复平面上玻恩传输特征值的分布

IF 1.1 4区数学 Q2 MATHEMATICS, APPLIED

Asymptotic Analysis Pub Date : 2023-09-29 DOI:10.3233/asy-231868

Narek Hovsepyan

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引用次数: 0

摘要

本文分析了d = 2或d = 3条件下，基于变换光学隐身方案的传输问题，通过将折射率替换为一阶近似无界函数得到的近似内部传输特征值问题。利用径向对称证明了(无穷多个)复传输特征值的存在性，并证明了它们的离散性。此外，还证明了在复平面上围绕实轴存在一条不包含任何传输特征值的水平线。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the distribution of Born transmission eigenvalues in the complex plane

We analyze an approximate interior transmission eigenvalue problem in R d for d = 2 or d = 3, motivated by the transmission problem of a transformation optics-based cloaking scheme and obtained by replacing the refractive index with its first order approximation, which is an unbounded function. Using the radial symmetry we show the existence of (infinitely many) complex transmission eigenvalues and prove their discreteness. Moreover, it is shown that there exists a horizontal strip in the complex plane around the real axis, that does not contain any transmission eigenvalues.

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来源期刊

Asymptotic Analysis 数学-应用数学

CiteScore

1.90

自引率

7.10%

发文量

审稿时长

6 months

期刊介绍： The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand. Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.