Abstract: Analytic expressions are developed for integrals over curvilinear domains where the integrands are the product of polynomial bases with natural logarithm kernels whose arguments are ...

In this paper, an efficient method is presented for solving two dimensional Fredholm and Volterra integral equations of the second kind. Chebyshev polynomials are applied to approximate a solution for ...

How can the behavior of elementary particles and the structure of the entire universe be described using the same mathematical concepts? This question is at the heart of recent work by the ...

Polynomial equations are a cornerstone of modern science, providing a mathematical basis for celestial mechanics, computer graphics, market growth predictions and much more. But although most high ...

This is the way I am currently evaluating the integrals of shape functions in neighboring elements (not in the element they belong to): To test my results I also compute the integral of Lagrange ...

Anthony Bonato: It’s a bit of an urban legend in mathematics. There’s a sort of a romance to the story, in a way. If you're enjoying this article, consider supporting our award-winning journalism by ...

Google's DeepMind AI has been used for a multitude of ground-breaking research. For example, the artificial intelligence model is planned to be used to design new pharmaceuticals via machine learning.

Mathematica code for integrating even polynomials of speed in Boltzmann collision integrals. All the code is in the notebook. One can choose some predefined polynomials, corresponding to aggregation ...