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Latest updated: Quadratic Equation, Worksheet Generator - added multiplication and division of fractions, Probability - Bayes' Theorem, Matrix Calculators, Gauss-Jordan Elimination - automatically append Identity Matrix, Simultaneous Linear Equations, Probability: Bayes' Theorem, Significant Figures Calculator, Geometric Linear Transformation,

Mathematics News

» Math journal puts Rauzy fractcal image on the cover
Fri, 12 Sep 2014 08:42:49 EDT
An image created by geometer Edmund Harriss made the cover of the mathematics journal Notices, published by the American Mathematical Society. The image, created in collaboration with Bill Casselman, appeared on the August 2014 edition (Volume 61 Number 7). It shows a stepped path winding through space with the corners of the path projected onto a plane. On the plane each type of corner lives in its own region. The collection of these regions is the Rauzy Fractal.
» Heat distributions help researchers to understand curved space
Tue, 26 Aug 2014 07:50:06 EDT
The heat equation is one of the most important partial differential equations. The behavior of the solution to the equation reflects the geometry of the underlying space very well. Therefore, this equation has been investigated very extensively in both analysis and geometry. The solution evolves over time so that the Dirichlet's energy functional decreases most efficiently. Recently, F. Otto introduced another characterization: the solution evolves so that the Boltzmann entropy increases most efficiently from the viewpoint of optimal transportation. Both of these characterizations enable us to study the heat equation on spaces admitting singularities, where usual differential calculus does not work. However, their identification in such spaces is unknown.

Provided courtesy of: Phys.org: Mathematics News
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