July 2011
Mathematics is the music of the reason →
cab1729:
Mathematical Poetics: Boundaries and Flows
isomorphismes:
Gauß’ divergence theorem states that, unless matter is created or destroyed, the density within a region of space V can change only by flowing through its boundary ∂V. Therefore
i.e., you can measure the changes in an entire region by simply measuring what passes in and out of…
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I just looked up how to convert PSI to lbs/ sq. in.
…I need a vacation!!
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intothecontinuum:
In this iterated function system, a Möbius transformation is applied in succession to the white circle yielding the blue and yellow circles. Varying the characteristic constant of the transformation gives the different arrangements seen in each frame of the animation. More IFS here GIF source: Java app
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intothecontinuum:
A pretty wild narcissistic number is an integer N that can be represented by mathematically manipulating its digits (in order) using only the arithmetical operations of + - x ÷ ^ √ ! . Here are some examples:
There are plenty more listed here.
An elementary way to approach Fourier transforms →
cab1729:
Why another introduction to the Fourier transform?There are many elementary introductions to the discrete Fourier transform on the web. But this one is going to be a little different.
The Euler-Maclaurin formula, Bernoulli numbers,... →
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Mental Math in Infants →
cab1729:
Babies understand counting before they utter numbers
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Superadditivity
isomorphismes:
“The whole is more than the sum of the parts”
Who says scientists are reductionistic? Any superadditive system (due to complexity, interaction terms, valuation by an Lp norm with 0<p<1 [-1<p<1?], or some other reason) adds up to more in total than the pieces individually do.
Semimetric but not a seminorm.
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Notes on Ding-Iohara algebra and AGT conjecture. →
arxiv-nlin:
Authors: H. Awata, B. Feigin, A. Hoshino, M. Kanai, J. Shiraishi, S. Yanagida
We study the representation theory of the Ding-Iohara algebra to find -analogues of the Alday-Gaiotto-Tachikawa (AGT) relations. We introduce the endomorphism of the Ding-Iohara algebra, having two parameters and . We define the vertex operator by specifying the permutation relations with the...
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The Cutting-Edge Physics of Jackson Pollock
jonprins:
The Cutting-Edge Physics of Jackson Pollock
youmightfindyourself:
Jackson Pollock, famous for his deceptively random-seeming drip paintings, took advantage of certain features of fluid dynamics years before physicists thought to study them.
(snipped wall of text; click through to original quotation)
Another interesting note about Pollock’s paintings; they’re...
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Number systems and the Chinese Remainder Theorem. →
arxiv-nlin:
Authors: Christiaan E. van de Woestijne
A well-known generalisation of positional numeration systems is the case where the base is the residue class of modulo a given polynomial with coefficients in (for example) the integers, and where we try to construct finite expansions for all residue classes modulo , using a suitably chosen digit set. We give precise conditions under which...
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Multiplicity and regularity of periodic solutions... →
arxiv-nlin:
Authors: Jean Marcel Fokam
We prove the existence of infinitely many classical periodic solutions for a class of degenerate semilinear wave equations: \[ u_{tt}-u_{xx}+|u|^{s-1}u=f(x,t), \] for all . In particular we prove the existence of infinitely many classical solutions for the case posed by Brézis in \cite{BrezisBAMS}. The proof relies on a new upper a priori estimates for...
