Vodev, Georgi
Published in
Research in the Mathematical Sciences

We introduce an analog of the Dirichlet-to-Neumann map for the Maxwell equation in a bounded domain. We show that it can be approximated by a pseudodifferential operator on the boundary with a matrix-valued symbol and we compute the principal symbol. As an application, we obtain a parabolic region free of the transmission eigenvalues associated wit...

Ding, Lingyun Hunt, Robert McLaughlin, Richard M. Woodie, Hunter
Published in
Research in the Mathematical Sciences

We develop a theory of enhanced diffusivity and skewness of the longitudinal distribution of a diffusing tracer advected by a periodic time-varying shear flow in a straight channel. Although applicable to any type of solute and fluid flow, we restrict the examples of our theory to the tracer advected by flows which are induced by a periodically osc...

Bhattacharya, Soumya
Published in
Research in the Mathematical Sciences

The levels of the factors of a holomorphic eta quotient f are bounded above with respect to the weight and the level of f. Unfortunately, this bound remains implicit due to the ineffectiveness of Mersmann’s finiteness theorem. On the other hand, for checking whether f is irreducible, it is essential to know at least an explicit upper bound for the ...

Crooks, Peter Weitsman, Jonathan
Published in
Research in the Mathematical Sciences

This paper considers the enhanced symplectic “category” for purposes of quantizing quasi-Hamiltonian (G)-spaces, where (G) is a compact simple Lie group. Our starting point is the well-acknowledged analogy between the cotangent bundle T∗G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssym...

Harris, Isaac
Published in
Research in the Mathematical Sciences

In this paper, we consider the numerical approximation of the Steklov eigenvalue problem that arises in inverse acoustic scattering. The underlying scattering problem is for an inhomogeneous isotropic medium. These eigenvalues have been proposed to be used as a target signature since they can be recovered from the scattering data. A Galerkin method...

Tong, Xin T. Choi, Kwok Pui Lai, Tze Leung Wong, Weng Kee
Published in
Research in the Mathematical Sciences

Particle swarm optimization (PSO) is a member of nature-inspired metaheuristic algorithms. Its formulation is simple and does not need the computation of derivatives. It and its many variants have been applied to many different types of optimization problems across several disciplines. There have been many attempts to study the convergence properti...

Chen, Bohan Peng, Kaiyan Parkinson, Christian Bertozzi, Andrea L. Slough, Tara Lyn Urpelainen, Johannes
Published in
Research in the Mathematical Sciences

Deforestation is a major threat to global environmental wellness, with illegal logging as one of the major causes. Recently, there has been increased effort to model environmental crime, with the goal of assisting law enforcement agencies in deterring these activities. We present a continuous model for illegal logging applicable to arbitrary domain...

Venturi, Daniele Dektor, Alec
Published in
Research in the Mathematical Sciences

We present a rigorous convergence analysis for cylindrical approximations of nonlinear functionals, functional derivatives, and functional differential equations (FDEs). The purpose of this analysis is twofold: First, we prove that continuous nonlinear functionals, functional derivatives, and FDEs can be approximated uniformly on any compact subset...

Tripathi, Mohit Barman, Rupam
Published in
Research in the Mathematical Sciences

In this article, we find finite field analogues of certain identities satisfied by the classical 4F3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${_4}F_3$$\end{docume...

Larson, Hannah Vogt, Isabel
Published in
Research in the Mathematical Sciences

Recent work of Kass–Wickelgren gives an enriched count of the 27 lines on a smooth cubic surface over arbitrary fields. Their approach using A1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-6...