Spectral Geometry and Inverse Scattering Theory

Diao, Huaian, Liu, Hongyu

Spectral Geometry and Inverse Scattering Theory
  • 出版商: Springer
  • 出版日期: 2024-10-03
  • 售價: $5,690
  • 貴賓價: 9.5 折 $5,406
  • 語言: 英文
  • 頁數: 387
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3031346173
  • ISBN-13: 9783031346170

    • 海外代購書籍(需單獨結帳)

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商品描述

Inverse scattering problems are a vital subject for both theoretical and experimental studies and remain an active field of research in applied mathematics. This book provides a detailed presentation of typical setup of inverse scattering problems for time-harmonic acoustic, electromagnetic and elastic waves. Moreover, it provides systematical and in-depth discussion on an important class of geometrical inverse scattering problems, where the inverse problem aims at recovering the shape and location of a scatterer independent of its medium properties. Readers of this book will be exposed to a unified framework for analyzing a variety of geometrical inverse scattering problems from a spectral geometric perspective.

This book contains both overviews of classical results and update-to-date information on latest developments from both a practical and theoretical point of view. It can be used as an advanced graduate textbook in universities or as a referencesource for researchers in acquiring the state-of-the-art results in inverse scattering theory and their potential applications.

商品描述(中文翻譯)

反散射問題是理論與實驗研究的重要主題，並且在應用數學中仍然是一個活躍的研究領域。本書詳細介紹了時間諧波聲波、電磁波和彈性波的反散射問題的典型設置。此外，本書對一類重要的幾何反散射問題進行了系統且深入的討論，這類反問題旨在恢復散射體的形狀和位置，而不依賴於其介質特性。本書的讀者將接觸到一個統一的框架，從光譜幾何的角度分析各種幾何反散射問題。

本書包含了經典結果的概述以及從實用和理論角度出發的最新發展資訊。它可以作為大學的高級研究生教科書，或作為研究人員獲取反散射理論及其潛在應用的最新成果的參考資料。

作者簡介

Hongyu Liu is a Professor and the Associate Head at the Department of Mathematics, City University of Hong Kong. Before taking up the current position, he worked as a Professor and the Associate Head at the Department of Mathematics, Hong Kong Baptist University (2014--2020). Prior to that, he held faculty positions at University of North Carolina, Charlotte, USA (2011--2014), University of Reading, UK (2010/11), and University of Washington, Seattle, USA (2007--2010). He obtained his PhD in Mathematics from The Chinese University of Hong Kong (2007). His research focuses on the analysis, computations and applications of inverse problems and imaging, wave propagation, partial differential equations, mathematical materials science, scattering theory and spectral theory. He has also been working on the interplay among inverse scattering techniques, bionic learning and artificial intelligence. He has published over peer-reviewed 150 research papers in leading journals, and in addition he has 16 research preprints under review to leading journals. He coauthored one research monograph by Societe Mathematique de France.

Huaian Diao is a Professor at School of Mathematics, Jilin University, China, from October 2021. He obtained his PhD in Mathematics from City University of Hong Kong (2007). From September 2007 to June 2021, he worked as a lecture and then an associate professor at School of Mathematics and Statistics, Northeast Normal University, China. His research interests include inverse scattering problems, numerical algebra and spectral theory. He has published over 50 peer-reviewed papers in international journals and conferences including J. Math. Pures Appl., Calc. Var. Partial Differential Equations, Comm. Partial Differential Equations, SIAM J. Math. Anal., SIAM J. Appl. Math., J. Differential Equations, Math. Comp., Inverse Problems, and NeurIPS 2019.


作者簡介(中文翻譯)

Hongyu Liu 是香港城市大學數學系的教授及副系主任。在擔任目前職位之前，他曾於香港浸會大學數學系擔任教授及副系主任（2014--2020）。在此之前，他曾在美國北卡羅來納州夏洛特大學（2011--2014）、英國雷丁大學（2010/11）及美國華盛頓大學西雅圖校區（2007--2010）擔任教職。他於香港中文大學獲得數學博士學位（2007）。他的研究專注於逆問題與成像的分析、計算及應用、波的傳播、偏微分方程、數學材料科學、散射理論及譜理論。他也在研究逆散射技術、生物學習及人工智慧之間的相互作用。他在領先期刊上發表了超過150篇經過同行評審的研究論文，此外，他還有16篇研究預印本正在領先期刊審核中。他與法國數學學會共同撰寫了一本研究專著。

Huaian Diao 自2021年10月起擔任中國吉林大學數學學院的教授。他於香港城市大學獲得數學博士學位（2007）。從2007年9月到2021年6月，他在中國東北師範大學數學與統計學院擔任講師及後來的副教授。他的研究興趣包括逆散射問題、數值代數及譜理論。他在國際期刊和會議上發表了超過50篇經過同行評審的論文，包括 J. Math. Pures Appl.、Calc. Var. Partial Differential Equations、Comm. Partial Differential Equations、SIAM J. Math. Anal.、SIAM J. Appl. Math.、J. Differential Equations、Math. Comp.、Inverse Problems 及 NeurIPS 2019。

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