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andrewcharlesjones.github.io

In many types of programming, random seeds are used to make computational results reproducible by generating a known set of random numbers. However, the choice of a random seed can affect results in non-trivial ways.

gregorygundersen.com

gregory gundersen is a researcher in new york.

projecteuclid.org

In 1691, James (Jacob) Bernoulli proposed a problem called elastica problem: What shape of elastica, an ideal thin elastic rod on a plane, is allowed? Daniel Bernoulli discovered its energy functional, Euler-Bernoulli energy function, and the minimal principle of the elastica. Using it, Euler essentially solved the problem in 1744 by developing the variational method, elliptic integral theory and so on. This article starts with a review of its mathematical meaning and historical background. After that we present one of its extensions, statistical mechanics of elastica as a model of the DNA and the large polymers. We will call it a quantized elastica, and show that it is connected with the modified Korteweg-de Vries hierarchy, loop space, submanifold Dirac operators, moduli spaces of the real hyperelliptic curves and so on. By reviewing the other extensions of the elastica problem, we will see that elastica is in the center of mathematics even now.

albany.edu

Discovery and Learning for the Betterment of AllAt the University at Albany, public engagement has been at the center of our research and teaching since the founding of our institution 180 years ago.

google.com

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jeffreygwang.com

I love to write. My work has been featured in The Wall Street Journal, The Adroit Journal, and several other literary publications.