Creative Commons (CC): This is a Creative Commons license. Attribution (BY): Credit must be given to the creator. We present a reduced density operator for electronically open molecules by explicitly ...

An illustration of a magnifying glass. An illustration of a magnifying glass.

Polynomial solutions to the Heine-Stieltjes equation, the Stieltjes polynomials, and the associated Van Vleck polynomials have been studied since the 1830's in various contexts including the solution ...

ABSTRACT: In the author’s recent publications, a parametric system biorthogonal to the corresponding segment of the exponential Fourier system was unusually effective. On its basis, it was discovered ...

Royalty-free licenses let you pay once to use copyrighted images and video clips in personal and commercial projects on an ongoing basis without requiring additional payments each time you use that ...

Not revised: This Reviewed Preprint includes the authors’ original preprint (without revision), an eLife assessment, public reviews, and a provisional response from the authors. The paper of Mao et al ...

The present paper introduces a method of basis transformation of a vector space that is specifically applicable to polynomials space and differential equations with certain polynomials solutions such ...

Recent advances in deep learning have bolstered our ability to forecast the evolution of dynamical systems, but common neural networks do not adhere to physical laws, critical information that could ...