OpenAI’s trove of new math results doesn’t fully solve any of these highly prestigious open questions, but it seems to make ...
A new open-source radiative transfer solver called EigenFlux combines mesh-based angular discretization, natural-reflectance ...
Mind’s AI system, AlphaProof, provided Lean with proofs of three of the competition’s problems. A year later, four AI systems performed at the level of a gold medalist. However, problems posed at the ...
Such a glut has left some queasy. The excitement of potential new mathematical truths is, for many researchers, freighted ...
Mathematicians love to collect elegant, profound questions that defy proof: the longer the holdout, the better. And one day ...
A collection of precise open problems drawn from books and research publications, with references and dated checks for subsequent solutions. I have several motivations for starting this repository: We ...
Scientific computing increasingly requires both accurate simulations of physical systems as well as optimizing them over many parameters for tasks such as inverse ...
ABSTRACT: Darcy’s law is the fundamental equation describing the flow of a fluid through a porous medium. Combined with the principle of mass conservation, it leads to the diffusion Equation (e.g., ...
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The efficient calculation of eigenvalues and eigenvectors constitutes a fundamental problem across numerous scientific and engineering disciplines, from quantum mechanics to structural analysis.
The study of nonlinear eigenvalue problems (NEPs) has matured into a vibrant field at the intersection of numerical analysis, operator theory and applied mathematics. In contrast to the classical ...
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