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

#3694Fetching Sponsored Content...

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

#3682Fetching Sponsored Content...

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
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

#3670Fetching Sponsored Content...

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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