mm-553 === Subject: Re: On Papers of Cockle (1860) and Harley (1862) To answer the question: still some Journals left to answer particularly the British, the plan B would be writing my lecture notes and disseminate it myself (someday). Dr.M.Basti === Subject: Re: On Papers of Cockle (1860) and Harley (1862) Yes, I will type it on Latex, with proper editing, and printing with printing professionals. I have materials for several lecture notes. 20-30, times more than those of Harley and Cockle and Watson. Possibly a software will be attached for its computer Codes. Dr.Mehran Basti === Subject: Re: On Papers of Cockle (1860) and Harley (1862) > To answer the question: still some Journals left to answer particularly the > British, the plan B would be writing my lecture notes and disseminate it myself > (someday). OK, lets jump in the future... Please, I want to ask you in advance: for the lecture notes - use some form of TeX. --JS === Subject: lookning for a HP 41CV or HP 41CX calculator I am lookning for a HP 41CV or HP 41CX calculator, mine is on it's last leg and I need a replacement. If you have one you would like to === Subject: Maple vs Mathematica questions: symbolic & MacOS aspects only. Bonjour A long time user of Maple, working under MacOS, I feel the time has perhaps come to change CAS. I am thus looking for information (NOT Brießy, I currently do symbolic computations using Maple, and numeric computations using Matlab. I will keep on using Matlab at this point due to mission constraints, so I am only investigating the symbolic (as opposed to numeric) aspects of the problem. I am aware that Mathematica is supposed to be much more powerful than Maple where numerics are concerned. I did not look into [CapitalThorn]nancial details (is there a price gap between the two?). I am familiar with Maple's possibilities, but not with Mathematica's. The Wolfram Research website does not seem to contain *detailed* information of the symbolic capacities of Mathematica. I have not yet downloaded a demo version of Mathematica, but will do so. There is supposed to be a bridge between Matlab and Maple, but it is not working on the Mac, at least with the versions I have (Maple 5 to 9, Matlab 5.2.1), and I do not own the symbolic toolbox for Matlab (which is always built upon an older version of Maple), so the lack of link (if any) between Mathematica and Matlab would not be an issue. At any rate, the need for such direct link has been fairly low in my workaday existence (and when it did crop up, I went from symbolic to handwritten C++ implementation, to Matlab exploitation of output). A converter from Maple documents to Mathematica documents would be nice, but not strictly a necessity. Is there one? How do Maple and Mathematica compare, from a symbolic viewpoint, in term of breadth of [CapitalThorn]eld covered (base package, add-ons?), ef[CapitalThorn]ciency of solving algorithms, number of prominent bugs? Can any symbolic computation carried out under Maple be carried out under Mathematica? If not, which kinds fail? Any important gotchas to be aware of? by what I perceive is the lack of commitment (I remember the long dearth of upgrades between 7 and 9) and reactivity of Maplesoft towards my platform of choice (which will *NOT* change). I have the impression that Wolfram Research is better in that respect, is this true? Finally, part of my current insatisfaction with Maple undoubtedly comes from a feeling that Maplesoft may have been highjacked a couple of years ago by a bunch of marketing bozos out there to milk us for what we're worth, an insatisfaction culminating with the 9.5 upgrade disgrace. I have heard that Wolfram Research is quite wol[CapitalThorn]sh as well. Would I be changing a blind horse for an unseeing one? Am I completely wrong in my assumptions? Also, there is a community of astoundingly helpful individuals knowledgeable with Maple, is there one as well with respect to Mathematica? Merci Hubert Holin === Subject: Re: Maple vs Mathematica questions: symbolic & MacOS aspects only. > Bonjour *snip* > There is supposed to be a bridge between Matlab and Maple, but > it is not working on the Mac, at least with the versions I have > (Maple 5 to 9, Matlab 5.2.1), and I do not own the symbolic toolbox > for Matlab (which is always built upon an older version of Maple), so > the lack of link (if any) between Mathematica and Matlab would not be > an issue. At any rate, the need for such direct link has been fairly > low in my workaday existence (and when it did crop up, I went from > symbolic to handwritten C++ implementation, to Matlab exploitation of > output). Just FYI, MATLAB 6.5 (R13) and the new MATLAB 7.0 (R14) are available for the Mac, as are versions 3.0.1 (for R13) and 3.1 (for R14) of the Symbolic Math Toolbox. With version 3.0 of the toolbox, we updated the Maple kernel version used by the toolbox to Maple 8. I don't know if the functionality of the Maple 8 kernel is suf[CapitalThorn]cient for your symbolic calculation needs, but if it is you might want to contact your local MathWorks of[CapitalThorn]ce to see if you can get a trial of the newer versions of MATLAB and the Symbolic Math Toolbox. If you're not sure whom you should contact, select your country from the menu on this page: http://www.mathworks.com/company/aboutus/contact_us/ -- Steve Lord slord@mathworks.com === Subject: 1st World Congress and School on Universal Logic (UNILOG 2005) ************************************************************* *************** ************************************************************* **************** ********** 1st World Congress and School on Universal Logic (UNILOG 2005) http://www.uni-log.org Montreux Switzerland, School : March 26-30 ; Congress : March 31 - April 3, 2005 This event will focus on: 1) Techniques that can be used for a general theory of logics (Labelled deductive systems, Kripke structures, Logical matrices, etc.) ; 2) Studies of classes of logics (Substructural logics, Non monotonic logics, Paraconsistent logics, etc.) 3) Scope of validity and domain of application of fundamental theorems of logic (Completeness, Deduction, Cut-elimination, etc.) 4) Philosophical considerations about the nature of logic and the universality of some logical laws or axioms The school is intended for advanced students and young researchers. There will be about 20 tutorials on many subjetcs: combination of logics, multiple conclusion logic, combinatory logic, logics and games, abstract model theory, logic as language vs. logic as calculus, category theory for logics, etc. Invited speakers of the congress will include A.Avron, D.Batens, J.Corcoran, M.Dunn, D.Gabbay, R.Jansana, A.Koslow, V.de Paiva, K.Segerberg. Contributed papers for the congress can be submitted before October 30, More information on the website: http://www.uni-log.org ************************************************************* *************** ************************************************************* *** === Subject: Re: sin(x1)*exp(-(1/2)*transpose(x)*inv(P)*x) > |>I was using MATLAB 6.1 to access MAPLES symbolic package. > |>The symbolic variables were > |>syms p11 p12 p22 mu1 mu2 x1 x2 > |>I made the assumptions > |>maple(?assume','p11>0',[Capit alOTilde]p22>0','p22*p11>p12^2') > |>Now if: > |>P=[p11 p12; > |> p12 p22] > |>mu=[x1; > |> x2] > |>Then why can't maple integrate: > |>sin(x1)*exp(-(1/2)*transpose(x)*inv(P)*x) > I assume x = mu? Close enough, I actually meant: sin(x1)*exp(-(1/2)*transpose(x-mu)*inv(P)*(x-mu)) Anyway, The two integrals are pretty equivalent, so if maple can do one it should be able to do the other. I guess, the version of MAPLE used by MATLAB 6.1 is just too old to do this integral. I wonder what version of maple MATLAB 6.1 uses, what version MATLAB 6.5 uses and what, the most current version of MAPLE is. I also wonder if someone had a different version of MAPLE if you can tell MATLAB to use that version instead. Is: P:= <,: Equivalent to: array([[p11,p12],[p12,p22]]) > |>over the range from x1=-inf to inf > I don't know which version of Maple Matlab is using. I can't help > you with the Matlab part, but any recent Maple version should be > able to do this. > with(LinearAlgebra): > P:= <,: > mu:= : > assume(p11>0, p22>0, p11*p22>p12^2); > int(sin(x1)*exp(-1/2*Transpose(mu).P^(-1).mu),x1=-in[CapitalThorn]nity.. in[CapitalThorn]nity); > / / 2 2 > 1 |1 (1/2) | -p12~ + 2 I x2 p12~ + x2 + p11~ p22~| (1/2) > - --------- |- I Pi exp|- --------------------------------------| 2 > (1/2) 2 2 p22~ / > p22~ > (1/2) > / /2 I x2 p12~ / 2 | > |exp|-----------| - 1| p11~ p22~ - p12~ / | > p22~ / / / > Robert Israel israel@math.ubc.ca > Department of Mathematics http://www.math.ubc.ca/~israel > University of British Columbia > Vancouver, BC, Canada V6T 1Z2 === Subject: Re: sin(x1)*exp(-(1/2)*transpose(x)*inv(P)*x) >Is: >P:= <,: Oops, this should have been <| >Equivalent to: >array([[p11,p12],[p12,p22]]) That would be for the linalg package as opposed to the newer LinearAlgebra package. You could use > with(linalg): P:= array([[p11,p12],[p12,p22]]): mu:= vector([x1,x2]): assume(p11>0, p22>0, p11*p22>p12^2); int(sin(x1)*exp(-1/2*evalm(transpose(mu) &* P^(-1) &* mu)), x1=-in[CapitalThorn]nity..in[CapitalThorn]nity); Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 === Subject: Re: What happened for 140 years? > To answer the question, I would like to say that Harley did not associate > solvable differential equations to the polynomials (beyond degree 3), and once > my papers are published, it can be compared with the past. > Here we are not talking about approximation methods. > Dr.M.Basti I am sure I am wasting my breath, but to solve a linear differential equation with constant coef[CapitalThorn]cients you need to [CapitalThorn]nd the roots of the characteristic equation or equivalently the eignvalues of the state space matrix. Thus you are no further ahead. You could [CapitalThorn]nd a series solution based upon the matrix exponential. In some cases this could be related to the eignvalues of a state space matrix. But I am not sure that if in these cases one couldn't one use some other technique to factor the polynomial anyway, such as the rational root theorem. Maybe, some examples could be helpful. I might post one. I am sure if this works in some cases it is probably published somewhere. === Subject: Re: What happened for 140 years? > I am sure I am wasting my breath, but to solve a linear differential > equation with constant coef[CapitalThorn]cients Basti's differential equations are generally not linear and with nonconstant coef[CapitalThorn]cients. === Subject: Is this Maple's code written correctly? by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i52GtZI27740; There is a problem that I have translated into Maple code but which doesn't yield the awaited results. The problem is to determine the sign of the function f(r,d)= r^2+1-d^2 + ((1+d-r)*(d+1+r)*(-r-1+d)*(d-1+r))^(1/2) under the assumptions r>0, d>r+1. When I run: assume( r,real ): additionally( r>0 ): assume( d,real ): additionally( d>r+1 ): signum(r^2+1-d^2+((1+d-r)*(d+1+r)*(-r-1+d)*(d-1+r))^(1/2)); Maple's answer is -signum(-r^2-1+d^2-sqrt((1+d-r)*(d+1+r)*(-r-1+d)*(d-1+r))) Is this code written correctly? I have the intuition that the sign should be negative (that's what I noticed when testing it numerically with 1<=r<=100 and r+1The problem is to determine the sign of the function |> f(r,d)= r^2+1-d^2 + ((1+d-r)*(d+1+r)*(-r-1+d)*(d-1+r))^(1/2) |>under the assumptions r>0, d>r+1. |>When I run: |> assume( r,real ): |> additionally( r>0 ): |> assume( d,real ): |> additionally( d>r+1 ): |> signum(r^2+1-d^2+((1+d-r)*(d+1+r)*(-r-1+d)*(d-1+r))^(1/2)); |>Maple's answer is |> -signum(-r^2-1+d^2-sqrt((1+d-r)*(d+1+r)*(-r-1+d)*(d-1+r))) |>Is this code written correctly? It's not incorrect, it's just that you have too much faith in Maple's ability to answer this type of question. You might try using simplify, but that doesn't help in this case. |>I have the intuition that the sign should be negative (that's what I |>noticed when testing it numerically with 1<=r<=100 and r+1 Q:=r^2+1-d^2+((1+d-r)*(d+1+r)*(-r-1+d)*(d-1+r))^(1/2); R:=r^2+1-d^2-((1+d-r)*(d+1+r)*(-r-1+d)*(d-1+r))^(1/2); > signum(expand(R*Q)/R); -1 Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 === Subject: Re: Is this Maple's code written correctly? Perhaps it can't perform the calculation, and returns a noun form. Macsyma would do the same in such a case. But you can apply some reasoning and see what happens. f(r,d) is of the form A+sqrt(B). Look at A^2-B^2=C^2 and expand it out. If A^2 is bigger, write B=sqrt(A^2-C^2), and vice versa. Once you eliminate A or B using C, you will see which expression contributes more, remember that d>r+1. > There is a problem that I have translated into Maple code but which > doesn't yield the awaited results. > The problem is to determine the sign of the function > f(r,d)= r^2+1-d^2 + ((1+d-r)*(d+1+r)*(-r-1+d)*(d-1+r))^(1/2) > under the assumptions r>0, d>r+1. > When I run: > assume( r,real ): > additionally( r>0 ): > assume( d,real ): > additionally( d>r+1 ): > signum(r^2+1-d^2+((1+d-r)*(d+1+r)*(-r-1+d)*(d-1+r))^(1/2)); > Maple's answer is > -signum(-r^2-1+d^2-sqrt((1+d-r)*(d+1+r)*(-r-1+d)*(d-1+r))) > Is this code written correctly? > I have the intuition that the sign should be negative (that's what I > noticed when testing it numerically with 1<=r<=100 and r+1 Olivier === Subject: Re: Is this Maple's code written correctly? by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i52IALk02979; Okay, you gave me the right way toward the solution. I now put the problem in the form of signum( A + sqrt(B )) and I denote by H my assumptions on r and d. Maple returns -1 for signum( A - sqrt(B )) under H On the other hand, if I compute (A^2 - B), I get: 4*r^2 . Hence signum(A + sqrt(B)) is necessarily negative. === Subject: Re: Handheld computer with math software > Hello! > Does anyone know if MATLAB, Maple, Mathematica or any such program (are > there others?) are available for any handheld computer like Palm? Axiom will shortly be running on a Sharp Zaurus 5600. Magnus already runs there (special purpose CA). Yacas already runs there. Tim Daly axiom at tenkan.org === Subject: Re: Handheld computer with math software Originator: ix@io.com (Lupo LeBoucher) > You won't have to wait too much to see handheld computer based in Linux > with nice CAS features, but with keyboard. >The best handheld computers have performances enough to run MATLAB (right?). >That would be awesome. Maybe Lyme, XCAS and the other programs mentioned >have equivalent capability, I'll check them out. Waiting a year or so before >investing might be a good idea. Linux is very much preferable. I recently had the decision made for me; my HP200LX's keyboard kicked the bucket. Importing the Zaurus SL-C860 was an excellent solution for me. It's not quite as useful (yet) as the HP200LX, but it does a lot of things the HP couldn't, like run python and common lisp. And there are several very serious CAS available for it (Macsyma/Maxima is pretty exciting, though it lacks a useful UI for this form factor). -Lupo We must free ourselves from the prison of public education and politics. -Epicurus, 300B.C.E. === Subject: Re: Handheld computer with math software > Does anyone know if MATLAB, Maple, Mathematica or any such program (are > there others?) are available for any handheld computer like Palm? One option is to use the Palm-like device to simply access one of the packages mentioned above running on an normal desktop system through the use of something like the free vnc virtual network client. I have a Treo-600 Palm phone (Sprint variety) for which unlimited data access costs me $10/month (may be more now) and on which I can use PalmVNC to access my desktop at work where I have Mathematica among other things. Using the (not free) Mergic VPN software you can even make this connection securely. The usability of such a solution will depend on the volume of use and the desperation of the user :-) Some applications work better on a tiny screen with limited keyboard functionality than others. But the best solution is generally to bring along a computer capable of running the software you want to use. You might look at some of the tiny notebook computers from Japan that are imported and resold by Dynamism (http://www.dynamism.com) some of which are approaching pocket sized yet run full Windows versions. G. === Subject: Re: Handheld computer with math software How would you like a CAS that speaks math out loud? I can do this (in lisp, presumably on a PDA), but would not seriously consider it as sole output except perhaps for visually disabled people. But then I don't understand the attraction of a computer without a keyboard or decent display for math, so maybe speech + a PDA makes sense to someone. Similarly, I also would not try to write a novel on PostIts. But it could be done. === Subject: Pythagorean triples in Mathematica Does anyone have, or know of, a function that will return as output all the Pythagorean triples (both primitive and non-primitive) that contain its argument. For example AllTriples[20] would return and , which is an exhaustive list of all the triples that contain 20, either as a leg or as the hypotenuse. Tony begin 666 clip_image002.gif === Subject: Re: Pythagorean triples in Mathematica by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i52Kv4219146; >Does anyone have, or know of, a function that will return as output all the >Pythagorean triples (both primitive and non-primitive) that contain its >argument. For example >AllTriples[20] would return and , which is an exhaustive list of all the >triples that contain 20, either as a leg or as the hypotenuse. >Tony You can use Reduce with stipulations that variables are integer valued and positive. allPythagoreanTriples[n_Integer] /; n>0 := With[ {result = Reduce[((x^2+y^2==n^2 && x>y) || x^2+n^2==y^2) && Element[{x,y},Integers] && x>0 && y>0]}, Sort[Map[Sort, {x,y,n} /. {ToRules[result]}]] ] ] A few examples: In[31]:= InputForm[allPythagoreanTriples[20]] Out[31]//InputForm= {{12, 16, 20}, {15, 20, 25}, {20, 21, 29}, {20, 48, 52}, {20, 99, 101}} In[32]:= InputForm[allPythagoreanTriples[120]] Out[32]//InputForm= {{22, 120, 122}, {27, 120, 123}, {35, 120, 125}, {50, 120, 130}, {64, 120, 136}, {72, 96, 120}, {90, 120, 150}, {119, 120, 169}, {120, 126, 174}, {120, 160, 200}, {120, 182, 218}, {120, 209, 241}, {120, 225, 255}, {120, 288, 312}, {120, 350, 370}, {120, 391, 409}, {120, 442, 458}, {120, 594, 606}, {120, 715, 725}, {120, 896, 904}, {120, 1197, 1203}, {120, 1798, 1802}, {120, 3599, 3601}} In[33]:= InputForm[allPythagoreanTriples[544]] Out[33]//InputForm= {{33, 544, 545}, {256, 480, 544}, {408, 544, 680}, {450, 544, 706}, {544, 1020, 1156}, {544, 1092, 1220}, {544, 2142, 2210}, {544, 2280, 2344}, {544, 4335, 4369}, {544, 4608, 4640}, {544, 9240, 9256}, {544, 18492, 18500}, {544, 36990, 36994}, {544, 73983, 73985}} In[35]:= InputForm[allPythagoreanTriples[2544]] Out[35]//InputForm= {{742, 2544, 2650}, {1060, 2544, 2756}, {1344, 2160, 2544}, {1908, 2544, 3180}, {2233, 2544, 3385}, {2544, 2915, 3869}, {2544, 3392, 4240}, {2544, 4770, 5406}, {2544, 5330, 5906}, {2544, 7420, 7844}, {2544, 8235, 8619}, {2544, 10017, 10335}, {2544, 11092, 11380}, {2544, 15158, 15370}, {2544, 16758, 16950}, {2544, 22400, 22544}, {2544, 25217, 25345}, {2544, 30475, 30581}, {2544, 33660, 33756}, {2544, 44908, 44980}, {2544, 50530, 50594}, {2544, 67392, 67440}, {2544, 89870, 89906}, {2544, 101108, 101140}, {2544, 134820, 134844}, {2544, 179767, 179785}, {2544, 202240, 202256}, {2544, 269658, 269670}, {2544, 404492, 404500}, {2544, 539325, 539331}, {2544, 808990, 808994}, {2544, 1617983, 1617985}} Daniel Lichtblau Wolfram Research === Subject: Re: Pythagorean triples in Mathematica Tony >Does anyone have, or know of, a function that will return as output > all the >Pythagorean triples (both primitive and non-primitive) that contain > its >argument. For example >AllTriples[20] would return and , which is an exhaustive list of all > the >triples that contain 20, either as a leg or as the hypotenuse. >Tony > You can use Reduce with stipulations that variables are integer valued > and positive. > allPythagoreanTriples[n_Integer] /; n>0 := With[ > {result = Reduce[((x^2+y^2==n^2 && x>y) || x^2+n^2==y^2) && > Element[{x,y},Integers] && x>0 && y>0]}, > Sort[Map[Sort, {x,y,n} /. {ToRules[result]}]] > ] > A few examples: > In[31]:= InputForm[allPythagoreanTriples[20]] > Out[31]//InputForm= > {{12, 16, 20}, {15, 20, 25}, {20, 21, 29}, {20, 48, 52}, {20, 99, > 101}} > In[32]:= InputForm[allPythagoreanTriples[120]] > Out[32]//InputForm= > {{22, 120, 122}, {27, 120, 123}, {35, 120, 125}, {50, 120, 130}, > {64, 120, 136}, {72, 96, 120}, {90, 120, 150}, {119, 120, 169}, > {120, 126, 174}, {120, 160, 200}, {120, 182, 218}, {120, 209, 241}, > {120, 225, 255}, {120, 288, 312}, {120, 350, 370}, {120, 391, 409}, > {120, 442, 458}, {120, 594, 606}, {120, 715, 725}, {120, 896, 904}, > {120, 1197, 1203}, {120, 1798, 1802}, {120, 3599, 3601}} > In[33]:= InputForm[allPythagoreanTriples[544]] > Out[33]//InputForm= > {{33, 544, 545}, {256, 480, 544}, > {408, 544, 680}, {450, 544, 706}, {544, 1020, 1156}, {544, 1092, > 1220}, > {544, 2142, 2210}, {544, 2280, 2344}, {544, 4335, 4369}, {544, 4608, > 4640}, > {544, 9240, 9256}, {544, 18492, 18500}, {544, 36990, 36994}, > {544, 73983, 73985}} > In[35]:= InputForm[allPythagoreanTriples[2544]] > Out[35]//InputForm= > {{742, 2544, 2650}, {1060, 2544, 2756}, {1344, 2160, 2544}, > {1908, 2544, 3180}, {2233, 2544, 3385}, {2544, 2915, 3869}, > {2544, 3392, 4240}, {2544, 4770, 5406}, {2544, 5330, 5906}, > {2544, 7420, 7844}, {2544, 8235, 8619}, {2544, 10017, 10335}, > {2544, 11092, 11380}, {2544, 15158, 15370}, {2544, 16758, 16950}, > {2544, 22400, 22544}, {2544, 25217, 25345}, {2544, 30475, 30581}, > {2544, 33660, 33756}, {2544, 44908, 44980}, {2544, 50530, 50594}, > {2544, 67392, 67440}, {2544, 89870, 89906}, {2544, 101108, 101140}, > {2544, 134820, 134844}, {2544, 179767, 179785}, {2544, 202240, > 202256}, > {2544, 269658, 269670}, {2544, 404492, 404500}, {2544, 539325, > 539331}, > {2544, 808990, 808994}, {2544, 1617983, 1617985}} > Daniel Lichtblau > Wolfram Research === Subject: Re: A proof for Goldbach's conjecture by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i52KKvq16159; >hello. >I claim that i have proven goldbach conjecture. >Masoud Sheykhi >Hello. >I believe that my proof is the best and the interesting proof for >goldbach conjecture . Now , I am waitting to hearing further about my >proof. I am an engineer in sarcheshmeh copper complex ,working as an >technical inspector in iran. >Masoud Sheykhi >Hello. >After i informed of goldbach's conjecture challenge from channel 4 of >I.R.I.B news agency in iran , I prepared my previous idea in 25th 2000 >at 18:30 PM. Then my researchs started for correcting and compeleting Professor >Eric Bedford from indiana university is knowing it very good.Also i >have sent my some elementary works and my [CapitalThorn]nal proof to london >mathematical society;professor Burstall,professor J.E.Toland >,professor J.E Cremona at the university of Bath, professor >Radjabalipour in iran and professor Eric Bedford at the indiana >university. Also i have sent my some elementary idea to professor >francois hennecart in France , managing-editor@cms.math.ca and iran >mathematical society.i have studied in chemical >engineering,exteractive metallurgy and mathematics .My hard working >conditions in sarcheshmeh copper complex and suffering caused that i >have studing and working on goldbach conjecture.I am from sheshjavan >,boien miyandasht,daran,feraidan ,isfahan ,iran. >Sarcheshmeh copper complex is in kerman ,iran. >Masoud Sheykhi If you have a proof submit to a journal. Nobody will believe you until they see it published in a peer reviewed journal. You should know people claim to have solved the Goldbach conjecture every day! I suggest, submit to a journal. If you're lucky it will get reviewed, you will wait between 4-9months for a reply detailing your error (there usually is an error - some more basic than others). If you are unlucky you will just get a letter (after 4-9 months) telling you you do not have a proof and giving no reason whatsoever, and you will have wasted a year of your life just submitting a failed proof and ghetting no feedback. If you still believe, you will rework the proof (if lucky to [CapitalThorn]nd the error) and resubmit. Whereupon you will wait another 4-9 months, until some referee discovers another irritating error and so the cycle goes on. If your proof involves no analysis, the chances are, you cannot possibly have a proof. If it does, there is usually some basic gap in the analysis (though you may be the exception!). Unless you are a known entity in the mathematics community (even if you do have a proof) nobody may care! [Simply because they don't have the time to wade through lines of (usually) badly written mathematics]. But if you do have a proof and believe it in the core of your soul (make sure to look within yourself and ensure you do not have even the slightest inkling of doubt - because if you do your intuition is telling you that you're wrong!) then go for it. But you must have iron resolve to persevere. Try to concemtrate on explaining your proof as simply as possible. people don't have the time to bust their heads over a proof, which in all likelihood is false. Why not start by trying to explain the essentials of your proof in a few lines here in already have discovered your error - there usually is one. Don't mean to dampen you ardour. But when someone does eventually [CapitalThorn]nd a proof, the most dif[CapitalThorn]cult thing won't have been [CapitalThorn]nding the proof as much as convincing others that it is indeed a proof. kamalu