subject: Re: math -- elements of Z_p[x] which permute Z_p >Suppose there is an f in Z_p[X] of degree p-1 >such that f(x) = x for all x in Z_p. > But f is not required to be the identity map on Z_p, it only has to > permute Z_p. > Did you miss that? > I haven't yet looked at the rest of your proof -- I first just wanted > to make sure that the problem you worked on is the correct problem. Ah. I forgot that. If f is a degree (p-1) polynomial such that >it permutes the elements of Z_p, then the p-th >composition of f with itself, g = f o f o ... o f is a polynomial of degree p(p-1) which leaves >every element of Z_p fixed. Now every such >polynomial can be `reduced' in a straightforward >way to produce another polynomial h of degree at >exactly p-1 which fixes every element of Z_p. Why _exactly_ p - 1? Why couldn't the reduced degree be less than p - 1? >This is the polynomial which leads to a >contradiction in my previous post. quasi === Subject: Re: Look What I Bought posting-account=1nOeKQkAAABD2jxp4Pzmx9Hx5g9miO8y Gecko/20080311 Firefox/2.0.0.13,gzip(gfe),gzip(gfe) > What are you going to do when you learn General-Relativity, build an > atomic bomb? General Relativity is not relevant to building atomic bombs, fortunately. John Savard === Subject: Re: Look What I Bought :: The Starmaker :: What are you going to do when you learn General-Relativity, build an :: atomic bomb? No. GPS. Though of course you could fumble one together without knowing about GR, much as you can build a house without learning any principles of carpentry. : Quadibloc : General Relativity is not relevant to building atomic bombs, : fortunately. Nor special relativity, for the most part. Sure, E=mc^2, but that's remarkably little help in actually *building* nuclear weapons, or designing them. Though, to be fair, not many *components* of a GPS satellite require GR to design either. But the point is, the facts of nucleonics needed to model fission contain the energy yields emperically, but the design of clocks doesn't contain information on relative time rates in the same way. Ah well. Whatever. Ha! You said new-kle-er. It's newk-you-ler! The s is silent! --- Peter Griffin Wayne Throop throopw@sheol.org http://sheol.org/throopw === Subject: Re: Look What I Bought posting-account=1nOeKQkAAABD2jxp4Pzmx9Hx5g9miO8y Gecko/20080311 Firefox/2.0.0.13,gzip(gfe),gzip(gfe) > On Apr 8, 2:58 am, Agent Smith to > find the answer to Why Are We Here? from *any* book on this planet, > nobody knows. > They just they pretend they do, to sell books... We're here, because we're here, because, we're here..http://youtube.com/watch?v=V-4XKOv_Z4Q&feature=related General Relativity is science fiction. Math is science fiction. The > Bible is science fiction. No, math and the General Theory of Relativity are very much fact. But they don't pretend to answer the big questions of Why Are We Here either. A book on General Relativity is as legitimate and practical a thing as a book on carpentry. John Savard === === Subject: Re: Scientists Confirm Absolute Logic.By Aiya-Oba Bassan King Karzeddin: Absolute logic is Equator of self-contradiction, not conflict of contradictions or interests. It is a discovery, that calls for humanity's departure from the limitations of regional interpretations of religion, philosophy, and science, to the unified understanding of the cosmic Equator of All in all- (Spacetime-Continuum). -Aiya-Oba(Poet/Philosopher) === Subject: Re: Scientists Confirm Absolute Logic.By Aiya-Oba > Absolute logic is Equator of self-contradiction, not conflict of contradictions or interests. It is a discovery, that calls for humanity's departure from the limitations of regional interpretations of religion, philosophy, and science, to the unified understanding of the cosmic Equator of All in all- (Spacetime-Continuum). -Aiya-Oba(Poet/Philosopher) Butt of course, Anthony, for the universal truth belongs to the Queen. And of course, you know that it is the province of the Prophet Mohammed (P.B.U.H.) to expound on this universal truth and your absolute logic. For Mohammed is a QUEEN! Allah-Akbar!! Now go blow yourself up, Anthony A. Aiya-Oba! For great justice! Launch all ZIG! === Subject: A lot of Solution Manuals in Electronic (PDF)Format! posting-account=AIT25goAAAD4PInVOqQYW2U7xf3SSqUF QQDownload 1.7),gzip(gfe),gzip(gfe) A lot of Solution Manuals in Electronic (PDF)Format! A lot of Solutions Manuals in Electronic (PDF)Format! 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Freedman, use with Fundamentals of Corporate Finance, 4th Edition By Bruce Swenson Vector Mechanics for Engineers: Dynamics, 7th By Ferdinand P. Beer(selected chapters) E. R. Johnston Vector Mechanics for Engineers: Statics, 7th By Ferdinand P. Beer(selected chapters) Vector Mechanics for Engineers: Statics, 7th Edition ,By Ferdinand P. Beer, E. Russell Johnston Jr., ElliotR Visual C++ How to Program, (3rd Edition) ,by Harvey & Paul Deitel & Associates Wireless communication and networks 2th by willian stallings Zill's a First Course in Differential Equations with boundary value problem 5th Zill's a First Course in Differential Equations with Modeling Applicants 7/e.81isolitions manual.81j http://solutionsmanual.spaces.live.com === Subject: Re: NP vs. co-NP > co-L is clearly in NP because one could guess a divisor and test it. Yes, it is. If an input is in co-L, a divisor is a certificate. > But then L should be in NP too because one could easily negate the > answer. Negate what answer? Given a guess, verifying that it is not a divisor? That's not enough to show that the input is in L. It does happen to be true that both L is in both NP and co-NP (and in fact even in P), but not for any reason of simple negation of output. - Tim === Subject: Re: NP vs. co-NP posting-account=R7AgUAoAAADVFAtIe36IBmgohoHjZsKW Gecko/20080325 Ubuntu/7.10 (gutsy) Firefox/2.0.0.13,gzip(gfe),gzip(gfe) Ok, I see that PRIME is in P and P is the same as co-P. But the question remains: Why can't I negate each NP problem and get that NP=co-NP? === Subject: Re: NP vs. co-NP > Ok, I see that PRIME is in P and P is the same as co-P. But the > question remains: Why can't I negate each NP problem and get that > NP=co-NP? Because for a problem to be in NP, there must be a way to verify a yes answer, but there doesn't have to be a way to verify a no answer. For example, take CLIQUE: given a graph G and a positive integer k, does G contain a clique of size k. This is in NP because if the answer is yes, you could guess a clique of size k, and then easily verify that it is a clique and is of size k. But if G does not have a clique of size k, there is no known polynomial-time way to verify that fact. So the negation of CLIQUE is not, as far as we know, in NP, i.e. CLIQUE may not be in co-NP. -- Robert Israel israel@math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: Finding minimum in arithmetic series modulo N > Consider the sequence of values generated by: > x(k) = (A + kD) mod N > where A, D and N are positive non-zero integers, and k takes values 0, > 1, 2 ... M-1. > Other then brute force search, is there is a way to determine the > minimum value for x(k) and the value of k for which that minimum value > occurs. Here's an idea to consider; still a brute force search, but > with a good chance of terminating much earlier than when > Euclid's algorithm, let a,b be such that 1 = aD+bN, so that > aD == 1 mod N. Let i be the smallest integer such that > 0 < -a + iN < N. (i exists since (D,N) = 1.) > Let c = -a+iN and k = Ac mod N. (Now A + kD == 0 mod N.) > Until k is in range, set k to k+a mod N. > Afterward, compute min = A+kD modulo N. > (I haven't figured out how to adapt this if gcd(D,N) > 1.) Hmm... if d = gcd(D,N) > 1, surely you could just take D' = D/d, N' = N/d and A' = floor(A/d), so that gcd(D',N') = 1, and apply your method (or any other) to these reduced values? Anyway, let me see if I understood your suggestion correctly: 1. Assume gcd(D,N) = 1 and A > 0. 2. Choose 0 < a < N such that aD mod N = 1 using Euclid's algorithm. 3. Let k := -aA mod N (= (N-a)A mod N). 4. If k < M, let k_min := k and stop. 5. Otherwise, let k := k+a mod N and return to step 4. The loop over steps 4 and 5 can take no more than N/a iterations. The number of iterations may be further reduced, especially if a is small, by changing step 5 to let k := k-N mod a (= k-N+aN mod a). This makes the loop terminate in at most min(a, N/a) iterations (and in particular, if a < M, in at most one iteration). The expected number of iterations should in any case be roughly inversely proportional to M; for very low M, it may be faster to just check all possible 0 <= k < M instead. -- Ilmari Karonen To reply by e-mail, please replace .invalid with .net in address. === Subject: Re: Finding minimum in arithmetic series modulo N > When considering the sequence of floor(N/D) iterations, the > resulting sequence is decreasing, I think, if D < N, and increasing > if D > N. (There is a trivial result if D = N.) If D > N then the sequence is identical to one with D' = D mod N. > I do wonder if there's a more efficient approach. I doubt it. This approach has the same complexity as the Euclidean algorithm. - Tim === Subject: Re: Integer factorization, etc. > Pubkeybreaker is Robert Silverman, also known as Bob Silverman, the > Prince of Primes. Robert did seminal work with RSA Labs in the study of the math of > public keys and both trying to break them and make them safer/ > stronger. I reckon that may be the reason for his handle, but I'm > guessing. Robert Silverman is a true math legend. He has likely published more > important math papers than the amount of years you've been alive. He > has worked for decades and produced at the highest levels of math and > crypto in the trenches of real work and discovery in this world. You really should get your Google on and see what I'm talking about, > and when you do you will also see that Bob (Pubkeybreaker) has a > record of not suffering fools easily. It is also very safe to say that he (Pubkeybreaker) has forgotten more > about the subject you are on than you will ever know. I recommend you both show some respect and really try hard to see his > point. None of the above, though, is inconsistent with being a jerk. -- --Tim Smith === Subject: Re: Integer factorization, etc. posting-account=a6woBRAAAADpNFZJBA7ZBx35zXaKmaP4 Gecko/20080311 Firefox/2.0.0.13,gzip(gfe),gzip(gfe) > You really should get your Google on and see what I'm talking about, > and when you do you will also see that Bob (Pubkeybreaker) has a > record of not suffering fools easily. > It is also very safe to say that he (Pubkeybreaker) has forgotten more > about the subject you are on than you will ever know. > I recommend you both show some respect and really try hard to see his > point. Am I the only one who feels a curious loss at learning this? One of my favorite book authors and one of more coherent >frequent newsgroup contributors turn out to be the same >person. Somehow I feel I now have fewer folk heroes to >look up to... I think you might be confusing two different Silvermans. I suspect the author you alluded to is Joseph H. Silverman quasi Ah, right you are! Equilibrium restored (for now). --c === Subject: Re: Base Converter Calcultor > Int2Dec allows converting base 10 numbers to any base between 2 and 16 > (inclusive). You may enter -ve numbers as well. Download it for free athttp://www.thinkanddone.com/prog/cs/integer2decimal.html When I want base conversion, I use Python. Can do base 2 to base 36 inclusive: I use dc. It limits bases to integers > 1. > 7777777777777 base 9 to base 51: $ dc -e '9i 51o 7777777777777 p' > ?05 04 34 32 11 16 39 01 Interesting. Does the use of number pairs instead > of glyphs only happen at large bases or all bases? If so, it wouldn't be of much use in computer > science. It uses the conventional representations for bases > through 16. Here is the output of the conversion of > 666 to base b for b = 2 .. 100 except that I folded > it into columns 26 25 16 51 13 03 76 08 58 > 2 1010011010 27 24 18 52 12 42 77 08 50 > 3 220200 28 23 22 53 12 30 78 08 42 > 4 22122 29 22 28 54 12 18 79 08 34 > 5 10131 30 22 06 55 12 06 80 08 26 > 6 3030 31 21 15 56 11 50 81 08 18 > 7 1641 32 20 26 57 11 39 82 08 10 > 8 1232 33 20 06 58 11 28 83 08 02 > 9 820 34 19 20 59 11 17 84 07 78 > 10 666 35 19 01 60 11 06 85 07 71 > 11 556 36 18 18 61 10 56 86 07 64 > 12 476 37 18 00 62 10 46 87 07 57 > 13 3C3 38 17 20 63 10 36 88 07 50 > 14 358 39 17 03 64 10 26 89 07 43 > 15 2E6 40 16 26 65 10 16 90 07 36 > 16 29A 41 16 10 66 10 06 91 07 29 > 17 02 05 03 42 15 36 67 09 63 92 07 22 > 18 02 01 00 43 15 21 68 09 54 93 07 15 > 19 01 16 01 44 15 06 69 09 45 94 07 08 > 20 01 13 06 45 14 36 70 09 36 95 07 01 > 21 01 10 15 46 14 22 71 09 27 96 06 90 > 22 01 08 06 47 14 08 72 09 18 97 06 84 > 23 01 05 22 48 13 42 73 09 09 98 06 78 > 24 01 03 18 49 13 29 74 09 00 99 06 72 > 25 01 01 16 50 13 16 75 08 66 100 06 66 And here is the dc code. People have gone and invented > inpenetrable computer languages when dc has been available > all along. Whitespace is optional except to separate input > of two numbers. 666sn > 2sb > 100sl > [10o lbdno 32P lnp lbll>i]sx > [lb1+sblxx]si > lxx or > 666sn2sb100sl[10olbdno32Plnplbll>i]sx[lb1+sblxx]silxx Nice. dc -e'[q]sq16i3ADAAA893BE8B8DB1162094FD51711722A89C7[d0=q6D~9+Plxx]dsxx' dc -e'[[dc -e]P39P91PP93P[dx]P39PAP]dx' Much shorter than the C implementation. I should have made more of an effort. dc -e '666 2[d10ono9PpO1+d100! What's wrong with this link? It doesn't work, even for me. In theory it should, but browser support for such URLs is apparently limited; see http://www.cs.tut.fi/~jkorpela/HTML3.2/news.html . -- Ilmari Karonen To reply by e-mail, please replace .invalid with .net in address. === Subject: Re: In need of the revision of the standard theory of logic in the20th century <47FFA342.94C6B9@gmail.com> posting-account=weMSdQoAAADZJGKnAqDaw4DRn4AHCKC4 Did you see http://philosophy.hku.hk/think/sl/properties.php > I have a look at There are no good reasons to define P entails (or material implies) Q by the truth table. === Subject: Re: In need of the revision of the standard theory of logic in the20th century <47FFA342.94C6B9@gmail.com> posting-account=weMSdQoAAADZJGKnAqDaw4DRn4AHCKC4 > Fregeans(including Goedel) have had mistakenly considered that > not-P or Q is equivalent to P implies Q. Actually its not a consideration. Its a definition. > Not-P or Q is equivalent by definition to P materially implies Q. P implies Q is equivalent by definition to not-P or Q is a tautology > (or, more generally, a validity). If so, the problem is whether it is proper or not.81@to define P(materially) implies Qto mean not-P or Q. And the answer is it is improper to do so. === Subject: Re: Help me sort though some complex math posting-account=kTs1ygoAAACgG1TSoyECpovEyy-V6_8b 1.1.4322),gzip(gfe),gzip(gfe) The questions stem from the following URL http://64.233.167.104/search?q=cache:R1ERKgiy5L8J:www.phrack.org/issu... > Such an operation on bytes is called linear mixing and its goal is > to provide the diffusion of information (according to the well known > Shannon theory). Mathematically, it's no more than a linear map > between two GF(2) vector spaces of dimension 128. Indeed, if U and V > are vectors over GF(2) representing respectively the input and the > output of rbytechain() then V = M.U where M is a 128x128 matrix over > GF(2) of the linear map where coefficients of the matrix are trivial > to find. What is a liner map between two GF(2) vector spaces of 128 dimensions? > Actually, I also don't see how they get 128 dimensions. Perhaps some clarification of more basic concepts first is in order: The elements of GF(2) are single bits, with addition corresponding to > the XOR operation (and multiplication to AND). æAnother way of looking > at it is to say that all arithmetic in GF(2) is done modulo 2. A 128-dimensional vector over GF(2) is simply a 128-bit bitstring, > again with addition corresponding to (bitwise) XOR. A linear map g: GF(2)^128 -> GF(2)^128 is a function mapping 128-bit > bitstrings to other 128-bit bitstrings which is compatible with vector > addition (i.e. g(x) XOR g(y) = g(x XOR y)) and scalar multiplication > (which, for vectors over GF(2), simply requires that g(0) = 0 where 0 > is a string of 128 zero bits and is trivially true if the additivity > condition is satisfied). æIt turns out that all such functions can be > represented by multiplication with some 128x128-bit matrix, using the > ordinary definition of matrix multiplication and the GF(2) definitions > of scalar arithmetic (i.e. addition = XOR, multiplication = AND). More concretely: Let x = be a k-bit bitstring, > and let M = [M 1, M 2, ..., M k] be a matrix consisting of k n-bit > bitstrings. æThen y = M * x is an n-bit bitstring given by XORing > together all those bitstrings M i (where 1 <= i <= k) for which the > corresponding bit x i is one. -- > Ilmari Karonen > To reply by e-mail, please replace .invalid with .net in address.- Hide quoted text - - Show quoted text - Okay, let's try this one more time. What would be the matrix consisting of k n-bit bitstrings in chise case? === Subject: Re: Help me sort though some complex math > A linear map g: GF(2)^128 -> GF(2)^128 is a function mapping 128-bit > bitstrings to other 128-bit bitstrings which is compatible with vector > addition (i.e. g(x) XOR g(y) = g(x XOR y)) and scalar multiplication > (which, for vectors over GF(2), simply requires that g(0) = 0 where 0 > is a string of 128 zero bits and is trivially true if the additivity > condition is satisfied). æIt turns out that all such functions can be > represented by multiplication with some 128x128-bit matrix, using the > ordinary definition of matrix multiplication and the GF(2) definitions > of scalar arithmetic (i.e. addition = XOR, multiplication = AND). Okay, let's try this one more time. What would be the matrix consisting of k n-bit bitstrings in chise > case? You mean the one for the function described in your original post? Since I trimmed it from my earlier response, I'll quote it for context below: > rbytechain() is described by the following C function: void rbytechain(unsigned char *block) > { > int i; > for (i = 0; i < DPA_BLOCK_SIZE; ++i) > block[i] ^= block[(i + 1) % DPA_BLOCK_SIZE]; > return; > } where: > - block is the 128b input > - DPA_BLOCK_SIZE equals 16 So block[] is a 128-bit bitstring given as a array of 16 8-bit values block[0] ... block[15]. The operations done by the function can be written out as: block[0] ^= block[1]; block[1] ^= block[2]; block[2] ^= block[3]; block[3] ^= block[4]; block[4] ^= block[5]; block[5] ^= block[6]; block[6] ^= block[7]; block[7] ^= block[8]; block[8] ^= block[9]; block[9] ^= block[10]; block[10] ^= block[11]; block[11] ^= block[12]; block[12] ^= block[13]; block[13] ^= block[14]; block[14] ^= block[15]; block[15] ^= block[0]; (Where, for those unfamiliar with the C language, x ^= y is an operation assigning (x XOR y) to the variable x.) The modification of the array is done in place, so the function rbytechain() doesn't actually return anything, but if we write equate the vector x = with the value of block[] _before_ it is modified by the function (using the obvious correspondence block[0] = , block[1] = , etc.) and the vector y = with the value of block[] _after_ the function call, we can write: y = M * x, where the 128x128 bit matrix M can be built from 8x8 blocks as follows: M = [ I I o o o o o o o o o o o o o o ] [ o I I o o o o o o o o o o o o o ] [ o o I I o o o o o o o o o o o o ] [ o o o I I o o o o o o o o o o o ] [ o o o o I I o o o o o o o o o o ] [ o o o o o I I o o o o o o o o o ] [ o o o o o o I I o o o o o o o o ] [ o o o o o o o I I o o o o o o o ] [ o o o o o o o o I I o o o o o o ] [ o o o o o o o o o I I o o o o o ] [ o o o o o o o o o o I I o o o o ] [ o o o o o o o o o o o I I o o o ] [ o o o o o o o o o o o o I I o o ] [ o o o o o o o o o o o o o I I o ] [ o o o o o o o o o o o o o o I I ] [ I I o o o o o o o o o o o o o I ] where I is the 8x8 identity matrix and o is the 8x8 null matrix. Thus, the elements of the full matrix M will be mostly zeroes, but there will be a line of ones on the main diagonal, another line of ones offset 8 columns to the right of the main diagonal, and 16 ones on two short diagonal lines in the bottom left corner arising from the last XOR operation (block[15] ^= block[0]). The reason why there are _two_ blocks containing ones in the lower left corner is that the function, as specified, does not save the original value of block[0]; by the time block[15] is XORed with it, it has already been XORed with block[1] earlier. -- Ilmari Karonen To reply by e-mail, please replace .invalid with .net in address. === === Subject: math -- (f(x) - f(y))/(x - y) = (x^3 + y^3)*g(x,y) Problem: Does there exist a nonconstant polynomial f in C[x] such that f(x) - f(y) = (x - y)*(x^3 + y^3)*g(x,y) for some g in C[x,y]? quasi === Subject: Re: math -- (f(x) - f(y))/(x - y) = (x^3 + y^3)*g(x,y) >Problem: Does there exist a nonconstant polynomial f in C[x] such that f(x) - f(y) = (x - y)*(x^3 + y^3)*g(x,y) for some g in C[x,y]? When I posted the above problem, I missed the obvious -- it's easy. The answer, as expected, is no. quasi === Subject: Re: math -- (f(x) - f(y))/(x - y) = (x^3 + y^3)*g(x,y) >Problem: >Does there exist a nonconstant polynomial f in C[x] such that > f(x) - f(y) = (x - y)*(x^3 + y^3)*g(x,y) >for some g in C[x,y]? When I posted the above problem, I missed the obvious -- it's easy. The answer, as expected, is no. Oops -- maybe not so obvious. The easy argument I envisioned just fell through. Thus, the problem is still open. quasi === Subject: Linear algebra with pitfall.. Hello teacher~ A, B in Matrix_2x2. E is identity matrix. True or false. (A+B)(A-B) = E ==> AB = BA. === Subject: Re: Linear algebra with pitfall.. > Hello teacher~ A, B in Matrix_2x2. > E is identity matrix. True or false. > (A+B)(A-B) = E ==> AB = BA. > AA + BA - AB - BB = E AA - AB + BA - BB = E BA - AB = - AB + BA AB + BA = BA + AB Hm... === Subject: Re: Linear algebra with pitfall.. > Hello teacher~ > A, B in Matrix_2x2. > E is identity matrix. > True or false. > (A+B)(A-B) = E ==> AB = BA. >AA + BA - AB - BB = E >AA - AB + BA - BB = E BA - AB = - AB + BA AB + BA = BA + AB Hm... You lost an E. quasi === Subject: Re: Linear algebra with pitfall.. >A, B in Matrix_2x2. >E is identity matrix. True or false. >(A+B)(A-B) = E ==> AB = BA. True. Since (A+B)(A-B) = E, A-B is invertible. Thus, there is a C so that (A-B)C = E. Thus, A+B = (A+B)E = (A+B)(A-B)C = EC = C. Therefore, we have that (A-B)(A+B) = E. This means that (A+B)(A-B) = E = (A-B)(A+B) A^2 + BA - AB - B^2 = A^2 + AB - BA - B^2 2 BA = 2 AB AB = BA Rob Johnson take out the trash before replying === Subject: Re: Linear algebra with pitfall.. >A, B in Matrix_2x2. >E is identity matrix. >True or false. >(A+B)(A-B) = E ==> AB = BA. True. Since (A+B)(A-B) = E, A-B is invertible. Thus, there is a C so that >(A-B)C = E. Thus, A+B = (A+B)E = (A+B)(A-B)C = EC = C. Therefore, >we have that (A-B)(A+B) = E. This means that (A+B)(A-B) = E = (A-B)(A+B) A^2 + BA - AB - B^2 = A^2 + AB - BA - B^2 2 BA = 2 AB AB = BA Essentially the same argument, but perhaps slightly simpler to see, (and what I should have seen right away) is the following ... (A + B) (A - B) = E => A + B and A - B are inverses of each other => (A - B) (A + B) = E => (A + B) (A - B) = (A - B) (A + B) => AB = BA (after expanding and simplifying) quasi === Subject: Re: Linear algebra with pitfall.. A, B in Matrix_2x2. >E is identity matrix. True or false. >(A+B)(A-B) = E ==> AB = BA. >True. >Since (A+B)(A-B) = E, A-B is invertible. Thus, there is a C so that >(A-B)C = E. Thus, A+B = (A+B)E = (A+B)(A-B)C = EC = C. Therefore, >we have that (A-B)(A+B) = E. This means that > (A+B)(A-B) = E = (A-B)(A+B) > A^2 + BA - AB - B^2 = A^2 + AB - BA - B^2 > 2 BA = 2 AB > AB = BA Essentially the same argument, but perhaps slightly simpler to see, >(and what I should have seen right away) is the following ... (A + B) (A - B) = E >=> A + B and A - B are inverses of each other >=> (A - B) (A + B) = E >=> (A + B) (A - B) = (A - B) (A + B) >=> AB = BA >(after expanding and simplifying) Here's a quick followup. If A, B are n x n matrices A,B with complex coefficients such that A*(B^2) = I must A commute with B? quasi === Subject: Re: Linear algebra with pitfall.. >A, B in Matrix_2x2. >E is identity matrix. >True or false. >(A+B)(A-B) = E ==> AB = BA. True. Since (A+B)(A-B) = E, A-B is invertible. Thus, there is a C so that >(A-B)C = E. Thus, A+B = (A+B)E = (A+B)(A-B)C = EC = C. Therefore, >we have that (A-B)(A+B) = E. This means that (A+B)(A-B) = E = (A-B)(A+B) A^2 + BA - AB - B^2 = A^2 + AB - BA - B^2 2 BA = 2 AB AB = BA >Essentially the same argument, but perhaps slightly simpler to see, >(and what I should have seen right away) is the following ... >(A + B) (A - B) = E >=> A + B and A - B are inverses of each other >=> (A - B) (A + B) = E >=> (A + B) (A - B) = (A - B) (A + B) >=> AB = BA >(after expanding and simplifying) Here's a quick followup. If A, B are n x n matrices with complex coefficients such that A*(B^2) = I must A commute with B? Ok, the answer is yes (I can prove it). So now, let me ask this ... Question: If A,B are n x n matrices with complex coefficients such that f(A,B)*g(A,B) = 1 for some nonconstant polynomials f,g in C[x,y], must A and B commute? Remark: I suspect the answer is no. quasi === Subject: Re: Linear algebra with pitfall.. >A, B in Matrix_2x2. >E is identity matrix. True or false. >(A+B)(A-B) = E ==> AB = BA. >True. >Since (A+B)(A-B) = E, A-B is invertible. Thus, there is a C so that >(A-B)C = E. Thus, A+B = (A+B)E = (A+B)(A-B)C = EC = C. Therefore, >we have that (A-B)(A+B) = E. This means that > (A+B)(A-B) = E = (A-B)(A+B) > A^2 + BA - AB - B^2 = A^2 + AB - BA - B^2 > 2 BA = 2 AB > AB = BA Essentially the same argument, but perhaps slightly simpler to see, >(and what I should have seen right away) is the following ... (A + B) (A - B) = E >=> A + B and A - B are inverses of each other >=> (A - B) (A + B) = E >=> (A + B) (A - B) = (A - B) (A + B) >=> AB = BA >(after expanding and simplifying) >Here's a quick followup. >If A, B are n x n matrices with complex coefficients such that > A*(B^2) = I >must A commute with B? Ok, the answer is yes (I can prove it). So now, let me ask this ... Question: If A,B are n x n matrices with complex coefficients such that f(A,B)*g(A,B) = 1 for some nonconstant polynomials f,g in C[x,y], must A and B commute? Remark: I suspect the answer is no. If the answer happens to be yes (fat chance, but hey, you never know (until you do)), we could allow f,g to be in C, the ring of polynomials, with coefficients in C, in the non-commuting variables x,y, and then re-ask the same question. quasi === Subject: Re: Linear algebra with pitfall.. >A, B in Matrix_2x2. >E is identity matrix. >True or false. >(A+B)(A-B) = E ==> AB = BA. True. Since (A+B)(A-B) = E, A-B is invertible. Thus, there is a C so that >(A-B)C = E. Thus, A+B = (A+B)E = (A+B)(A-B)C = EC = C. Therefore, >we have that (A-B)(A+B) = E. This means that (A+B)(A-B) = E = (A-B)(A+B) A^2 + BA - AB - B^2 = A^2 + AB - BA - B^2 2 BA = 2 AB AB = BA Sneaky -- finding an inverse yields it's a 2-sided inverse, hence a new equation. quasi === Subject: Re: Linear algebra with pitfall.. >Hello teacher~ A, B in Matrix_2x2. Complex coefficients? >E is identity matrix. True or false. >(A+B)(A-B) = E ==> AB = BA. Seems unlikely. Why would you expect it to be true? quasi === Subject: Re: Linear algebra with pitfall.. >Hello teacher~ >A, B in Matrix_2x2. Complex coefficients? >E is identity matrix. >True or false. >(A+B)(A-B) = E ==> AB = BA. Seems unlikely. Why would you expect it to be true? Well, whether or not you expected it (and as you can see, I didn't), it actually _is_ true (as shown by Rob Johnson's clever solution). quasi === Subject: Re: relative error of product of two variables > Hi http://mathworld.wolfram.com/RelativeError.html > The relative error of the quotient or product of a number of > quantities is less than or equal to the sum of their relative errors. > I am wondering why? I'll be as polite as possible: this statement is approximately true. Using d to denote lowercase delta and following the notation of that page otherwise, you can write: x_0 = x(1 + dx) y_0 = y(1 + dy) Then it is easy to conclude: x_0 y_0 = x y (1 + dx + dy + dx dy) ~= x y (1 + dx + dy) x_0/y_0 = x/y (1 + dx - dy + dy(dy - dx)/(1 + dy)) ~= x/y (1 + dx - dy) provided that dx and dy are small compared to 1, so that (dx dy) and dy^2 are negligeable. In fact, the inequality you mention is true, unless dx > 0 and dy > 0 in the case of multiplication, or unless dx > 0 and dy < 0 in the case of division. -- Niels Diepeveen === Subject: Does a false proposition imply every proposition ? posting-account=weMSdQoAAADZJGKnAqDaw4DRn4AHCKC4 Fregeans have had maintained that a false proposition implies every proposition. However, it is very clear that their view above is totally mistaken. Take for example, The surface of the Earth is a triangle, whichi is a falsity. It does imply The surface of the Earth is not a rectangle but it does not imply The surface of the Earth is round. The truth is that not a falsity but an absurdity (or a contradiction) implies every proposition in the same discourse universe. See === Subject: Re: Does a false proposition imply every proposition ? posting-account=_1L2VwoAAAABLeh6wAVsRU5qDtLWenNS Gecko/20070508 Firefox/1.5.0.12,gzip(gfe),gzip(gfe) > Fregeans have had maintained that a false proposition implies every > proposition. No, they hadn't. A contradiction implies every proposition. And this isn't specific to Frege, but to propositional logic generally. === Subject: Re: Does a false proposition imply every proposition ? > Fregeans have had maintained that a false proposition implies every > proposition. Is a Fregean something like a Cantorian or in which sense are they different? Ciao Karl === === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=yxbZkgkAAABQBvyYeebYQ-PAvi0uT3tG Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) > You seem to saying that since N is a set of finite elements, > N must itself be finite. ?Why? I just posted it. But I repeat it here. N cannot be actually (i.e. > surpassably) infinite because in the infinite triangle o > oo > ooo > ... height and width are identical. Height is the number of naturals, > width is the number of elements in FISONs. (There is no largest one, > but there is also none with infinitely many elements). That is correct. There are an infinite number of rows in your list, just as there are an infinite number of naturals. (I call it a list, since it is not a triangle because it does not have three sides.) And each row is a finite length, just as each natural is a finite number (or set). Therefore there are an infinite number of finite rows in your list, just as there are an infinite number of finite naturals in N. And there is no row of infinite length in the list, just as there is no natural in N that is an infinite natural. This is so simple that a child could understand it. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=yxbZkgkAAABQBvyYeebYQ-PAvi0uT3tG Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) > Removing every finite initial subset of N (FISON) that is not > the largest FISON results in an empty set. Which simply > proves that N does not have a largest finite subset, nor > a largest finite member. Which is the same as saying that > there is no largest natural. > But we already knew that. > You also say that none of the FISs of N is large enough to > cover (biject with) N. Which is the same as saying that > N is not a natural. No, it's not the same. Here we have three equivalent statements for N: > N is an infinite set. There are infinitely many natural numbers. N has > infinitely many elements. On the other hand we have for FISONs: > A FISON is not an infiite set. There is no FISON with infinitely many > natural numbers. And as all FISONs include the 1, the union of FISONs > is a FISON. Well, you got two out of three correct. If the union of all FISONs is itself a FISON, then there is a finite k in N such that FISON(k) is equal to that union. So what is that k? > These properties are not changed when an infinite union of FISONs is > considered. Otherwise we would obtain an infinite finite segment > which is obviously nonsense. True, an infinite finite segment is nonsense. But the union of an infinite number of (different) finite segments is not a finite segment, obviously. Otherwise it would be like saying that the sum of an infinite number of (different) finite naturals is a finite natural. Which is obviously nonsense. > This shows that an actually infinite set of finite numbers is > impossible. When the union of natural numbers is considered, this does > not immediately become clear. An infinite finite segment is more > alarming, I hope. I don't see how the two are related. > The principle is very simple: If you consider the infinite triangle o > oo > ooo > ... Sorry, the infinite /what/? I was taught that triangles have three sides. Your diagram above only has two sides. > then it is easy to believe that the height (vertical sequences) is > infinite. The width cannot become infinite, if the horizontal > sequences are all finite. Then, logically, the width must be finite if it's not infinite. If that's true, then what is that finite width? Are you talking about the width of the third side that does not exist? Or are you talking more generally about the maximum distance between the left side and the right side, which you are saying is finite? > But the symmetry of the triangle shows that > height and width are identical --- no matter how far the triangle is > extended. I agree. > Therefore there is no actual infinity. Finity is simply > going on and on. That's potential infinity. It cannot be surpassed. I think you mean that potential infinity is infinity that is never actually completed. You seem to be contradicting yourself. Is the height of your infinite triangle actually infinite, like you stated earlier, or only potentially infinite, like you're stating now? === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I > The following is valid for linear sets (linear with respect to the > property in question) according to logic, I mean real, unspoilt logic: > In case a sufficient linear set exists, it has a necessary linear > subset. No A simple counterexample is > subsets of N subsets of N are not in linear order in general. > However, N and all its subsets are. But if you prefer A simple counterexample is N and does not have a largest element (note some properties are properties of subsets not of elements, and a linear set can be linear with respect to such a property) A sufficient linear set exists but there is no necessary linear subset. - William Hughes === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > WM says... I'll try to answer this long letter tomorrow, because it's late. For today I'll restrict myself to an easy to understand argument concerning natural numbers and FISONs: o oo ooo ... No matter how far that triangle is extended, width and height are identical. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > WM says... I'll try to answer this long letter tomorrow, because it's late. For > today I'll restrict myself to an easy to understand argument > concerning natural numbers and FISONs: o > oo > ooo > ... No matter how far that triangle is extended, width and height are > identical. And when either has become 'infinite', meaning unbounded, so has the other. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > ... And when either has become 'infinite', meaning unbounded, so has the > other. That that would often imply their ratio is one, off into infinity, as a result of asymptotics, delta-epsilon and the whole bit, corresponds well with the notion of limit having any kind of well-defined meaning, for infinities. In the finite balanced binary tree, the ratio of nodes to paths as the count of levels diverges is two. In the infinite balanced binary tree, where any two paths, bit sequences, bitstreams, omega words with alphabet {0,1}, binary coded powersets of naturals, any two paths are distinct: limit loses real application, its foundation. Synthesize a fractal in a semi-infinite region of integration, that doubles in difference areas over the region, the limit no longer equals two, instead it's zero. That's about there being a binary tree of connected regions, in the correspondence between classical analysis and geometric area, the asymptotic limit of nodes to paths is 2:1, in connecting a node interior to the region through a boundary partitioning another region. Where instead in that construction there are infinitely many times more paths than nodes, the exponential 2^x, which happens to be the expression of nodes in terms of levels, that the limit fails to represent the sum, breaks the correspondence between integral and area. Ross === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > So a segment is useful and necessary when there is no larger segment. æAs > there is no largest segment, none of the segments is useful and necessary. > That does *still* not mean that you can remove *all* of them. For all of them we have: There is a larger one. forall FISON we have that! And we can remove all which are not the largest. Consider the following: I n = {1, ..., n}. æS = union [I 1, I 2, I 3, I 4]. > A segment is useful and necessary to cover 1 when there is no other segment > that covers 1. æClearly none of the segments is useful or necessary to > cover 1. æ I n is necessary, because there is no larger one. In this case useful and necessary are not identical. I 4 ... I n are all sufficient. > Nevertheless you can not remove all segments and still have 1 > covered. æThat is, while the individual segments are not useful or necessary, > it is not true that the collection of *all* of them is not useful or > necessary. No, see above. æ> æ> You are wrong. For every finite initial segment (in future I will use > æ> æ> FISON, I have seen it here already and it sound well) so for each of > æ> æ> the infinitely many FISONs there is a larger one. > æ æ> Yes. æBut this still is no proof. > æ æ> You should not reject everything that you don't understand, but rather > æ> try to understand. See above. Sorry, you did not understand. See above. æ> æ> No. I can remove every which is not a largest. That are infinitely > æ> æ> many, namely all. > æ æ> No, that is something you can not prove. > æ æ> I can remove every FISON which is not the largest, because being not > æ> the largest implies that there is a larger one. The existence of a > æ> larger one makes the use of the smaller one obsolete. This is a proof > æ> that I can remove every FISION. That is no proof of what you think. æIt proves that you can remove as > many as you wish *as long as there remains a larger one than the > largest one you did remove*. æSo you can remove each FISON individually, > but *not* all of them. æMoreover, when you remove the FISONs one by one > you will never end up having removed all of them. That's the same with the natural numbers. You cannot have all n, because everyone need have a larger one. But if you nevertheless believe that it is possible to have all, then you can also have all FISONs in the removed set. They are removed not one by one, but all together. (Similarly, adding natural numbers one by one you will never have an infinite set.) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor So a segment is useful and necessary when there is no larger segment. æAs > there is no largest segment, none of the segments is useful and > necessary. > That does *still* not mean that you can remove *all* of them. Not outside of WM's mytheology. in side that mytheology, WM can do whatever he wants, but outside mytheology one can only eliminate finitely many fisons without elimiating N. For all of them we have: There is a larger one. forall FISON we have > that! And we can remove all which are not the largest. We can remove any one fison and still cover N, or any finite number of them and still cover N, but not necessarily all of them and still cover N, unless there are only finitely many to start with Oor unless one is stuck in WM's anti-mathematical mytheology. Consider the following: I_n = {1, ..., n}. æS = union [I_1, I_2, I_3, I_4]. > A segment is useful and necessary to cover 1 when there is no other segment > that covers 1. æClearly none of the segments is useful or necessary to > cover 1. æ I_n is necessary, because there is no larger one. I_n is NOT necessary while there is a smaller one covering 1., stupid. In this case useful > and necessary are not identical. I_4 ... I_n are all sufficient but no single one is necessary to cover 1. Nevertheless you can not remove all segments and still have 1 > covered. æThat is, while the individual segments are not useful or > necessary, > it is not true that the collection of *all* of them is not useful or > necessary. No, see above. Yes, see above! > See above. Sorry, you did not understand. See above. We understand a lot of things that you do not understand, including your incompetence at things mathematical and logical. æ> æ> No. I can remove every which is not a largest. That are infinitely > æ> æ> many, namely all. > æ æ> No, that is something you can not prove. > æ æ> I can remove every FISON which is not the largest Then WM is claiming that N is empty, because WM claims to be able to remove every one of its elements without changing it. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > ... > æ> æ> æ> æ> What is time itself, if not measured? > æ> æ> æ æ> æ> æ> Just that, time. > æ> æ> æ æ> æ> æ> What time? Travelling with what velocity? Running relatively to > æ> æ> æ> what clock? > æ> æ æ> æ> Irrelevant. > æ> æ æ> æ> Not for the speed of time. > æ æ> We were not talking about the *speed* of time. > æ æ> That does not prove that time is absolute. Where did I state any such thing? > WM: What is time itself, if not measured? DTW: Just that, time. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=-eQqtQoAAACZVM-kNEsOn3k7GSvoJoS4 MathPlayer 2.0; .NET CLR 1.1.4322; InfoPath.1; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) YOUR REASONING IS INVALID > Have you ever heard of the theorem that the limit of the ratio is the > ratio of the limits, if existing, for converging sequences? > Now consider the sequences 1/L(X), 1/N(X) and (1/L(X))/(1/N(X)) where > X is in N. It's been several months and several thousand posts since I've > posted in this thread. I must admit that WM's reasoning is persuasive, here. As he's been > doing for the last 4000+ posts, he's wondering why there aren't more > paths as nodes in the finite case, but strictly more paths than nodes > in the finite case. Now he's using ratios. It's posts like these that warrant all the effort of keeping up with this thread. The problem with WM's geometric arguments about the tree is that they *are* damn persuasive, mostly because there is so little machinery available. But it is not too hard to figure out and explain the sleight of hand: The basic picture | o / does not work properly in the infinite case. Let's look at the argument: WM says that at every node one new line starts. (The vertical line comes from the previous node and continues on the left, while a new line starts on the right.) The problem is that in an infinite tree the slanted lines are in reality not single paths, but in themselves fully branching binary trees, and at every node further down the line you must make a choice of a single branch. Let's say you arbitrarily choose the left branch as the continuation. Then the two lines in the basic picture (ignoring any other branches for now) actually look like this: | o / o o / / o o / / o o / / .. .. What this picture shows is that in order to be counted, a line must end with an infinite sequence of left branches. Now consider the path that alternates left and right branches forever. At no finite level will this path ever be counted, because it does not fit the pattern for a line. Yet it is abundantly clear that the path is in the tree. Hence WM's counting method is inadequate. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) The basic picture > æ æ æ | > æ æ æ o > æ æ æ/ does not work properly in the infinite case. It is completely independent of the number of levels of the tree. > Let's look at the > argument: WM says that at every node one new line starts. (The > vertical line comes from the previous node and continues on the > left, while a new line starts on the right.) The problem is that in > an infinite tree the slanted lines are in reality not single paths, > but in themselves fully branching binary trees, and for every tree we have the same situation again, such that this explanation does not explain anything. > and at every node > further down the line you must make a choice of a single branch. You need not make a choice. The complete tree itself chooses every possible path. Let's say you arbitrarily choose the left branch as the continuation. > Then the two lines in the basic picture (ignoring any other branches > for now) actually look like this: > æ æ æ æ æ| > æ æ æ æ æo > æ æ æ æ / > æ æ æ æo æ o > æ æ æ / æ / > æ æ æo æ o > æ æ / æ / > æ æo æ o > æ / æ / > æ.. æ.. What this picture shows is that in order to be counted, a line must > end with an infinite sequence of left branches. No. You forget a lot of nodes in your picture of the CIBT --- or you forget the C. Now consider the path that alternates left and right branches forever. > At no finite level will this path ever be counted, At no finite level it is distinct from every other path. Alas, here are only finite levels in the tree. > because it does not > fit the pattern for a line. Yet it is abundantly clear that the path > is in the tree. > And it is as clear that for every other tree there is a node, where this path and the other split off. Otherwise this path could not exist in the tree. How can you be so short sighted? === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > The basic picture > æ æ æ | > æ æ æ o > æ æ æ/ does not work properly in the infinite case. It is completely independent of the number of levels of the tree. If does not prove anything about even finite cases. For one thing, it seems to indicate that for each node there are three edges, which is not true for any binary tree,. Let's look at the > argument: WM says that at every node one new line starts. (The > vertical line comes from the previous node and continues on the > left, while a new line starts on the right.) The problem is that in > an infinite tree the slanted lines are in reality not single paths, > but in themselves fully branching binary trees, and for every tree we have the same situation again, such that this > explanation does not explain anything. It explains why no line in the complete infinite binary tree is anything less than a complete infinite binary tree. and at every node > further down the line you must make a choice of a single branch. You need not make a choice. The complete tree itself chooses every > possible path. Trees do not chose paths, they contain them. Finite trees contain only finitely many paths, infinite trees, other than unary ones, contain countably many infinite trees and uncountably many infinite paths. Let's say you arbitrarily choose the left branch as the continuation. > Then the two lines in the basic picture (ignoring any other branches > for now) actually look like this: > æ æ æ æ æ| > æ æ æ æ æo > æ æ æ æ / > æ æ æ æo æ o > æ æ æ / æ / > æ æ æo æ o > æ æ / æ / > æ æo æ o > æ / æ / > æ.. æ.. What this picture shows is that in order to be counted, a line must > end with an infinite sequence of left branches. But since most paths don't end that way, or with any other periodic pattern of left-right branchings, of they cannot be counted, which is the whole point! No. You forget a lot of nodes in your picture of the CIBT --- or you > forget the C. Our picture of a CIBT omits nothing, not even those many paths that WM's trees all manage to omit. Now consider the path that alternates left and right branches forever. > At no finite level will this path ever be counted, At no finite level it is distinct from every other path. At no FINITE level is ANY path distinct from EVERY OTHER path. Not even in WM's incomplete infinite trees. > Alas, here > are only finite levels in the tree. At what finite level of such a tree is any path distinct from EVERY other path? It does not ever happen even in WM's infinite trees. because it does not > fit the pattern for a line. Yet it is abundantly clear that the path > is in the tree. And it is as clear that for every other tree there is a node, where > this path and the other split off. At what node does any path manage to be separate from ALL other paths, unless it is in a finite tee and is a terminal node? > Otherwise this path could not exist > in the tree. How can you be so short sighted? Compared to WM's mytheological myopia, we are all remarkably far sighted. > === Subject: Re: Eigenvector calculation by hand versus computer--getting different answers posting-account=_1L2VwoAAAABLeh6wAVsRU5qDtLWenNS Gecko/20070508 Firefox/1.5.0.12,gzip(gfe),gzip(gfe) On Apr 10, 11:27 pm, Tim Little You have a nasty case of round-off error. If you used the *exact* > eigenvalues, they'd be multiples. Since you only used approximations, > they aren't. >As I just pointed out, this was not the problem. I appreciate the >suggestion, though. No, that _was_ the problem. At least that's the problem with > the math and/or your understanding of it. No, it wasn't the problem. It is easy to reproduce the error I am mentioning, with the Matlab code I provided. It has nothing to do with rounding error, it has to do with me not realizing Matlab was doing strange things to the matrices when I mixed symbolic and floating representations. Yes, I made a mistake by calling a zero vector an eigenvector. > If you're using floating-point values then you are _not_ using > the exact eigenvalues, just better approximations! Hence you > get the wrong answer, indentity matrix for the echelon form. No, that is not why. See above, and see how my fix works, which it wouldn't if you were right. > Then later you say that when you do something, It works. > It's not clear to me what you mean by It works: does > that mean that it agrees with your impossible result about > the matrix being invertible and zero being an eigenvector, > or does that mean that it correctly says that the matrix is > not invertible and gives a non-zero eigenvector. The latter. It gives the correct result now. I never claimed the weird result was correct. I knew it was incorrect, and couldn't figure out why. That's why I posted. 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C. > Hibbeler.rar - 386587703 bytes > [Solutions manual] Oppenheim's Discrete Time Signal Processing > text.pdf - 7683829 bytes > [Solutions Manual] Probability And Statistics For Engineers And > Scientists .pdf - 5451525 bytes > [Solutions manual] Probability and Statistics for Engineers and > Scientists Manual HAYLER.pdf - 5459130 bytes > [Solutions Manual] Signals And Systems - 2nd Ed.- Oppenheim & > Wilsky.pdf - 182092264 bytes > [Solutions Manual] Signals and Systems 2nd Ed. - Haykin.pdf - 4605950 > bytes > [Solutions Manual] Thermodynamics - An Engineering Approach, 5Th > Cengal Boles.rar - 27314711 bytes > [Solutions Manual] University Physics - Sears and Zemansky's 11th > Ed.rar - 89269962 bytes > [Solu.8d.8bo dos problemas] Redes de Computadores - 4a ed. - ANDREW S. > TANENBAUM.pdf - 253221 bytes > A Guide to Physics Problems, Part 1 & Part 2 - Mechanics, Relativity, > and Electrodynamics and Thermodynamics,... > A Guide to Physics Problems, Part 1 & Part 2 - Mechanics, Relativity, > and Electrodynamics and Thermodynamics,... > A Guide to Physics Problems, Part 1 & Part 2 - Mechanics, Relativity, > and Electrodynamics and Thermodynamics,... > A Guide to Physics Problems, Part 1 - Mechanics, Relativity, and > Electrodynamics and Part 2 - Thermodynamics, Stati... > Manual.pdf - 1099572 bytes > Classical Mechanics - Goldstein Solved problems.pdf - 568477 bytes > Daniel Shanks - Solved And Unsolved Problems In Number Theory (2Nd > Ed), 1978.pdf - 12806778 bytes > Electric Machinery Fundamentals (Solutions Manual).doc - 3437568 > bytes > Elementary Differential Equations And Boundary Value Problems, 7Th Ed > - Boyce And Diprima Student Solutions Manual,... > Fundamentals of Logic Design 5Ed - Charles Roth - Solutions > Manual.pdf > - 7480931 bytes > Fundamentals of Thermodynamics 6th Ed (Solutions Manual) - Sonntag- > Borgnakke-Van Wylen.pdf - 21734813 bytes > Griffiths, David - Introduction To Electrodynamics Solutions Manual - > With Update.pdf - 88965016 bytes > Halliday, Resnick - Fundamentals Of Physics - 7Th Edition Instructors > Solutions Manual.rar - 21815286 bytes > Instructor's Solutions Manual - Marion, Thornton - Classical Dynamics > Instructors Solution Manual, Static- Meriam and L. G. Kraige.pdf - > 88821441 bytes > Introduction To Algorithms 2Nd Edition > Solutions(Instructor's.Manual).pdf - 1743296 bytes > Introduction to Probability - Solutions Manual.pdf - 630162 bytes > Juvinall, Marshek - Fundamentals of Machine Component Design, 3rd ed > - > Student Solutions Manual.pdf - 8771959 bytes > McgrawHill - William H. Hayt, John A. Buck - Engineering > Electromagnetics, 6th Edition Solutions Manual !!!!!!!!!!!... > Microwave Engineering 3E - David M Pozar - Solutions Manual.pdf - > 11552244 bytes > Microwave Engineering 3e - David M Pozar - Solutions Manual.rar - > 11393823 bytes > Munson - Young - Okiishi.rar - 370925506 bytes > Operating Systems Concepts 6th + SOLUTIONS MANUAL !!!.rar - 15530414 > bytes > Physical Chemistry 7ed - Peter Atkins - Julio de Paula - instructors > solution manual.rar - 8265455 bytes > Physics For Scientists And Engineers 6E By Serway And Jewett - > Solutions Manual Vol 2.pdf - 5916198 bytes > Proakis J. (2002) Communication Systems Engineering - Solutions > Manual > (299s).pdf - 1590792 bytes > Probability and Statistics for Engineering and the Sciences (with CD- > ROM and InfoTrac ) (Hardcover) by Jay L. Devor... > Probability Random Variables and Stochastic Processes Solutions > Manual.Papoulis.McGraw Hill.2002.pdf - 17104321 bytes > Problemas resueltos de Estad.92stica I.rar - 146917 bytes > Rubik - Solucao Do Cubo Magico.pdf - 229621 bytes > Schaums Mathematical Handbook of Formulas and Tables.pdf - 27472908 > bytes > Signal Processing and Linear Systems - B P Lathi - Solutions > Manual.pdf - 11426876 bytes > Solution Manual to engineering fluid mechanics 7e.pdf - 4351863 bytes > Solution To Two-Dimensional Incompressible Navier-Stokes Equations- > Maciej Matyka.pdf - 382211 bytes > Thomas' Calculus, Early Trascendentals 10th ed Instructors Solutions > Torrent downloaded from Demonoid.com.txt - 47 bytes > Wankat & Oreovicz - Teaching Engineering.rar - 932934 bytes > Wiley - Pozar - Microwave Engineering 3ed - Solutions Manual.rar - > 11394069 bytes > Wiley Chemical And Engineering Thermodynamics 3Ed Solutions > Manual.pdf > - 11188449 bytes > Zwillinger D. et al - CRC Standard Probability and Statistic Tables > and Formulae (1999).pdf mail: > lsms4@yahoo.com email: lsms4[at]yahoo.com === Subject: Re: Integer solutions for 60 and 120 degree triangles >I don't know, but here's some data to play with ... > 1, 1, 1 > 3, 7, 8 > 5, 7, 8 > 7, 13, 15 > 8, 13, 15 > 5, 19, 21 > 16, 19, 21 > 11, 31, 35 > 24, 31, 35 > 7, 37, 40 > 33, 37, 40 > 13, 43, 48 > 35, 43, 48 > 16, 49, 55 > 39, 49, 55 > 9, 61, 65 > 56, 61, 65 > 32, 67, 77 > 45, 67, 77 > 17, 73, 80 > 63, 73, 80 > 40, 79, 91 > 51, 79, 91 > 11, 91, 96 > 85, 91, 96 > 19, 91, 99 > 80, 91, 99 G'day G'day Quasi and Rob, Well play with the did is exactly what I did. Quasi had arranged his triples in order from shortest side to longest side. This brought out the pattern where apart from (1,1,1) they appeared in pairs. These pairs corresponded to one 60 degree triangle with two acute angles while the other one had contained and obtuse triangle as Rob pointed out in his solutions. I wanted to see if Rob's method of generating 60 degree triangles would provide the same set of triangles or whether one method would generate more than the other. An interesting possibility. So I used Excel to sort Rob data into the same form as Quasi's. There was only one different. This was probably a matter of the range of values covered. Whatever. I'm delighted to have the collection of triples which I can now use to prepare examples of phasor addition for electrical technicians. I'm very much an amateur mathematician and admire those who make it look simple but I'm a keen consumer. -- Quentin Grady ^ ^ / New Zealand, >#,#< [ / / ... and the blind dog was leading. http://homepages.paradise.net.nz/quentin === Subject: Proof by contradiction posting-account=sEiFsQoAAACi5Qt8ldP1A_wH2hdeku01 Gecko/20080311 Firefox/2.0.0.13,gzip(gfe),gzip(gfe) I'm having trouble with this proof: if n is an integer, and if log_2_n is rational, proof that log_2_n must be integer. Can anyone help? the base of the log is 2. === Subject: Re: Proof by contradiction >I'm having trouble with this proof: if n is an integer, and if log_2_n is rational, proof that log_2_n >must be integer. Can anyone help? the base of the log is 2. Suppose log_2(n) = p/q where p, q integers and the fraction is reduced to lowest terms. Then 2^(p/q) = n so 2^p = n^q What can n have for factors? Can you get a contradiction from this? --Lynn === Subject: Re: Proof by contradiction posting-account=sEiFsQoAAACi5Qt8ldP1A_wH2hdeku01 Gecko/20080311 Firefox/2.0.0.13,gzip(gfe),gzip(gfe) I'm having trouble with thisproof: if n is an integer, and if log_2_n is rational,proof that log_2_n >must be integer. Can anyone help? the base of the log is 2. Suppose log_2(n) = p/q where p, q integers and the fraction is reduced > to lowest terms. Then 2^(p/q) = n so 2^p = n^q What can n have for factors? Can you get a contradictionfrom this? --Lynn from 2^p = n^q, we can see that for the since all p, q, and n are integer: n must be an even integer and it must be in the from of (2^k) where k is an integer. therefore 2^p = (2^k)^q => 2^p = 2^(kq) so p = kq => p/q = k. but from our assumption that p/q has been reduced to lowest terms so k can't be an integer. <- here is the contradiction. is this right? === Subject: Re: Proof by contradiction >I'm having trouble with thisproof: >if n is an integer, and if log_2_n is rational,proof that log_2_n >must be integer. >Can anyone help? the base of the log is 2. > Suppose log_2(n) = p/q where p, q integers and the fraction is reduced > to lowest terms. > Then 2^(p/q) = n so 2^p = n^q > What can n have for factors? Can you get a contradictionfrom this? > --Lynn from 2^p = n^q, we can see that for the since all p, q, and n are >integer: n must be an even integer and it must be in the from of (2^k) >where k is an integer. >therefore 2^p = (2^k)^q => 2^p = 2^(kq) so p = kq => p/q = k. >but from our assumption that p/q has been reduced to lowest terms so k >can't be an integer. <- here is the contradiction. is this right? > That's the idea. If you are going to use an indirect proof, be sure to state your hypothesis with a little more care than I did, by assuming that log_2(n) = p/q where p, q integers, the fraction is reduced to lowest terms, and q not equal 1, so it isn't an integer. Actually, there is no real reason to use an indirect proof in the first place unless it is required for some reason. The argument shows that if it is rational then it is an integer... --Lynn === Subject: good time with math -sEung b. Kim posting-account=qttmhgkAAAChICW4cnappYtBT9kM3JuS CLR 1.1.4322),gzip(gfe),gzip(gfe) The Mass of the Ass / the torque of the pork = heat of the meat 2)the torque of the pork * the heat of the meat = the speed of the Deed a)the speed of the deed * the mass of the Ass = the torque of the pork b)heat of the meat ^ the speed of the deed = fin. mass in the Ass - sEung b. Kim I Divide, I Multiply, I subtract by 1 and simplify..I Divide, I Multiply, I subtract by 1 and simplify..I Divide, I Multiply, I subtract by 1 and simplify.. -sbk === Subject: Re: good time with math -sEung b. Kim > The Mass of the Ass / the torque of the pork = heat of the meat The angle of the dangle is directly proportional to the mass of the ass, providing the heat of the meat is consistent. === Subject: Volume of triangular solid Is there a simple way to calculate the volume of a triangular section solid? scooper === Subject: Re: Volume of triangular solid >Is there a simple way to calculate the volume of a triangular section solid? >scooper > Yes, but it depends on what you mean. If you are talking about a triangular pyramid (tetrahedron) volume is (1/3)*Area of base*height. If you mean a solid with constant triangular cross-section such as a prism, leave off the (1/3). If you mean something else, please elaborate. --Lynn === Subject: Re: Volume of triangular solid > Is there a simple way to calculate the volume of a triangular section > solid? scooper If we know the lengths edges, yes. But one mans simple is another mans headache. === Subject: Re: Volume of triangular solid > Is there a simple way to calculate the volume of a triangular section > solid? scooper Not sure of what you're asking for. The volume of a triangle is (1/2)bh -- Jim Langston tazmaster@rocketmail.com === === Subject: Re: JSH: James Harris Surrogate Factors RSA-100 and Louis Freeh asked Congress to raise : to 3,000 the number of FBI agents working counter-intelligence and counter- : terrorism. : : With the new legislation, the funding for just the FBI's counter-intelli- : gence/terror goals is now ONE BILLION DOLLARS a year, and their activities : will rise to a LEVEL HIGHER THAN AT ANY TIME DURING THE COLD WAR. 1984 means a constant State of War. Here's a new war: cyberwar. # Head of CIA Plans Center To Protect Federal Computers # By Tim Weiner, The New York Times, 6/26/96 # # John Deutch, Director of the CIA, is building a cyberwar center in the NSA. # # Mr. Deutch said cyberwar could become a 21st-century national security threat # second only to nuclear, biological and chemical weapons. # # The electron, Mr. Deutch warned, is the ultimate precision-guided weapon. Haven't I heard bad dialogue like this on Mystery Science Theater 3000? It is simply another in an endless series of requests for funding, for misuse of our tax money. ---- Louis Freeh's FBI: * FBI Scare Tactics, By Richard Moran, The New York Times, 1996 * * When the FBI reported that serious crime declined for the fourth year * in a row, it was still making the statistics sound worse than they * actually were. * * That's because Government tends to exaggerate the violent nature of crime. * * According to the Justice Department's Bureau of Justice Statistics, less * than a third of the 6.6 million violent crimes committed in the U.S in 1992 * resulted in injury; most of the victims suffered only minor cuts, scratches * or bruises. * * About 20 percent of them needed minor medical care; 7 percent went to * emergency rooms. Only 1 percent of the victims were hurt seriously enough * to require h === Subject: Re: JSH: James Harris Surrogate Factors RSA-100 ----------------------------------- * Air Force News Agency : DSN: 945-1281 * AFNEWS/IICT : (210) 925-1281 * 203 Norton Street : sysop@afnews.pa.af.mil * Kelly AFB, TX 78241-6105 : ftp.pa.af.mil * ---------------------------------------------------------------------- Read car's license plates at night? Phillips's Lasers and Imaging Directorate? What is this? * http://www.rockwell.com/te/itsinca.html * * TraffiCam Vehicle Detection Sensor * * Rockwell is working with a variety of state and local authorities, * including several in California, for the introduction of a new, advanced * technology sensor called TraffiCam. The sensor uses machine vision * technology to detect vehicles. The capabilities of the sensor make it * useful for a variety of applications, including freeway surveillance Ugh oh, 'machine vision', I don't like the sound of that... * http://hippo.mit.edu/projects/projects.html#sensor * * NEW TRAFFIC SENSOR TECHNOLOGY * * MIT was responsible for the concept, overall design, and testing of the * sensor. Travel time is measured by video license plate recognition or * radio transponders. Video recognition of the license plate if no transponder!!! === === Subject: Re: JSH: James Harris Surrogate Factors RSA-100 government uses these wars to claim ever greater power over us. To justify violent no-knock searches by agents not even carrying warrants. To justify killing the 'exclusion rule' to protect police not citizens. To justify draconian asset forfeiture laws. To justify using deadly force. It's no longer the 1920s, but our government still has reefer madness. In another astonishing case of corruption due to Congressional asset forfeiture laws, and yet another violent result of marijuana's Schedule I Substances classification: Trail's End. It was owned by a private family. They refused to sell. The reporter is in the helicopter with the agent who identified marijuana growing on the property from an identical helicopter fly-over. The agent said he specializes in that sort of thing, and he was flown over the property for an evaluation. He told the other federal agents that he could not determine that there was any. The G-MEN flew him over again: they pressured me to change my evaluation, and I did, even though I couldn't detect any marijuana. They got me to say 'maybe I see some for sure'. A large multi-departmental group of federal and county agents stormed the house, and shot the male owner to death. The widow continues to live there. Before moving in, law enforcement had the property appraised for its value. Eventually, the county admitted it wanted the property. This is our Drug War for national security reasons. The government now says it regrets calling it a Drug War. Then appointed a retired Military === Subject: Re: JSH: James Harris Surrogate Factors RSA-100 twenty times more * than it did when the program began in 1985. And what were some of the reasons of the dramatic increase in forfeitures between 1985 and 1993? What caused it to increase by more than a MAGNITUDE? * Above the Law, by David Burnham, ISBN 0-684-80699-1, 1996 * * In June 1989, the Deputy Attorney General ordered the nation's U.S. * attorneys to take all possible actions on forfeitures, even if it meant * dropping other matters. You will be expected to divert personnel from * other activities. * * One year later, the Attorney General himself warned the U.S. attorneys * that the Justice Department had fallen far behind its budget projection * in the collection of assets. We must significantly increase production * to reach our budget target... Failure to achieve the $470 million * projection would expose the Department's forfeiture program to criticism * and undermine confidence in our budget projections. Every effort must be * made to increase forfeiture income during the remaining three months of * fiscal year 1990. * * In addition, forfeiture activities affect === Subject: Re: JSH: James Harris Surrogate Factors RSA-100 it arrives at the station. This is the work of the Dictionary program. It reads every word and number in every single incoming message and picks out all the ones containing target keywords and numbers. Thousands of simultaneous messages are read in 'real time' as they pour into the station, hour after hour, day after day, as the computer finds intelligence needles in the telecommunications haystack. Telephone calls containing keywords are automatically extracted from the masses of other calls and digitally recorded to be listened to by analysts back in the agency headquarters. The implications of this capability are immense. The UKUSA agencies can use machines to search through all the telephone calls in the world, just as they do for written messages. It has nothing to do with whether someone is deliberately tapping your phone, simply whether you say a keyword or combination of keywords that is of interest to one of the UKUSA agencies. P47 The keywords include such things as names of people, ships, organizations, countries and subjects. They also include the known telex and phone numbers and Internet addresses of the individuals, businesses, organizations and government offices they may want to target. The agencies also specify combinations of these keywords to help sift out communications of interest. For example, they might search for diplomatic cables containing both the words 'Suva' and 'aid', or cables containing the word 'Suva' but NOT the word 'consul' (to avoid the masses of routine consular communications). It is these sets of words and numbers (and combinations of them), under a particular category, that are plac === Subject: Re: JSH: James Harris Surrogate Factors RSA-100 the Waco compound came after she had discussions with senior It is a Challenger type disaster, where public pressure caused them to screw up. The same irony: they didn't want to look bad. Janet Reno was asked to take off her safety hat and put on her management hat. She did. She's a good ol' boy. My apolitical reasons for saying Janet Reno's decision to move against Waco the way they did was reckless endangerment of life, entirely from C-SPAN testimony: o pumped in CS tear gas, which the US has signed a chemical weapons treaty not to use against countries we go to war against. They were aware of the indoor lethal capabilities of C.S. gas, because these were spelled out in the manual. o pumped in an extra heavy amount of it due to OUTSIDE winds. o Reno had NO reliable data from her FBI-referred military expert on the affects of the gas on children or the elderly, yet proceeded. o turned off the electricity, and knew they were using candles as a result. The F.B.I. and the A.T.F. were fully aware that the Davidians were using kerosene lanterns inside the compound both day and night. They knew this because they had infrared surveillance equipment i === Subject: Re: JSH: James Harris Surrogate Factors RSA-100 * * All federal agencies are being integrated into this data net. These Police * State agencies constitute a clear and present danger, not only to the * privacy and constitutional rights of Americans but to our very lives! * * A Hitler, a Pol Pot, or a Stalin would have loved to have had the * microchips, surveillance cameras, lasers, computers, satellites, weapons, * wiretap circuits and communications gadgetry of today's Dick Tracy Police * State. * * Perhaps FBI Director Louis Freeh said it best shortly after his * appointment to the Federal Bureau of Investigation in 1993. Referring * to the incredible array of computerized control and battle gadgetry * available to federal law enforcement, Freeh, stressing cooperation * between his own FBI and the other alphabet police agencies, sardonically * remarked, LET'S SHARE OUR TOYS. * * Dick Tracy, of course, was a good guy. But Dick Tracy would have * recognized as unconstitutional the worldwide comprehensive Orwellian * system that has been installed, and reject it as a menace to true law * and order. ! Welfare Recipients Lose Benefits Through Glitches in Computers ! By Joe Sexton, The New York Times, 5/16/96 ! ! The fingerprint-imaging system that is a central element of the Giuliani === Subject: Re: JSH: James Harris Surrogate Factors RSA-100 National Job Training and Employment database. * * George Orwell, in 1984, his classic novel of Big Brother and a coming * totalitarian state, observed that very few people are awake and alert * to the machinations and manipulations of the controllers. Thus, the * people, as a whole, fall victim to a colossal conspiracy out of ignorance * and because of apathy and denial of reality: * * The people could be made to accept the most flagrant violations of * reality, because they never fully grasped the enormity of what was * demanded of them, and were not sufficiently interested in public * events to notice what was happening. [ By Walter Cronkite: Orwell's '1984'---Nearing?, NYT, June 5 1983 In our world, where a Vietnam village can be destroyed so it can be saved; where the President names the latest thing in nuclear missiles Peacekeeper---in such a world, can the Orwellian vision be very far away? Big Brother's ears have plugs in them right now (or they are, by law, supposed to), at least on the domestic telephone and cable traffic. But the National Security Agency's ability to monitor microwave transmissions, to scoop out of the air VAST numbers of communications, including telephone conversations, store them in computers, play them back later, has a truly frightening potential for abuse. George Orwell issued a warning. He told us that freedom is too much taken for granted, that it needs to be carefully watched and protected. His last word on the subject was a plea to his readers: Don't let it happen. It depends on you. ] * * The National Security Agency's Project L.U.C.I.D., with all its * technological wizardry, is a future, planetary dictator's dream---and a * Christian and national patriot's nightmare. Someday, the H === Subject: Re: JSH: James Harris Surrogate Factors RSA-100 is filled with fascinating information, highly useful for securing one's systems. Here's a random sample factoid from 2600: although on-site company switches are commonly programmed to block '900' number calls, there is a hole in the programming logic that always lets '555' exchange numbers through. (Information wants to be free) Companies that advertise 900 numbers take advantage of this. For example, even though you can't dial most 900 numbers, you can still call numbers like USA Today's 1-900-555-5555, which are specifically chosen to get around the 900 programming restrictions. Oh yeah: I remember another one that triggered firm-wide security checks: 2600 described a hole in DOS that could allow others to execute commands on your system by virtue of defining function key contents (F1, F2..) on the fly AND THEN EXECUTING THEM. ] > Cummings apologized to the court for his odd curiosity of the past, > insisting that he merely collected books and information and never > caused harm to anyone. His lawyer pleaded with the judge to allow > Cummings to pick up the pieces of his life and not be subjected to > any more inhumane treatment. [ I feel sick upon reading he felt compelled to apologize for books. ] > Judge Panella passed sentence: 6 to 24 months plus a $3,000 fine. > > We have also learned of a very similar case that took place in Kentucky > late last year where a man was accused of the same offense that Cummings > was. In this instance, however, he was accused of actually selling the > black box that allowed cellular phones to be cloned. > > This was far more than Ed was ever accused of - he merely sold kits that > could be built into boxes. Th === Subject: Re: JSH: James Harris Surrogate Factors RSA-100 and appreciate this. Picture yourself as the monitored group. Shortly after starting out, they were pulled over by police for a search. Not one, but two squad cars came to do the search. Because they crossed lanes while going through an intersection. If you are white, when was the last time two squad cars searched your vehicle inch-by-inch because you crossed lanes while passing through an intersection? Never happened to me. The police were recorded saying a container they found probably had drugs in it. It was a make-up container. [All you little people are probably guilty] When ABC asked the police chief later why they were pulled over, he said for crossing lanes while going through an intersection. ABC's cameras then showed cars doing that constantly at the same intersection. They said they counted hundreds the same night. The police chief then tacitly admitted they were pulling over black people on purpose. ---- [ Yes, I am aware of the cocaine/crack sentencing discrimination. ] You monitor any group real close, you'll get many arrests. The implications of heavy monitoring are serious. * * Blacks make up 51 percent of the 1.1 million inmates in state and * Federal prisons, the Sentencing Project study said, though * blacks are only 14 percent of the nation's population. * * Of a total voting age population of 10.4 million black m === Subject: Re: JSH: James Harris Surrogate Factors RSA-100 locked secret court located within the main Justice Department building that only government employees can visit. It has never turned down a request, and doesn't even need suspicion of a crime to authorize a black-bag job burglary. Question: Then why bother? Answer: To give the illegal activity the imprimatur of constitutionality. And presidents issue secret directives that obliterate constitutional rights. Like the creation of the NSA. NSA testimony to Congress: There is no law that prevents our domestic spying. Such is the unconstitutional power of the Presidential Magic Order. It is even threatened to be used to wipe out Congressional legislation: : However, President Clinton has threatened to veto ProCode. : If Congress over-rides a VETO President Clinton signed an : executive order (11/15/96) which states he can revoke any law : passed on national security grounds: : : Upon enactment of any legislation reauthorizing the : administration of export controls, the Secretary of Defense, : the Secretary of State, and the Attorney General shall : reexamine whether adequate controls on encryption products can : be maintained under the provisions of the new statute and : advise the Secretary of Commerce of their conclusions as well : as any recommendations for action. If adequate controls on : encryption products cannot be maintained under a new statute, : then such products shall, where consistent with law, be : 2778(a)(1), to be placed on the United Sta === Subject: Re: JSH: James Harris Surrogate Factors RSA-100 are... So GCHQ asked CSE operators to come to London to bug the ministers ] Increasingly though, both because it's possible and because it's desired, individuals are caught in the broad net of electronic surveillance. The experts can record and analyze all your communications at will. SIGINT organizations in Canada, US, UK, Australia, and New Zealand use supercomputers such as the Cray to select items of interest. The list is very fluid and is adapted rapidly to monitor people and policy areas. At any time, it is likely to contain names of all world leaders, terrorists, drug lords, mafia dons, members of radical groups, labor union activists and leaders, types of weaponry, explosives, financial dealings, money transfers, airline destinations, stock information, international conferences, demonstrations, and politically suspect groups and individuals. As is the case with operations, countries maintain deniability by getting information gathered on their domestic situations by allies. Under development is even more sophisticated topic recognition which can home in on guarded conversations that avoid potential trigger words. Nothing and no one is exempt. For example, you are talking on the telephone to a friend discussing your son's school play. Boy, you say sadly, Bobby really bombed last night, or perhaps you use the word assassination or sabotage or any one of the key words the computer has been told to flag. A hard copy of your conversation is produced, passed to the appropriate section (in this case terrorism), and probably ends up in the garbage. But perhaps the conversation is not so clear-cut or the analyst has poor judgement. Then your name is permanently filed under possible terrorist. Weeks or even years later, you have a similar conversation and use the same words; the computer filters it out again. Since this is your sec === Subject: Re: JSH: James Harris Surrogate Factors RSA-100 decades now. Politicians constantly beating the drums of war ('1984': The Song of Hate), causing the erroneous public perception crime is out of control. Anyone remember the scare ads that got crooked Nixon elected over Humphrey? This constant 1984 state of war has caused massive damage to our country. Picture what life would be like without the constant hysteria. If you can. It's been so long. You are sitting back on your porch, sipping a cold one, smoking a warm one, whatever. Relaxed, calm, at peace. You home was still your castle. Peace. Then, during one single day in Congress: o All Americans must allow companies to withdraw fluids from their bodies to check for drugs. Nevermind that that would be a dire last resort and that dignified non-invasive techniques are available for safety-related jobs. o Libraries are checked to see if you are looking at the wrong kind of books. Read the wrong book and the government will call you a 'potential terrorist' in court. o Studies on the feasibility of monitoring all bank transactions in real-time are ordered. (So we can compute FDIC insurance requirements in real-time) Recommendation to proceed is given by law enforcement. o Loss of rights if you are receiving government benefits: - public housing ordered searched without warrants by the president [A DIRECT VIOLATION OF OUR CONSTITUTION!] - suspicionless searches of cars (NJ, for example) - no California driver's license without fingerprinting, eventually all U.S. citizens are fingerprinted - no welfare benefits (NY for example) without fingerprinting - illegal immigrant kids denied me === === === === === === === === === === === === === === === === === === === === === === === === === === === === === === === === === === === Subject: Re: Solution Manual for Electric Circuits by Nilsson and Riedel posting-account=ZnyDdwoAAAChHnYo8DDH_nOZCgbhC0Kp 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > If anyone has the solutions and coul email them to me at > mapuha...@yahoo.com , that would be greatly appreciated. I need one too!! ss19t@hanmail.net === Subject: Re: Solution Manual for Electric Circuits by Nilsson and Riedel posting-account=AIT25goAAAD4PInVOqQYW2U7xf3SSqUF QQDownload 1.7),gzip(gfe),gzip(gfe) i have it A lot of Solution Manuals in Electronic (PDF)Format! A lot of Solutions Manuals in Electronic (PDF)Format! Just contact with trustsolution (at) hotmail.com (my email address), these are parts of our solutions, if the solution you want isnÍt on the list, donÍt give up,please email to me. DonÍt comment in here,please email to me A Course in Modern Mathematical Physics By Peter Szekeres(solution manual) A First Course in String Theory(solution manual) A Quantum Approach to Condensed Matter Physics By Philip ,Taylor(solution manual) A Quantum Approach to Condensed Matter Physics(2002) (.83.83) A Short Introduction to Quantum Information and Quantum Computation(2006) accompany Analysis and Design of Integrated Circuits, 4th by Gray, Hurst, Lewis Advanced Dynamics(2006) advanced engineering mathematics (8/e) by ERWIN KREYSZIG advanced engineering mathematics (8/e)( korean version) by ERWIN KREYSZIG advanced engineering mathematics.81i9/e.81j (even solutions) by ERWIN KREYSZIG advanced macroeconomics By Romer Advanced Modern Engineering Mathematics (3rd Edition) By Glyn James AISC Manual of Steel Construction: Load and Resistance Factor Design, Third Edition (LRFD 3rd Edition) An Introduction to Economic Dynamics An Introduction to Ordinary Differential Equations An Introduction to Partial Differential Equations (2005) By Yehuda Pinchover An Introduction To The Finite Element Method, 3rd Editionby J. N. Reddy Analytical Mechanics (7/e) By Grant R. Fowles, George L. Cassiday Analytical Mechanics, 5th ,By Grant R. Fowles, George L. Cassiday, APPLIED MATHEMATICS AND MODELLING FOR CHEMICAL ENGINEERS, 8th, By Erwin Kreyszig Applied Quantum Mechanics Applied Statisticsand Probability for Engineers,3rd.81Cby Douglas C (selected problem) Applied Strength of Materials (4th Edition) by Robert MoTT Calculus I, II, Transidentals 10e BY George B. Thomas Calculus with Analytic Geometry Calculus, 4th edition by James Stewart Chemical and Engineering Thermodynamics- 3rd Chemical And Engineering Thermodynamics 3Ed Solutions Manual .81iwiley) Classical Electrodynamics 2Ed by Jackson Classical Mechanics - An Undergraduate Text Communication Systems Engineering.81C2nd, John G. Proakis ,Masoud Salehi Computational Techniques for Fluid Dynamics By Karkenahalli Srinivas, Clive A. J. Fletcher Computer Organization and Design: The Hardware/Software Interface.81i3/e) by David A. Patterson, John Control Systems Engineering, 4th Edition Corporate Finance ,By ROSS Data & Computer Communications, 7th Edition By Stallings Derivatives Markets, 2nd Edition by Robert L. McDonald C. Montgomery Design of Analog CMOS Integrated Circuits (2000) Device Electronics for Integrated Circuits, By Richard S. Muller, Theodore I. Kamins Digital and Analog Communication Systems 7th(international version) by LEON W. COUCH Digital and Analog Communication Systems .81C5th, by Leon W. Couch, Leon W., II Couch . Digital Image Processing,2 nd, byRafael C. Gonzalez Richard E. Woods Digital Signal Processing by Proakis & Manolakis Digital Signal Processing: Principles, Algorithms and Applications, 3rd Edition, By John G. Proakis Digital Signal Processing; A Computer-Based Approach 1st ed by Sanjit K. Mitrol Discrete Time Signal Processing by Oppenheim DISCRETE-TIME SIGNAL PROCESSING/2e by Oppenheim.81ASchafer Dynamics of Mechanical Systems by harveyv echniques of Problem Solving By Luis Fernandez.81i1997-12.81j Econometric Analysis (6/e) by willian H.GREENE Econometric Analysis 5th,by Williame H. Greene Electric Machinery 6th by Fitzgerald, Kingsley, Uman 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. Electrical Machines, Drives and Power Systems (2005) By Theodore Wildi Electromagnetic Harrington (chapter1-chapter3) Elementary Differential Equations and Boundary Value Problems , 8th.81Cby William E. Boyce (Author), Richard C Elementary Differential Equations And Boundary Value Problems, 7Th Ed - Boyce And Diprima Elementary Mechanics & Thermodynamics ,2000, by Jhon W. Norbury Elementary Principles of Chemical Processes By Richard M.Felder elements of Chemical Reaction Engineering (3rd)by H.Scott Fogler Elements of Chemical Reaction Engineering ,1999,By H Fogler Elements of engineering electromagnetics (6/e) by N.N.RAO Energy Management 2005-12 5th ed,By Klaus-Dieter E. Pawlik Engineering - Materials Science,by Milton Ohring Engineering circuit analysis 6 ed,By William Hart Hayt Engineering electromagnetics (6/e) by HAYT Engineering electromagnetics (7/e) by HAYT Engineering Electromagnetics, 6th .81Cby William H. Hayt, John A. Buck 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 Fundamentals of Electric Circuits(2th ) By Charles Alexander, Matthew Sadiku Engineering Mechanics, Dynamics ,By J. L. Meriam, L. G. Kraige, Engineering Mechanics, Dynamics 5th By J. L. Meriam, L. G. Kraige(chapter1,2,3,4) Engineering Mechanics: Statics ,10th ,by R.C.Hibbeler, Equilibrium and Non-Equilibrium Statistical Thermodynamics field and wave electromagnetics (2/e) by David Cheng Financial Accounting 6th edition by Harrison Flex Solutions: Essential Techniques for Flex 2 and 3 Developers By Marco Casario Fluid Mechanics (2006) By CENGEL Fourier and Laplace Transform ,by Antwoorden Fundamental of Heat and Mass Transfer by Frank P. Incropera and David P.DeWitt (ANOTHER EDITION) Fundamental of Heat and Mass Transfer by Frank P. Incropera and David P.DeWitt Fundamentals of Chemical Reaction Engineering By Mark E. E. Davis, Robert J. J. Davis Fundamentals of Engineering Thermodynamics by Moran, M.J. & Shapiro H.N. Fundamentals of Fluid Mechanics by Bruce R. Munson Fundamentals Of Fluid Mechanics 3Rd And 4Th Edition Fundamentals of Fluid Mechanics, 5th by By Bruce,R. Munson, Donald, Fundamentals of Logic Design 5th by Charles Roth Fundamentals of Machine Component Design, 3rd Juvinall, Marshek Fundamentals of Organic Chemistry, 5E Fundamentals of Physics (7th ) by Halliday, Resnick and Walker Fundamentals of Physics.81C7th, by David Halliday, Robert Resnick Fundamentals of Probability 3/e Fundamentals of Quantum Mechanics: For Solid State Electronics and Optics By: C. L. Tang Fundamentals of Thermal-Fluid Sciences Fundamentals of Thermodynamics 6th Ed by Sonntag,Borgnakke and Van Wylen HARCOURT MATHEMATICS 12 Advanced Functions and Introductory Calculus he Econometrics of Financial Markets by Petr Adamek John Y. Campbell Andrew Heat Transfer Heat transfer: a pritical approach 2th by Yunus A. Cengel,& Yunus Cengel How to Program C, 3RD Edition 2000 By Harvey M. Deitel Introduction To Algorithms,2nd,by Thomas H.Cormen Introduction to Chemical Engineering Thermodynamics By J.M. Smith, Hendrick Introduction To Electric Circuits 6th By Richard C. Dorf, James A. Svoboda Introduction to Electrodynamics(3/e) by David J. Griffiths Introduction to Fluid Mechanics 5th by Fox Introduction to Heat Transfer 4th Edition By Frank P. Incropera, David Introduction to Linear Algebra--3rd Edition - Gilbert Strang Introduction to Mathematical Statistics 6/E Robert V. Hogg Introduction to Probability by Charles M. Grinstead and J. Laurie Snell(ODD) Introduction to Quantum Mechanics (1 & 2 Edition), By David J. Griffiths Introduction to Solid State Physics (8 ED) by Charles.Kittel Introduction to VLSI Circuits and Systems (2001 )byJohn P Uyemura Introductory Quantum Optics ,By Christopher Gerry and Peter Knight Investment Analysis and Portfolio Management(7th) By Frank K. et al. Reilly Kinetics of Catalytic Reactions (2005) By M. Albert Vannice Lectures on Corporate Finance.81i2th.81j by Peter Bossaerts and Bernt Linear Algebra and its Applications [Solutions Manual] 3rd ed - D. Lay WW Logic and Computer Design Fundamentals4E by Mano and Kime.3th Logic and Computer Design Fundamentals4E by Mano and Kime.4th Materials Science and Engineering: An Introduction 6E ,By William D. Callister Jr. MATHEMATICAL ANALYSIS (2/e) (chapter1-9) by Tom M. Apostol Mathematical Models in Biology: An Introduction Mathematical Olympiad in China: Problems and Solutions By Bin Xiong, Yee Lee Peng Mechanical Engineering Design By Joseph Shigley, Charles Mischke, Mechanics of Fluids Solutions Manual ,8 ed,By John Ward-Smith Mechanics Of Materials ,3rd , By Beer, Johnston, & Dewolf Mechanics of Materials (6/E) by R.C.Hibbeler Mechanics Of Materials ,3rd , By Beer, Johnston, & Dewolf Microeconomic Analysis, 3rd Edition, by Hal R. Varian Microeconomic Theory by Andreu Mas-Colell, Michael D. Whinston, Microelectronic Circuits, Sedra, 4th edition Microwave Engineering 3ed - by david pozar Modern Control Engineering/ 4E by K.OGATA Modern Digital and Analog Communication Systems (3/e) Numerical methods for engineers by Chapra Numerical Solution of Partial Differential Equations: An Introduction.81i2 th.81j Operating Systems Concepts 6th byAbraham Silberschat Optics: Major American Universities Ph. D. Qualifying Questions and Solutions By Chung-Kuo Transport Phenomena by Bird, Stewart & Lightfoot, 2nd edition. Options, Futures and Other Derivatives (4th) By John Hull, John C. Hull Options, Futures and Other Derivatives (5th) By John Hull, John C. Hull Organic Chemistry(2th) by Hornback Physical Chemistry (2001) By Julio de Paula, Peter Atkins Physical Chemistry (7/e) by Peter Atkins and Julio de Paula Physics , 5th,( Vol 2)by Resnick Halliday Krane, Physics for Scientists and Engineers by Serway& Jewett Physics for Scientists and Engineers (7th ) Volume One by Serway and Jewett Physics For Scientists And Engineers 6E By Serway And Jewett - Solutions Manual Vol 2 Principles of Electronic Materials and Devices, 2th,By Safa O. Kasap 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 and Statistics for Engineers and Scientists by HAYLER Probability, Random Variables and Stochastic Processes,3rd, by Athanasios Papoulis Probability,Random Variables and Stochastic Processes,4th,by Athanasios Papoulis Quantum Field Theory (draft version) ,By Mark Srednicki Quantum Field Theory (draft version) ,By Mark Srednicki Quantum Physics, Third Edition, By Stephen Gasiorowicz Quantum Physics, Third Edition, By Stephen Gasiorowicz Recursive Methods in Economic Dynamics By Claudio Irigoyen, Esteban Rossi-Hansberg, Hans , Yorick Semiconductor Devices Second Edition By S.M.Sze Semiconductor Physics and Devices Third Edition By Donald Neamen Separation Process Principles, 2nd Ed., by Seader, Henley Shigley's Mechanical Engineering Design, (8/e) by Richard G. Budynas Signal Processing and Linear Systems (2001) by B P Lathi Signal Processing and Linear Systems, By B.P. Lathi Signals and Systems (2nd Edition) By Oppenheim, Willsky and Nawab Signals and Systems 2nd by Haykin Statistical Digital Signal Processing and Modeling By Monson H. Hayes Statistical Inference (2th) By CASELLA System Dynamics 3rd Ed ,By Katsuhiko Ogata The Economics of Financial Markets.81i2005.81j By Roy E. Bailey Theoretical & Mathematical Physics: Advanced Level(2th) By Willi- Hans Steeb Thermodynamics: An Engineering Approach,6th Ed. by Cengel Thomas' Calculus (11th Edition) by George B Thomas Thomas' Calculus, Early Trascendentals 10th ed Instructors Solutions Manual Two-Dimensional Incompressible Navier-Stokes Equations- Maciej Matyk Unit Operations of Chemical Engineering (7th) By Warren McCabe, Julian Smith University Physics with Modern Physics:,11 ed By Hugh D. Young, Roger A. Freedman, use with Fundamentals of Corporate Finance, 4th Edition By Bruce Swenson Vector Mechanics for Engineers: Dynamics, 7th By Ferdinand P. Beer(selected chapters) E. R. Johnston Vector Mechanics for Engineers: Statics, 7th By Ferdinand P. Beer(selected chapters) Vector Mechanics for Engineers: Statics, 7th Edition ,By Ferdinand P. Beer, E. Russell Johnston Jr., ElliotR Visual C++ How to Program, (3rd Edition) ,by Harvey & Paul Deitel & Associates Wireless communication and networks 2th by willian stallings Zill's a First Course in Differential Equations with boundary value problem 5th Zill's a First Course in Differential Equations with Modeling Applicants 7/e.81isolitions manual.81j don't leave a message here,please send email to solutionpay@hotmail.com, i will tell you how to do to get the solution A lot of Solution Manuals in Electronic (PDF)Format! A lot of Solutions Manuals in Electronic (PDF)Format! Just contact with trustsolution (at) hotmail.com (my email address), these are parts of our solutions, if the solution you want isn.81ft on the list, don.81ft give up,please email to me. Don.81ft comment in here,please email to me A Course in Modern Mathematical Physics By Peter Szekeres(solution manual) A First Course in String Theory(solution manual) A Quantum Approach to Condensed Matter Physics By Philip ,Taylor(solution manual) A Quantum Approach to Condensed Matter Physics(2002) (.81c.81c) A Short Introduction to Quantum Information and Quantum Computation(2006) accompany Analysis and Design of Integrated Circuits, 4th by Gray, Hurst, Lewis Advanced Dynamics(2006) advanced engineering mathematics (8/e) by ERWIN KREYSZIG advanced engineering mathematics (8/e)( korean version) by ERWIN KREYSZIG advanced engineering mathematics.81i9/e.81j (even solutions) by ERWIN KREYSZIG advanced macroeconomics By Romer Advanced Modern Engineering Mathematics (3rd Edition) By Glyn James AISC Manual of Steel Construction: Load and Resistance Factor Design, Third Edition (LRFD 3rd Edition) An Introduction to Economic Dynamics An Introduction to Ordinary Differential Equations An Introduction to Partial Differential Equations (2005) By Yehuda Pinchover An Introduction To The Finite Element Method, 3rd Editionby J. N. Reddy Analytical Mechanics (7/e) By Grant R. Fowles, George L. Cassiday Analytical Mechanics, 5th ,By Grant R. Fowles, George L. Cassiday, APPLIED MATHEMATICS AND MODELLING FOR CHEMICAL ENGINEERS, 8th, By Erwin Kreyszig Applied Quantum Mechanics Applied Statisticsand Probability for Engineers,3rd.81Cby Douglas C (selected problem) Applied Strength of Materials (4th Edition) by Robert MoTT Calculus I, II, Transidentals 10e BY George B. Thomas Calculus with Analytic Geometry Calculus, 4th edition by James Stewart Chemical and Engineering Thermodynamics- 3rd Chemical And Engineering Thermodynamics 3Ed Solutions Manual .81iwiley) Classical Electrodynamics 2Ed by Jackson Classical Mechanics - An Undergraduate Text Communication Systems Engineering.81C2nd, John G. Proakis ,Masoud Salehi Computational Techniques for Fluid Dynamics By Karkenahalli Srinivas, Clive A. J. Fletcher Computer Organization and Design: The Hardware/Software Interface.81i3/e) by David A. Patterson, John Control Systems Engineering, 4th Edition Corporate Finance ,By ROSS Data & Computer Communications, 7th Edition By Stallings Derivatives Markets, 2nd Edition by Robert L. McDonald C. Montgomery Design of Analog CMOS Integrated Circuits (2000) Device Electronics for Integrated Circuits, By Richard S. Muller, Theodore I. Kamins Digital and Analog Communication Systems 7th(international version) by LEON W. COUCH Digital and Analog Communication Systems .81C5th, by Leon W. Couch, Leon W., II Couch . Digital Image Processing,2 nd, byRafael C. Gonzalez Richard E. Woods Digital Signal Processing by Proakis & Manolakis Digital Signal Processing: Principles, Algorithms and Applications, 3rd Edition, By John G. Proakis Digital Signal Processing; A Computer-Based Approach 1st ed by Sanjit K. Mitrol Discrete Time Signal Processing by Oppenheim DISCRETE-TIME SIGNAL PROCESSING/2e by Oppenheim.81ASchafer Dynamics of Mechanical Systems by harveyv echniques of Problem Solving By Luis Fernandez.81i1997-12.81j Econometric Analysis (6/e) by willian H.GREENE Econometric Analysis 5th,by Williame H. Greene Electric Machinery 6th by Fitzgerald, Kingsley, Uman 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. Electrical Machines, Drives and Power Systems (2005) By Theodore Wildi Electromagnetic Harrington (chapter1-chapter3) Elementary Differential Equations and Boundary Value Problems , 8th.81Cby William E. Boyce (Author), Richard C Elementary Differential Equations And Boundary Value Problems, 7Th Ed - Boyce And Diprima Elementary Mechanics & Thermodynamics ,2000, by Jhon W. Norbury Elementary Principles of Chemical Processes By Richard M.Felder elements of Chemical Reaction Engineering (3rd)by H.Scott Fogler Elements of Chemical Reaction Engineering ,1999,By H Fogler Elements of engineering electromagnetics (6/e) by N.N.RAO Energy Management 2005-12 5th ed,By Klaus-Dieter E. Pawlik Engineering - Materials Science,by Milton Ohring Engineering circuit analysis 6 ed,By William Hart Hayt Engineering electromagnetics (6/e) by HAYT Engineering electromagnetics (7/e) by HAYT Engineering Electromagnetics, 6th .81Cby William H. Hayt, John A. Buck 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 Fundamentals of Electric Circuits(2th ) By Charles Alexander, Matthew Sadiku Engineering Mechanics, Dynamics ,By J. L. Meriam, L. G. Kraige, Engineering Mechanics, Dynamics 5th By J. L. Meriam, L. G. Kraige(chapter1,2,3,4) Engineering Mechanics: Statics ,10th ,by R.C.Hibbeler, Equilibrium and Non-Equilibrium Statistical Thermodynamics field and wave electromagnetics (2/e) by David Cheng Financial Accounting 6th edition by Harrison Flex Solutions: Essential Techniques for Flex 2 and 3 Developers By Marco Casario Fluid Mechanics (2006) By CENGEL Fourier and Laplace Transform ,by Antwoorden Fundamental of Heat and Mass Transfer by Frank P. Incropera and David P.DeWitt (ANOTHER EDITION) Fundamental of Heat and Mass Transfer by Frank P. Incropera and David P.DeWitt Fundamentals of Chemical Reaction Engineering By Mark E. E. Davis, Robert J. J. Davis Fundamentals of Engineering Thermodynamics by Moran, M.J. & Shapiro H.N. Fundamentals of Fluid Mechanics by Bruce R. Munson Fundamentals Of Fluid Mechanics 3Rd And 4Th Edition Fundamentals of Fluid Mechanics, 5th by By Bruce,R. Munson, Donald, Fundamentals of Logic Design 5th by Charles Roth Fundamentals of Machine Component Design, 3rd Juvinall, Marshek Fundamentals of Organic Chemistry, 5E Fundamentals of Physics (7th ) by Halliday, Resnick and Walker Fundamentals of Physics.81C7th, by David Halliday, Robert Resnick Fundamentals of Probability 3/e Fundamentals of Quantum Mechanics: For Solid State Electronics and Optics By: C. L. Tang Fundamentals of Thermal-Fluid Sciences Fundamentals of Thermodynamics 6th Ed by Sonntag,Borgnakke and Van Wylen HARCOURT MATHEMATICS 12 Advanced Functions and Introductory Calculus he Econometrics of Financial Markets by Petr Adamek John Y. Campbell Andrew Heat Transfer Heat transfer: a pritical approach 2th by Yunus A. Cengel,& Yunus Cengel How to Program C, 3RD Edition 2000 By Harvey M. Deitel Introduction To Algorithms,2nd,by Thomas H.Cormen Introduction to Chemical Engineering Thermodynamics By J.M. Smith, Hendrick Introduction To Electric Circuits 6th By Richard C. Dorf, James A. Svoboda Introduction to Electrodynamics(3/e) by David J. Griffiths Introduction to Fluid Mechanics 5th by Fox Introduction to Heat Transfer 4th Edition By Frank P. Incropera, David Introduction to Linear Algebra--3rd Edition - Gilbert Strang Introduction to Mathematical Statistics 6/E Robert V. Hogg Introduction to Probability by Charles M. Grinstead and J. Laurie Snell(ODD) Introduction to Quantum Mechanics (1 & 2 Edition), By David J. Griffiths Introduction to Solid State Physics (8 ED) by Charles.Kittel Introduction to VLSI Circuits and Systems (2001 )byJohn P Uyemura Introductory Quantum Optics ,By Christopher Gerry and Peter Knight Investment Analysis and Portfolio Management(7th) By Frank K. et al. Reilly Kinetics of Catalytic Reactions (2005) By M. Albert Vannice Lectures on Corporate Finance.81i2th.81j by Peter Bossaerts and Bernt Linear Algebra and its Applications [Solutions Manual] 3rd ed - D. Lay WW Logic and Computer Design Fundamentals4E by Mano and Kime.3th Logic and Computer Design Fundamentals4E by Mano and Kime.4th Materials Science and Engineering: An Introduction 6E ,By William D. Callister Jr. MATHEMATICAL ANALYSIS (2/e) (chapter1-9) by Tom M. Apostol Mathematical Models in Biology: An Introduction Mathematical Olympiad in China: Problems and Solutions By Bin Xiong, Yee Lee Peng Mechanical Engineering Design By Joseph Shigley, Charles Mischke, Mechanics of Fluids Solutions Manual ,8 ed,By John Ward-Smith Mechanics Of Materials ,3rd , By Beer, Johnston, & Dewolf Mechanics of Materials (6/E) by R.C.Hibbeler Mechanics Of Materials ,3rd , By Beer, Johnston, & Dewolf Microeconomic Analysis, 3rd Edition, by Hal R. Varian Microeconomic Theory by Andreu Mas-Colell, Michael D. Whinston, Microelectronic Circuits, Sedra, 4th edition Microwave Engineering 3ed - by david pozar Modern Control Engineering/ 4E by K.OGATA Modern Digital and Analog Communication Systems (3/e) Numerical methods for engineers by Chapra Numerical Solution of Partial Differential Equations: An Introduction.81i2 th.81j Operating Systems Concepts 6th byAbraham Silberschat Optics: Major American Universities Ph. D. Qualifying Questions and Solutions By Chung-Kuo Transport Phenomena by Bird, Stewart & Lightfoot, 2nd edition. Options, Futures and Other Derivatives (4th) By John Hull, John C. Hull Options, Futures and Other Derivatives (5th) By John Hull, John C. Hull Organic Chemistry(2th) by Hornback Physical Chemistry (2001) By Julio de Paula, Peter Atkins Physical Chemistry (7/e) by Peter Atkins and Julio de Paula Physics , 5th,( Vol 2)by Resnick Halliday Krane, Physics for Scientists and Engineers by Serway& Jewett Physics for Scientists and Engineers (7th ) Volume One by Serway and Jewett Physics For Scientists And Engineers 6E By Serway And Jewett - Solutions Manual Vol 2 Principles of Electronic Materials and Devices, 2th,By Safa O. Kasap 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 and Statistics for Engineers and Scientists by HAYLER Probability, Random Variables and Stochastic Processes,3rd, by Athanasios Papoulis Probability,Random Variables and Stochastic Processes,4th,by Athanasios Papoulis Quantum Field Theory (draft version) ,By Mark Srednicki Quantum Field Theory (draft version) ,By Mark Srednicki Quantum Physics, Third Edition, By Stephen Gasiorowicz Quantum Physics, Third Edition, By Stephen Gasiorowicz Recursive Methods in Economic Dynamics By Claudio Irigoyen, Esteban Rossi-Hansberg, Hans , Yorick Semiconductor Devices Second Edition By S.M.Sze Semiconductor Physics and Devices Third Edition By Donald Neamen Separation Process Principles, 2nd Ed., by Seader, Henley Shigley's Mechanical Engineering Design, (8/e) by Richard G. Budynas Signal Processing and Linear Systems (2001) by B P Lathi Signal Processing and Linear Systems, By B.P. Lathi Signals and Systems (2nd Edition) By Oppenheim, Willsky and Nawab Signals and Systems 2nd by Haykin Statistical Digital Signal Processing and Modeling By Monson H. Hayes Statistical Inference (2th) By CASELLA System Dynamics 3rd Ed ,By Katsuhiko Ogata The Economics of Financial Markets.81i2005.81j By Roy E. Bailey Theoretical & Mathematical Physics: Advanced Level(2th) By Willi- Hans Steeb Thermodynamics: An Engineering Approach,6th Ed. by Cengel Thomas' Calculus (11th Edition) by George B Thomas Thomas' Calculus, Early Trascendentals 10th ed Instructors Solutions Manual Two-Dimensional Incompressible Navier-Stokes Equations- Maciej Matyk Unit Operations of Chemical Engineering (7th) By Warren McCabe, Julian Smith University Physics with Modern Physics:,11 ed By Hugh D. Young, Roger A. Freedman, use with Fundamentals of Corporate Finance, 4th Edition By Bruce Swenson Vector Mechanics for Engineers: Dynamics, 7th By Ferdinand P. Beer(selected chapters) E. R. Johnston Vector Mechanics for Engineers: Statics, 7th By Ferdinand P. Beer(selected chapters) Vector Mechanics for Engineers: Statics, 7th Edition ,By Ferdinand P. Beer, E. Russell Johnston Jr., ElliotR Visual C++ How to Program, (3rd Edition) ,by Harvey & Paul Deitel & Associates Wireless communication and networks 2th by willian stallings Zill's a First Course in Differential Equations with boundary value problem 5th Zill's a First Course in Differential Equations with Modeling Applicants 7/e.81isolitions manual.81j don't leave a message here,please send email to trustsolution@hotmail.com, i will tell you how to do to get the solution rephire .8eæ.93.b9.81F > If anyone has the solutions and coul email them to me at > mapuha...@yahoo.com , that would be greatly appreciated. I need one too!! > ss19t@hanmail.net === Subject: Re: need solution manual posting-account=I4LMEgoAAABgwkvbBt_YLmArZhfVF8gI Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) I have the following solution manuals. If you are interested in any of them, contact me at books of interest (at) gmail (dot) com booksofinterest@gmail.com Only Paypal payments accepted Please check first if the solution manual you want is in the list, and then contact me instead of posting here. * Solutions manual for Brief Calculus and Its Applications (11th Ed., Larry J Goldstein, Schneider, Nakhle Asmar) * Solutions manual for Finite Math and Its Application (9th Ed., Larry J Goldstein, Schneider & Siegel) * Solutions manual for ñModern Control Systems, 11/E, Richard C Dorf, Robert H. Bishopî * Solutions manual for ñEngineering Mechanics Dynamics, 5/E, Anthony M Bedford, Wallace Fowlerî Solutions manual for ñEngineering Mechanics: Statics, 5/E, Anthony M Bedford, Wallace Fowlerî Solutions manual for ñPhysics for Scientists and Engineers with Modern Physics and Mastering Physics, 4/E, Douglas C. Giancoliî * Solutions manual for ñElements of Engineering Electromagnetics, 6/E, Nannapaneni Narayana Raoî * Solutions manual for ñElectrical Engineering: Principles and Applications, 4/E, Allan R. Hambleyî * Solutions manual for ñMechanics of Materials, 7/E, by Russell C. Hibbelerî * Solutions manual for ñPrinciples of Statics and Dynamics, 10/E, by Russell C. Hibbelerî * Solutions manual for ñStatics and Mechanics of Materials, 2/E., By Russell C. Hibbelerî * Solutions manual for ñIntroduction to Materials Management, 6/E, by Tony Arnold, Steve Chapman, Lloyd Cliveî * Solutions manual for ñFundamentals of Production Planning and Control, by Stephen N. 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If you are interested in any ofthem, contact me at books of interest (at) gmail (dot) com booksofinterest@gmail.com Only Paypal payments accepted Please check first if the solution manual you want is in the list, andthen contact me instead of posting here. * Solutions manual for Brief Calculus and Its Applications (11th Ed.,Larry J Goldstein, Schneider, Nakhle Asmar) * Solutions manual for Finite Math and Its Application (9th Ed., Larry JGoldstein, Schneider & Siegel) * Solutions manual for .89´[Thorn]Modern Control Systems, 11/E, Richard C Dorf,Robert H. Bishop.89´Ø * Solutions manual for .89´[Thorn]Engineering Mechanics Dynamics, 5/E, Anthony MBedford, Wallace Fowler.89´Ø Solutions manual for .89´[Thorn]Engineering Mechanics: Statics, 5/E, Anthony MBedford, Wallace Fowler.89´Ø Solutions manual for .89´[Thorn]Physics for Scientists and Engineers with ModernPhysics and Mastering Physics, 4/E, Douglas C. 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Arnold.89´Ø If you are interested in any of them, contact me at booksofinterest (at) gmail (dot) com booksofinterest@gmail.com Only Paypal payments accepted --Message posted using http://www.talkabouteducation.com/group/alt.math.undergrad/More information at http://www.talkabouteducation.com/faq.html === Subject: Solutions Manual posting-account=AIT25goAAAD4PInVOqQYW2U7xf3SSqUF QQDownload 1.7),gzip(gfe),gzip(gfe) Solutions Manual A lot of Solutions Manuals in Electronic (PDF)Format! Just contact with solutionpay@hotmail.com (my email address), these are parts of our solutions, if the solution you want isn.81ft on the list, don.81ft give up,please email to me. Don.81ft comment in here,please email to me A Course in Modern Mathematical Physics By Peter Szekeres(solution manual) A First Course in String Theory(solution manual) A Quantum Approach to Condensed Matter Physics By Philip ,Taylor(solution manual) A Quantum Approach to Condensed Matter Physics(2002) (.81c.81c) A Short Introduction to Quantum Information and Quantum Computation(2006) accompany Analysis and Design of Integrated Circuits, 4th by Gray, Hurst, Lewis Advanced Dynamics(2006) advanced engineering mathematics (8/e) by ERWIN KREYSZIG advanced engineering mathematics (8/e)( korean version) by ERWIN KREYSZIG advanced engineering mathematics.81i9/e.81j (even solutions) by ERWIN KREYSZIG advanced macroeconomics By Romer Advanced Modern Engineering Mathematics (3rd Edition) By Glyn James AISC Manual of Steel Construction: Load and Resistance Factor Design, Third Edition (LRFD 3rd Edition) An Introduction to Economic Dynamics An Introduction to Ordinary Differential Equations An Introduction to Partial Differential Equations (2005) By Yehuda Pinchover An Introduction To The Finite Element Method, 3rd Editionby J. N. Reddy Analytical Mechanics (7/e) By Grant R. Fowles, George L. Cassiday Analytical Mechanics, 5th ,By Grant R. Fowles, George L. Cassiday, APPLIED MATHEMATICS AND MODELLING FOR CHEMICAL ENGINEERS, 8th, By Erwin Kreyszig Applied Quantum Mechanics Applied Statisticsand Probability for Engineers,3rd.81Cby Douglas C (selected problem) Applied Strength of Materials (4th Edition) by Robert MoTT Calculus I, II, Transidentals 10e BY George B. Thomas Calculus with Analytic Geometry Calculus, 4th edition by James Stewart Chemical and Engineering Thermodynamics- 3rd Chemical_And_Engineering_Thermodynamics_3Ed_Solutions_Manual .81iwiley) Classical Electrodynamics 2Ed by Jackson Classical Mechanics - An Undergraduate Text Communication Systems Engineering.81C2nd, John G. Proakis ,Masoud Salehi Computational Techniques for Fluid Dynamics By Karkenahalli Srinivas, Clive A. J. Fletcher Computer Organization and Design: The Hardware/Software Interface.81i3/e) by David A. Patterson, John Control Systems Engineering, 4th Edition Corporate Finance ,By ROSS Data & Computer Communications, 7th Edition By Stallings Derivatives Markets, 2nd Edition by Robert L. McDonald C. Montgomery Design of Analog CMOS Integrated Circuits (2000) Device Electronics for Integrated Circuits, By Richard S. Muller, Theodore I. Kamins Digital and Analog Communication Systems 7th(international version) by LEON W. COUCH Digital and Analog Communication Systems .81C5th, by Leon W. Couch, Leon W., II Couch . Digital Image Processing,2 nd, byRafael C. Gonzalez Richard E. Woods Digital Signal Processing by Proakis & Manolakis Digital Signal Processing: Principles, Algorithms and Applications, 3rd Edition, By John G. Proakis Digital Signal Processing; A Computer-Based Approach 1st ed by Sanjit K. 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Whinston, Microelectronic Circuits, Sedra, 4th edition Microwave Engineering 3ed - by david pozar Modern Control Engineering/ 4E by K.OGATA Modern Digital and Analog Communication Systems (3/e) Numerical methods for engineers by Chapra Numerical Solution of Partial Differential Equations: An Introduction.81i2 th.81j Operating Systems Concepts 6th byAbraham Silberschat Optics: Major American Universities Ph. D. Qualifying Questions and Solutions By Chung-Kuo Transport Phenomena by Bird, Stewart & Lightfoot, 2nd edition. Options, Futures and Other Derivatives (4th) By John Hull, John C. Hull Options, Futures and Other Derivatives (5th) By John Hull, John C. 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Kasap 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 and Statistics for Engineers and Scientists by HAYLER Probability, Random Variables and Stochastic Processes,3rd, by Athanasios Papoulis Probability,Random Variables and Stochastic Processes,4th,by Athanasios Papoulis Quantum Field Theory (draft version) ,By Mark Srednicki Quantum Field Theory (draft version) ,By Mark Srednicki Quantum Physics, Third Edition, By Stephen Gasiorowicz Quantum Physics, Third Edition, By Stephen Gasiorowicz Recursive Methods in Economic Dynamics By Claudio Irigoyen, Esteban Rossi-Hansberg, Hans , Yorick Semiconductor Devices Second Edition By S.M.Sze Semiconductor Physics and Devices Third Edition By Donald Neamen Separation Process Principles, 2nd Ed., by Seader, Henley Shigley's Mechanical Engineering Design, (8/e) by Richard G. Budynas Signal Processing and Linear Systems (2001) by B P Lathi Signal Processing and Linear Systems, By B.P. Lathi Signals and Systems (2nd Edition) By Oppenheim, Willsky and Nawab Signals and Systems 2nd by Haykin Statistical Digital Signal Processing and Modeling By Monson H. Hayes Statistical Inference (2th) By CASELLA System Dynamics 3rd Ed ,By Katsuhiko Ogata The Economics of Financial Markets.81i2005.81j By Roy E. Bailey Theoretical & Mathematical Physics: Advanced Level(2th) By Willi- Hans Steeb Thermodynamics: An Engineering Approach,6th Ed. by Cengel Thomas' Calculus (11th Edition) by George B Thomas Thomas' Calculus, Early Trascendentals 10th ed Instructors Solutions Manual Two-Dimensional Incompressible Navier-Stokes Equations- Maciej Matyk Unit Operations of Chemical Engineering (7th) By Warren McCabe, Julian Smith University Physics with Modern Physics:,11 ed By Hugh D. Young, Roger A. Freedman, use with Fundamentals of Corporate Finance, 4th Edition By Bruce Swenson Vector Mechanics for Engineers: Dynamics, 7th By Ferdinand P. Beer(selected chapters) E. R. Johnston Vector Mechanics for Engineers: Statics, 7th By Ferdinand P. Beer(selected chapters) Vector Mechanics for Engineers: Statics, 7th Edition ,By Ferdinand P. Beer, E. Russell Johnston Jr., ElliotR Visual C++ How to Program, (3rd Edition) ,by Harvey & Paul Deitel & Associates Wireless communication and networks 2th by willian stallings Zill's a First Course in Differential Equations with boundary value problem 5th Zill's a First Course in Differential Equations with Modeling Applicants 7/e.81isolitions manual.81j don't leave a message here,please send email to solutionpay@hotmail.com, i will tell you how to do to get the solution A lot of Solution Manuals in Electronic (PDF)Format! A lot of Solutions Manuals in Electronic (PDF)Format! Just contact with solutionpay @ hotmail.com (my email address), these are parts of our solutions, if the solution you want isn.81ft on the list, don.81ft give up,please email to me. Don.81ft comment in here,please email to me A Course in Modern Mathematical Physics By Peter Szekeres(solution manual) A First Course in String Theory(solution manual) A Quantum Approach to Condensed Matter Physics By Philip ,Taylor(solution manual) A Quantum Approach to Condensed Matter Physics(2002) (.81c.81c) A Short Introduction to Quantum Information and Quantum Computation(2006) accompany Analysis and Design of Integrated Circuits, 4th by Gray, Hurst, Lewis Advanced Dynamics(2006) advanced engineering mathematics (8/e) by ERWIN KREYSZIG advanced engineering mathematics (8/e)( korean version) by ERWIN KREYSZIG advanced engineering mathematics.81i9/e.81j (even solutions) by ERWIN KREYSZIG advanced macroeconomics By Romer Advanced Modern Engineering Mathematics (3rd Edition) By Glyn James AISC Manual of Steel Construction: Load and Resistance Factor Design, Third Edition (LRFD 3rd Edition) An Introduction to Economic Dynamics An Introduction to Ordinary Differential Equations An Introduction to Partial Differential Equations (2005) By Yehuda Pinchover An Introduction To The Finite Element Method, 3rd Editionby J. 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