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Geodesic Beams in Eigenfunction Analysis

Author: Yaiza Canzani

Publisher: Springer Nature

Published: 2023-07-15

Total Pages: 123

ISBN-13: 3031315863

This book discusses the modern theory of Laplace eigenfunctions through the lens of a new tool called geodesic beams. The authors provide a brief introduction to the theory of Laplace eigenfunctions followed by an accessible treatment of geodesic beams and their applications to sup norm estimates, L^p estimates, averages, and Weyl laws. Geodesic beams have proven to be a valuable tool in the study of Laplace eigenfunctions, but their treatment is currently spread through a variety of rather technical papers. The authors present a treatment of these tools that is accessible to a wider audience of mathematicians. Readers will gain an introduction to geodesic beams and the modern theory of Laplace eigenfunctions, which will enable them to understand the cutting edge aspects of this theory.

From Classical Analysis to Analysis on Fractals

Author: Patricia Alonso Ruiz

Publisher: Springer Nature

Published: 2023-11-25

Total Pages: 294

ISBN-13: 3031378008

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Over the course of his distinguished career, Robert Strichartz (1943-2021) had a substantial impact on the field of analysis with his deep, original results in classical harmonic, functional, and spectral analysis, and in the newly developed analysis on fractals. This is the first volume of a tribute to his work and legacy, featuring chapters that reflect his mathematical interests, written by his colleagues and friends. An introductory chapter summarizes his broad and varied mathematical work and highlights his profound contributions as a mathematical mentor. The remaining articles are grouped into three sections – functional and harmonic analysis on Euclidean spaces, analysis on manifolds, and analysis on fractals – and explore Strichartz’ contributions to these areas, as well as some of the latest developments.

Geometric Analysis

Author: Hubert L. Bray

Publisher: American Mathematical Soc.

Published: 2016-05-18

Total Pages: 457

ISBN-13: 1470423138

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This volume includes expanded versions of the lectures delivered in the Graduate Minicourse portion of the 2013 Park City Mathematics Institute session on Geometric Analysis. The papers give excellent high-level introductions, suitable for graduate students wishing to enter the field and experienced researchers alike, to a range of the most important areas of geometric analysis. These include: the general issue of geometric evolution, with more detailed lectures on Ricci flow and Kähler-Ricci flow, new progress on the analytic aspects of the Willmore equation as well as an introduction to the recent proof of the Willmore conjecture and new directions in min-max theory for geometric variational problems, the current state of the art regarding minimal surfaces in R3, the role of critical metrics in Riemannian geometry, and the modern perspective on the study of eigenfunctions and eigenvalues for Laplace–Beltrami operators.

Eigenfunctions of the Laplacian on a Riemannian Manifold

Author: Steve Zelditch

Publisher: American Mathematical Soc.

Published: 2017-12-12

Total Pages: 410

ISBN-13: 1470410370

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Eigenfunctions of the Laplacian of a Riemannian manifold can be described in terms of vibrating membranes as well as quantum energy eigenstates. This book is an introduction to both the local and global analysis of eigenfunctions. The local analysis of eigenfunctions pertains to the behavior of the eigenfunctions on wavelength scale balls. After re-scaling to a unit ball, the eigenfunctions resemble almost-harmonic functions. Global analysis refers to the use of wave equation methods to relate properties of eigenfunctions to properties of the geodesic flow. The emphasis is on the global methods and the use of Fourier integral operator methods to analyze norms and nodal sets of eigenfunctions. A somewhat unusual topic is the analytic continuation of eigenfunctions to Grauert tubes in the real analytic case, and the study of nodal sets in the complex domain. The book, which grew out of lectures given by the author at a CBMS conference in 2011, provides complete proofs of some model results, but more often it gives informal and intuitive explanations of proofs of fairly recent results. It conveys inter-related themes and results and offers an up-to-date comprehensive treatment of this important active area of research.

Energy and Finite Element Methods in Structural Mechanics

Author: IrvingH Shames

Publisher: Routledge

Published: 2018-05-08

Total Pages: 784

ISBN-13: 1351451456

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THE FINITE ELEMENT METHOD : Basic Concepts and ApplicationsDarrell Pepper, Advanced Projects Research, Inc. California, and Dr . JuanHeinrich, University of Arizona, TucsonTh i s introductory textbook is designed for use in undergraduate, graduate, andshort courses in structural engineering and courses devoted specifically to thefinite element method. This method is rapidly becoming the most widely usedstandard for numerical approximation for partial differential equations definingengineering and scientific problems.The authors present a simplified approach to introducing the method and a coherentand easily digestible explanation of detailed mathematical derivations andtheory Example problems are included and can be worked out manually Anaccompanying floppy disk compiling computer codes is included and required forsome of the multi-dimensional homework problems.

Energy and Finite Element Methods in Structural Mechanics

Author: Irving Herman Shames

Publisher: New Age International

Published: 1995

Total Pages: 790

ISBN-13: 9788122407495

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This Book Is The Outcome Of Material Used In Senior And Graduate Courses For Students In Civil, Mechanical And Aeronautical Engineering. To Meet The Needs Of This Varied Audience, The Author Have Laboured To Make This Text As Flexible As Possible To Use.Consequently, The Book Is Divided Into Three Distinct Parts Of Approximately Equal Size. Part I Is Entitled Foundations Of Solid Mechanics And Variational Methods, Part Ii Is Entitled Structural Mechanics; And Part Iii Is Entitled Finite Elements.Depending On The Background Of The Students And The Aims Of The Course Selected Portions Can Be Used From Some Or All Of The Three Parts Of The Text To Form The Basis Of An Individual Course.The Purpose Of This Useful Book Is To Afford The Student A Sound Foundation In Variational Calculus And Energy Methods Before Delving Into Finite Elements. He Goal Is To Make Finite Elements More Understandable In Terms Of Fundamentals And Also To Provide The Student With The Background Needed To Extrapolate The Finite Element Method To Areas Of Study Other Than Solid Mechanics. In Addition, A Number Of Approximation Techniques Are Made Available Using The Quadratic Functional For A Boundary-Value Problem.Finally, The Authors; Aim Is To Give Students Who Go Through The Entire Text A Balanced And Connected Exposure To Certain Key Aspects Of Modern Structural And Solid Mechanics.

Energy Research Abstracts

Author:

Publisher:

Published: 1983

Total Pages: 444

ISBN-13:

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Planar Circuits for Microwaves and Lightwaves

Author: T. Okoshi

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 215

ISBN-13: 3642700837

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Until recently, three principal classes had been known in the electrical cir cuitry. They were as follows: 1) The lumped-constant circuit, which should be called a zero-dimensional circuit, in the sense that the circuit elements are much smaller in size as compared with the wavelength in all three spatial directions. 2) The distributed-constant circuit, which should be called a one-dimensional circuit, in the sense that the circuit elements are much smaller than the wavelength in two directions but comparable to the wavelength in one di rection. 3) The waveguide circuit, which should be called a three-dimensional circuit, in the sense that the circuit elements are comparable to the wavelength in all three directions. The principal subject of this book is the analysis and design (synthesis) theories for another circuit class which appeared in the late 1960s and became common in the 1970s. This new circuit class is 4) the planar circuit, which should be called a two-dimensional circuit, in the sense that the circuit elements are much smaller in size as compared with the wavelength in one direction, but comparable to the wavelength in the other two directions.