January 2012
1 tag
Polynomials as Sequences
isomorphismes:
One reason polynomials are interesting is that you can use them to encode sequences.
In fact some of the theory of abstract algebra (the theory of rings) deals specifically with how your perspective changes when you erase all of the x^297 and x^16 terms and think instead about a sequence of numbers, which actually doesn’t represent a sequence at all but one single functional.
...
8 tags
Mitt’s Income vs. Your Income →
How long would it take the GOP candidate to earn what you make in a year?
This makes me sad! :(
Get rid of the anti-Missing-E fear-mongering...
I use missing e! Do you?
If you do…
tj:
I am tired of Tumblr, Inc.’s ongoing tantrum about Missing E.
If they hadn’t grossly exaggerated and relied on FUD for their message, I might be more sympathetic.
Now I just want to make sure I never see it again.
If you feel the same way, here’s how to get rid of it.
~ Chrome ~
If you use Google Chrome, get Stylish and then install...
adelaide asked: Whoa, where in Texas do you live? I live in a suburb right outside of Ft. Worth...
3 tags
3 tags
Watchintothecontinuum:
Music: “The New Anthem” by Jan Jelinek & Computer Soup Created with Mathematica code:
Manipulate[
Graphics[
Line[
Table[
{-.999^n*Sin[n*a], .999^n*Cos[n/a]}, {n, 0, 200}]],
PlotRange -> 1.3],
{a, 3, 3.78, .0001}]
Distribution of periods of closed trajectories in... →
arxiv-nlin:
Authors: Vesselin Petkov, Luchezar Stoyanov
We examine the asymptotics of the number of the closed trajectories of hyperbolic flows whose primitive periods lie in exponentially shrinking intervals Our results holds for hyperbolic dynamical systems having a symbolic model with a non-lattice roof function under the assumption that the corresponding Ruelle operator related to ...
Watchisomorphismes:
3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 … modulo 89
An application of group theory to Navy sonar — can you generate a sequence whose 1-differences are random? (whose 1-autocorrelations are nil)
Also the patterns look a bit like low-discrepancy sequences:
A Riemannian Approach to Reduced Plate, Shell, and... →
arxiv-nlin:
Authors: Raz Kupferman, Jake P. Solomon
We derive a dimensionally-reduced limit theory for an -dimensional nonlinear elastic body that is slender along dimensions. The starting point is to view an elastic body as an -dimensional Riemannian manifold together with a not necessarily isometric -immersion in -dimensional Euclidean space. The equilibrium configuration is the embedding...
3 tags
Copy + paste this into google
sqrt(cos(x))*cos(200 x)+sqrt(abs(x))-0.7)*(4-x*x)^0.01, sqrt(9-x^2), -sqrt(9-x^2) from -4.5 to 4.5
Submitted by: olsonblog
Definitely go do this…you won’t regret it! :O
8 tags
Science Sparring Society: Newton Vs. Leibniz →
Submitted by: samuelhansen
samuelhansen has started a new podcast over at ACMEScience.com about the great rivalries behind science called Science Sparring Society. The first episode is Newton Vs. Leibniz, in other words the story of the Calculus War.
21 tags
Small systems of Diophantine equations which have... →
arxiv-nlin:
Authors: Apoloniusz Tyszka
Let E_n={x_i=1, x_i+x_j=x_k, x_i \cdot x_j=x_k: i,j,k \in {1,…,n}}. There is an algorithm that for every computable function f:N—>N returns a positive integer m(f), for which a second algorithm accepts on the input f and any integer n>=m(f), and returns a system S \subseteq E_n such that S has infinitely many integer solutions and each...
