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3696
Riemann zeta, why are the residues either zero or one? (*Riemann zeta, why are the residues either zero or one?*) Table[Residue[(Zeta[s] - Zeta'[s - 1 + ZetaZero[n]]/Zeta[s - 1 + ZetaZero[n]]), {s, 1}], {n, 1, 12}]
Mats Granvik
Apr 18
#3696
 
3695
Complex Algebraic Surfaces (London Mathematical Society Student Text http://www.amazon.com/Complex-Algebraic-Surfaces-Mathematical-Society/dp/0521498422/ref=sr_1_1?ie=UTF8&qid=1397746861&sr=8-1&keywords=Arnaud+Beauville The
Roger Bagula
Apr 17
#3695
 
3694
Senior wins Churchill Scholarship | Harvard Gazette http://news.harvard.edu/gazette/story/2014/04/senior-wins-churchill-scholarship/ Senior wins Churchill Scholarship Alpoge Æ14 to pursue graduate study at the
Roger Bagula
Apr 16
#3694
 
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3693
Proof Theory: Second Edition (Dover Books on Mathematics): Gaisi Tak http://www.amazon.com/Proof-Theory-Second-Edition-Mathematics/dp/0486490734/ref=pd_sim_b_3?ie=UTF8&refRID=00M12DE60266JV4FFRP5 Focusing on Gentzen-type proof
Roger Bagula
Apr 15
#3693
 
3692
a new sort of 3d parametric (I add my new color gradient to the post:) the idea of a Gauss map on a raw complex plane gave me this idea: colortab = Sort[Flatten[ Delete[ Sort[ Union[
Roger Bagula
Apr 14
#3692
 
3691
Martin Gardner, Genius Of Recreational Mathematics : NPR http://www.npr.org/2014/04/12/302166509/martin-gardner-a-genius-of-recreational-mathematics Martin Gardner, Genius Of Recreational Mathematics April 12, 2014
Roger Bagula
Apr 14
#3691
 
3690
How the unreasonable effectiveness of mathematics can work elsewhere http://www.irishtimes.com/news/science/how-the-unreasonable-effectiveness-of-mathematics-can-work-elsewhere-1.1730695 How the unreasonable effectiveness of
Roger Bagula
Apr 14
#3690
 
3689
Gaussian Prime Factorization Calculator http://www.had2know.com/academics/gaussian-prime-factorization-calculator.html How to Factor Integers Over the Gaussian Primes Gaussian Factorization
Roger Bagula
Apr 11
#3689
 
3688
a seven dimensional Gauss map for SO(4) ( or D_2) This solves for a 7 dimensional sphere as a projection of an SO(4) like matrix. the z[7] coordinate is chiral. In the half space to 7d sphere that results,
Roger Bagula
Apr 10
#3688
 
3687
Anima Ex Machina » Blog Archive » Leibniz medallion comes to life http://www.mathrix.org/liquid/archives/the-history-of-the-chaitin-leibniz-medallion
Roger Bagula
Apr 10
#3687
 
3686
SO(3) matrix group to 4d Gauss Map The U(1)*SU(2) matrix version made me think that a simple 3d to 4d Gauss map of this sort should exist: Clear[s, x, y, z, x1, y1, z1, t1] i3 =
Roger Bagula
Apr 9
#3686
 
3685
5d Gauss maps 5d hypersphere:elliptical Clear[x, y, z, t, x1, y1, z1, t1, tau1, r, w] r = Sqrt[x^2 + y^2 + z^2 + t^2]; x1 = 2*x/(1 + r^2); y1 = 2*y/(1 + r^2); z1 = 2*z/(1 +
Roger Bagula
Apr 9
#3685
 
3684
extending the spherical Gauss Map to an hperbolic four space The virtue to this method is that Expand[Sum[Tr[s[i].s[i]], {i, 0, 3}]/2]==t^2 - x^2 - y^2 - z^2 which is a special relativity like c=1 four space sphere. (*
Roger Bagula
Apr 8
#3684
 
3683
‘Infinitesimal,’ a Look at a 16th-Century Math Battle - NYTimes. http://www.nytimes.com/2014/04/08/science/infinitesimal-looks-at-an-historic-math-battle.html?_r=0
Roger Bagula
Apr 8
#3683
 
3682
Gaussian integer half plane to disk nn = 20; mm = 20; v = Table[N[Abs[(1 + n + I*m)/(1 - (n + I*m))]], {n, -nn, nn}, {m, -mm, mm}] ListDensityPlot[v] ListPlot3D[v, Mesh -> False, AspectRatio ->
Roger Bagula
Apr 7
#3682
 
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3681
Pascal 4d pyramid in Gaussian integers This program only shows the 2d sums, but a 4d pyramid that is equivalent to the 2d Pascal's triangle exists: ( and the results aren't integers) nn = 20; mm =
Roger Bagula
Apr 7
#3681
 
3680
The incredible history of infinitesimals and the birth of modern mat http://www.salon.com/2014/04/04/the_incredible_history_of_infinitesimals_and_the_birth_of_modern_mathematics_partner/ Friday, Apr 4, 2014 04:00 PM PDT The
Roger Bagula
Apr 5
#3680
 
3679
RE: [Active_Mathematica] The von Mangoldt function as a Fourier tran Clear[n, k, t, A, nn, B, g1, g2] nn = 32 A = Table[ Table[If[Mod[n, k] == 0, 1/(n/k)^(1/2 + I*t - 1), 0], {k, 1, nn}], {n, 1, nn}]; MatrixForm[A]; B =
Mats Granvik
Apr 3
#3679
 
3678
The von Mangoldt function as a Fourier transform of the Möbius func Clear[n, k, t, A, nn, B] nn = 60 A = Table[ Table[If[Mod[n, k] == 0, 1/(n/k)^(1/2 + I*t - 1), 0], {k, 1, nn}], {n, 1, nn}]; MatrixForm[A]; B = FourierDCT[
Mats Granvik
Apr 3
#3678
 
3677
Re: two time like projections [1 Attachment] I concluded that the 4d plot is pretty much a 4d torus where a sphere moves around a circle. The 2d version general projective line is just a unit for all
rlbagulatftn
Apr 3
#3677
 
3676
Re: two time like projections [1 Attachment] Interesting plots when you rotate them around. Diplomingenjör Mats Granvik http://math.stackexchange.com/users/8530/mats-granvik To:
Mats Granvik
Apr 2
#3676
 
3675
two time like projections Using a circle for a+I*b there are two time like ways to do the 4d projection: Clear[x, y, z, r, a, b, w, t, x1, y1, z1] (* Generalizing the projective line
Roger Bagula
Apr 2
#3675
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3674
some generalizations The traditional projective line parametric is: {(1-z^2)/(1+z^2),2*z/(1+z^2)} and the corresponding Gauss Map is: r=(x^2+y^2)^(1/2)
Roger Bagula
Apr 2
#3674
 
3673
Raspsberry Pi and Wolfram: a must-have for every child | Enterprise http://www.pcpro.co.uk/realworld/387928/raspsberry-pi-and-wolfram-a-must-have-for-every-child Gallery Raspsberry Pi and Wolfram: a must-have for every child
Roger Bagula
Apr 1
#3673
 
3672
Gauss map version of the 3rd type of projective line So far this is my best effort at a 3rd type hyperbolic projective line as a Gauss map: Clear[r, x, y] r = Sqrt[x^2 + y^2] (* Hermetian projection of zauss like
Roger Bagula
Mar 31
#3672
 
3671
a new sort of minimal surface function based on the Poisson kernel In a systems theory book ( a Schaum's outline) a discussion of the half plane to disk transform that developed the following Poisson Kernel: complex variables
Roger Bagula
Mar 29
#3671
 
3670
three projective lines: one elliptical and two hyperbolic The first of these I would never have suspected: x0 = (1 - t^2)/(2*t); y0 = (1 + t^2)/(2*t); x1 = (1 + t^2)/(1 - t^2); y1 = 2*t/(1 - t^2); x2 = (1 - t^2)/(1 +
Roger Bagula
Mar 29
#3670
 
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3669
Spectra with multiples of 2*Pi/Log[2] (*program start*) Clear[n, k, t, A, nn, h] nn = 70; h = 2; A = Table[ Table[If[Mod[n, k] == 0, If[Mod[n/k, h] == 0, 1 - h, 1]/(n/k)^(1/2 + I*t - 1), 0], {k, 1,
Mats Granvik
Mar 27
#3669
 
3668
Re: Very sharp spikes in spectrum, is it by accident? I confirmed it now, it is an error. Diplomingenjör Mats Granvik http://math.stackexchange.com/users/8530/mats-granvik To: active_mathematica@yahoogroups.com
Mats Granvik
Mar 27
#3668
 
3667
Re: Very sharp spikes in spectrum, is it by accident? It must be some error on my part, since it doesn't change by setting "nn" to less than 2. Diplomingenjör Mats Granvik
Mats Granvik
Mar 27
#3667
 
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