von Neumann’s trace inequality for Hilbert–Schmidt operators

von Neumann’s inequality in matrix theory refers to the fact that the Frobenius scalar product of two matrices is less than or equal to the scalar product of the respective singular values. Moreover, equality can only happen if the two matrices share a joint set of singular vectors, and this latter part is hard to find in the literature. We extend these facts to the separable Hilbert space setting, and provide a self-contained proof of the “latter part”.     

干式变压器有限元仿真模型的电磁和振动分析

随着电力需求的逐年增长,干式变压器的数量也在不断增加。干式变压器在运行时存在着振动和噪声的问题,为了对干式变压器振动的规律与特点进行研究,本文建立了干式变压器本体振动的有限元仿真模型,通过电磁分析获得相应的磁场分布,然后利用结构动力学分析得到其本体振动的相关规律。通过对处于运行状态的变压器振动数据进行实测分析,得到变压器振动的特征频率,然后对仿真结果进行对比分析,可以发现振动幅度与频率之间存在的关系。本文的研究结果可对干式变压器的减振降噪研究提供参考。     

Some properties of composition operators on Hilbert spaces of Dirichlet series

In this paper, we study some properties of composition operators on Hilbert spaces of Dirichlet series, which include the Fredholmness, Hilbert-Schmidtness, spectra, cyclic and hypercyclic phenomenons, and also answer a norm question raised by Cowen and MacCluer.     

Automorphisms of Hilbert schemes of points on a generic projective K3 surface

We study automorphisms of the Hilbert scheme of n points on a generic projective K3 surface S, for any . We show that is either trivial or generated by a non‐symplectic involution and we determine numerical and divisorial conditions which allow us to distinguish between the two cases. As an application of these results we prove that, for any , there exist infinitely many admissible degrees for the polarization of the K3 surface S such that admits a non‐natural involution. This provides a generalization of the results of [7] for .     

Continuum versus discrete networks,graph Laplacians,and reproducing kernel Hilbert spaces

Motivated by applications to machine learning, we construct a reversible and irreducible Markov chain whose state space is a certain collection of measurable sets of a chosen l.c.h. space $\mathfrak{X}$. We study the resulting network (connected undirected graph), including transience, Royden and Riesz decompositions, and kernel factorization. We describe a construction for Hilbert spaces of signed measures which comes equipped with a new notion of reproducing kernels and there is a unique solution to a regularized optimization problem involving the approximation of $L^2$ functions by functions of finite energy. The latter has applications to machine learning (for Markov random fields, for example).     

FLTD三电极场畸变气体开关寿命特性

针对设计的一种场畸变气体开关,研究中间电极材料分别为不锈钢和黄铜条件下的烧蚀特性,结合开关寿命期间静态与触发特性的变化规律,获得决定开关寿命的关键因素,为三电极场畸变气体开关的性能优化提供理论支撑。研究结果表明,采用不锈钢和黄铜作为中间电极的烧蚀区域以及表面粗糙度均随着放电次数增加而增大,黄铜电极烧蚀较为严重且表面有明显的烧蚀圆斑,不锈钢电极则具有更高的表面粗糙度,阴阳极表面烧蚀存在明显差异,随着放电次数的增加,击穿点向电极边缘区域集中,影响开关的沿面绝缘特性,是导致开关寿命终结的主要原因。     

Hilbert’s Nullstellensatz for analytic trigonometric polynomials

This paper proves such a new Hilbert’s Nullstellensatz for analytic trigonometric polynomials that if ${\left\{f_j\right\}}_{j=1}^{n\ge 2}$ are analytic trigonometric polynomials without common zero in the finite complex plane $?$ then there are analytic trigonometric polynomials ${\left\{g_j\right\}}_{j=1}^{n\ge 2}$ obeying ${\sum }_{j=1}^{n\ge 2}{f}_j{g}_j=1$ in $?$, thereby not only strengthening Helmer’s Principal Ideal Theorem for entire functions, but also finding an intrinsic path from Hilbert’s Nullstellensatz for analytic polynomials to Pythagoras’ Identity on $?$.