For decades, mathematicians have struggled to understand matrices that reflect both order and randomness, like those that ...

The subject of Prof. Titchmarsh's book is the expansion of an arbitrary function in terms of the eigenfunctions of linear differential equations; to be precise, in terms of functions which satisfy ...

This is a preview. Log in through your library . Journal Information Annals of Mathematics, a distinguished journal of research papers in pure mathematics, was founded in 1884. Annals of Mathematics ...

It has been shown previously that homogeneous time-invariant systems produce exponential outputs in response to similar exponential inputs, but that the concepts of "impulse response" and "frequency ...

数学家们数十年来一直致力于理解既具有秩序又包含随机性的矩阵，例如用于模拟半导体的矩阵。2025年8月15日，一篇发表在Quanta Magazine上的文章指出，一种新的物理学启发方法有望改变这一现状，为理解无序系统的边界提供了新的视角。

数学物理学领域迎来一项重大突破。2025年8月15日，莱拉·斯洛曼报道，一项受物理学启发的全新证明方法，有望帮助数学家们理解既包含有序性又具有随机性的矩阵，例如用于模拟半导体的矩阵。这项新方法可能会彻底改变该领域的研究现状。

We present a novel data-driven approach for learning linear representations of a class of stable nonlinear systems using Koopman eigenfunctions. Utilizing the spectral equivalence of topologically ...

We classify all weak * limits of squares of normalized eigenfunctions of the Laplacian on two-dimensional flat tori (called quantum limits). We also obtain several results about such limits in ...