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Research in the Mathematical Sciences Volume 9 Issue 1

Subject Areas: Applied Mathematics
Publisher: Springer International Publishing - Springer Journals
SJR: 17

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Journal Article

Weyl formula for the eigenvalues of the dissipative acoustic operator

Petkov, Vesselin

2022 Research in the Mathematical Sciences

doi:10.1007/s40687-021-00301-3

We study the wave equation in the exterior of a bounded domain K with dissipative boundary condition...
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Journal Article

On vanishing near corners of conductive transmission eigenfunctions

Deng, Youjun; Duan, Chaohua; Liu, Hongyu

2022 Research in the Mathematical Sciences

doi:10.1007/s40687-021-00299-8

This paper is concerned with the geometric structure of the transmission eigenvalue problem associated with a general conductive transmission condition. We prove that under a mild regularity condition in terms of the Herglotz approximations of one of the pair of the transmission eigenfunctions,...
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Journal Article

Generalization error of GAN from the discriminator’s perspective

Yang, Hongkang; E, Weinan

2022 Research in the Mathematical Sciences

doi:10.1007/s40687-021-00306-y

The generative adversarial network (GAN) is a well-known model for learning high-dimensional distributions, but the mechanism for its generalization ability is not understood. In particular, GAN is vulnerable to the memorization phenomenon, the eventual convergence to the empirical distribution....
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Journal Article

Modified transmission eigenvalues for inverse scattering in a fluid–solid interaction problem

Monk, Peter; Selgas, Virginia

2022 Research in the Mathematical Sciences

doi:10.1007/s40687-021-00300-4

Target signatures are discrete quantities computed from measured scattering data that could potentially be used to classify scatterers or give information about possible defects in the scatterer compared to an ideal object. Here, we study a class of modified interior transmission eigenvalues that...
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Journal Article

Special foliations on CP2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{ams ...

Alcántara, Claudia R.

2022 Research in the Mathematical Sciences

doi:10.1007/s40687-022-00311-9

In this work, we construct, for any d≥2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$d \ge 2$$\end{document}, a new...
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Journal Article

A perturbation problem for transmission eigenvalues

Ambrose, David M.; Cakoni, Fioralba; Moskow, Shari

2022 Research in the Mathematical Sciences

doi:10.1007/s40687-021-00308-w

In this paper, we consider a perturbation problem for real transmission eigenvalues. Real transmission eigenvalues are of particular interest in inverse scattering theory. They can be determined from scattering data and are related to injectivity of the related scattering operators. The goal of...
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Journal Article

G-invariant Hilbert schemes on Abelian surfaces and enumerative geometry of the orbifold Kummer surface

Pietromonaco, Stephen

2022 Research in the Mathematical Sciences

doi:10.1007/s40687-021-00298-9

For an Abelian surface A with a symplectic action by a finite group G, one can define the partition function for G-invariant Hilbert schemes...
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Journal Article

Cohomology of complements of toric arrangements associated with root systems

Bergvall, Olof

2022 Research in the Mathematical Sciences

doi:10.1007/s40687-021-00305-z

We develop an algorithm for computing the cohomology of complements of toric arrangements. In the case a finite group...
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Journal Article

Axisymmetric solutions of the shallow water equations with bottom topography

Liu, Shuzhi; Zhang, Qinglong

2022 Research in the Mathematical Sciences

doi:10.1007/s40687-022-00312-8

We construct a family of self-similar and bounded weak solutions for all positive time to the two-dimensional shallow water equations with the bottom topography a quadratic function with respect to the reciprocal of radius under axisymmetry assumptions. The source term generated from the bottom...
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Journal Article

Rees algebras of filtrations of covering polyhedra and integral closure of powers of monomial ideals

Grisalde, Gonzalo; Seceleanu, Alexandra; Villarreal, Rafael H.

2022 Research in the Mathematical Sciences

doi:10.1007/s40687-021-00310-2

The aims of this work are to study Rees algebras of filtrations of monomial ideals associated with covering polyhedra of rational matrices with nonnegative entries and nonzero columns using combinatorial optimization and integer programming and to study powers of monomial ideals and their...

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