Peter Kuchment's Books

The Radon Transform and Medical Imaging

By: Peter Kuchment

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The Radon Transform and Medical Imaging

By: Peter Kuchment

This book surveys the main mathematical ideas and techniques behind some well-established imaging modalities such as X-ray CT and emission tomography, as well as a variety of newly developing coupled-physics or hybrid techniques, including thermoacoustic tomography. The Radon Transform and Medical Imaging emphasizes mathematical techniques and ideas arising across the spectrum of medical imaging modalities and explains important concepts concerning inversion, stability, incomplete data effects, the role of interior information, and other issues critical to all medical imaging methods. For nonexperts, the author provides appendices that cover background information on notation, Fourier analysis, geometric rays, and linear operators. The vast bibliography, with over 825 entries, directs readers to a wide array of additional information sources on medical imaging for further study.

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238

Publisher

SIAM

Published Date

ISBN 10

1611973287

ISBN 13

9781611973280

Waves in Periodic and Random Media

Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Waves in Periodic and Random Media, June 22-28, 2002, Mount Holyoke College, South Hadley, MA

By: Peter Kuchment

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Waves in Periodic and Random Media

Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Waves in Periodic and Random Media, June 22-28, 2002, Mount Holyoke College, South Hadley, MA

By: Peter Kuchment

Science and engineering have been great sources of problems and inspiration for generations of mathematicians. This is probably true now more than ever as numerous challenges in science and technology are met by mathematicians. One of these challenges is understanding propagation of waves of different nature in systems of complex structure. This book contains the proceedings of the research conference, ``Waves in Periodic and Random Media''. Papers are devoted to a number of related themes, including spectral theory of periodic differential operators, Anderson localization and spectral theory of random operators, photonic crystals, waveguide theory, mesoscopic systems, and designer random surfaces. Contributions are written by prominent experts and are of interest to researchers and graduate students in mathematical physics.

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232

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821832867

ISBN 13

9780821832868

Introduction to Quantum Graphs

By: Gregory Berkolaiko,Peter Kuchment

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Introduction to Quantum Graphs

By: Gregory Berkolaiko,Peter Kuchment

A ``quantum graph'' is a graph considered as a one-dimensional complex and equipped with a differential operator (``Hamiltonian''). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., ``meso-'' or ``nano-scale'') system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on quantum graphs has brought together tools and intuition coming from graph theory, combinatorics, mathematical physics, PDEs, and spectral theory. This book provides a comprehensive introduction to the topic, collecting the main notions and techniques. It also contains a survey of the current state of the quantum graph research and applications.

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291

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American Mathematical Soc.

Published Date

ISBN 10

0821892118

ISBN 13

9780821892114

The Radon Transform and Medical Imaging

By: Peter Kuchment

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The Radon Transform and Medical Imaging

By: Peter Kuchment

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238

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SIAM

Published Date

ISBN 10

1611973295

ISBN 13

9781611973297

Voronezh Winter Mathematical Schools

Dedicated to Selim Krein

By: Peter Kuchment

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Voronezh Winter Mathematical Schools

Dedicated to Selim Krein

By: Peter Kuchment

The Voronezh Winter Mathematical School was an annual event in the scientific life of the former Soviet Union for 25 years. Articles collected here are written by prominent mathematicians and former lecturers and participants of the school, covering a range of subjects in analysis and geometry. Specific topics include global analysis, harmonic analysis, function theory, dynamical systems, operator theory, mathematical physics, spectral theory, homogenization, algebraic geometry, differential geometry, and geometric analysis. For researchers and graduate students in analysis, geometry, and mathematical physics. No index. Annotation copyrighted by Book News, Inc., Portland, OR

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308

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American Mathematical Soc.

Published Date

ISBN 10

0821809768

ISBN 13

9780821809761

Liouville-Riemann-Roch Theorems on Abelian Coverings

By: Minh Kha,Peter Kuchment

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Liouville-Riemann-Roch Theorems on Abelian Coverings

By: Minh Kha,Peter Kuchment

This book is devoted to computing the index of elliptic PDEs on non-compact Riemannian manifolds in the presence of local singularities and zeros, as well as polynomial growth at infinity. The classical Riemann–Roch theorem and its generalizations to elliptic equations on bounded domains and compact manifolds, due to Maz’ya, Plameneskii, Nadirashvilli, Gromov and Shubin, account for the contribution to the index due to a divisor of zeros and singularities. On the other hand, the Liouville theorems of Avellaneda, Lin, Li, Moser, Struwe, Kuchment and Pinchover provide the index of periodic elliptic equations on abelian coverings of compact manifolds with polynomial growth at infinity, i.e. in the presence of a "divisor" at infinity. A natural question is whether one can combine the Riemann–Roch and Liouville type results. This monograph shows that this can indeed be done, however the answers are more intricate than one might initially expect. Namely, the interaction between the finite divisor and the point at infinity is non-trivial. The text is targeted towards researchers in PDEs, geometric analysis, and mathematical physics.

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Springer Nature

Published Date

ISBN 10

3030674282

ISBN 13

9783030674281

Integral Geometry, Radon Transforms and Complex Analysis

Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Venice, Italy, June 3-12, 1996

By: Carlos A. Berenstein,Peter F. Ebenfelt,Simon Gindikin,Sigurdur Helgason,Alexander Tumanov

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Integral Geometry, Radon Transforms and Complex Analysis

Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Venice, Italy, June 3-12, 1996

By: Carlos A. Berenstein,Peter F. Ebenfelt,Simon Gindikin,Sigurdur Helgason,Alexander Tumanov

This book contains the notes of five short courses delivered at the "Centro Internazionale Matematico Estivo" session "Integral Geometry, Radon Transforms and Complex Analysis" held in Venice (Italy) in June 1996: three of them deal with various aspects of integral geometry, with a common emphasis on several kinds of Radon transforms, their properties and applications, the other two share a stress on CR manifolds and related problems. All lectures are accessible to a wide audience, and provide self-contained introductions and short surveys on the subjects, as well as detailed expositions of selected results.

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Page Count

166

Publisher

Springer

Published Date

ISBN 10

3540697020

ISBN 13

9783540697022

Quarantined

Life and Death at William Head Station, 1872-1959

By: Peter Wilton Johnson

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Quarantined

Life and Death at William Head Station, 1872-1959

By: Peter Wilton Johnson

A look at the William Head Quarantine Station in British Columbia and the thousands of immigrants who were housed there upon their arrival in Canada.

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312

Publisher

Heritage House Publishing Co

Published Date

ISBN 10

1927527317

ISBN 13

9781927527313

Caught by Disorder

Bound States in Random Media

By: Peter Stollmann

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Caught by Disorder

Bound States in Random Media

By: Peter Stollmann

Disorder is one of the predominant topics in science today. The present text is devoted to the mathematical studyofsome particular cases ofdisordered systems. It deals with waves in disordered media. To understand the significance of the influence of disorder, let us start by describing the propagation of waves in a sufficiently ordered or regular environment. That they do in fact propagate is a basic experience that is verified by our senses; we hear sound (acoustic waves) see (electromagnetic waves) and use the fact that electromagnetic waves travel long distances in many aspects ofour daily lives. The discovery that disorder can suppress the transport properties of a medium is oneof the fundamental findings of physics. In its most prominent practical application, the semiconductor, it has revolutionized the technical progress in the past century. A lot of what we see in the world today depends on that relatively young device. The basic phenomenon of wave propagation in disordered media is called a metal-insulator transition: a disordered medium can exhibit good transport prop erties for waves ofrelatively high energy (like a metal) and suppress the propaga tion of waves of low energy (like an insulator). Here we are actually talking about quantum mechanical wave functions that are used to describe electronic transport properties. To give an initial idea of why such a phenomenon could occur, we have to recall that in physical theories waves are represented by solutions to certain partial differential equations. These equations link time derivatives to spatial derivatives.

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177

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461201691

ISBN 13

9781461201694

Obstacles to Environmental Progress

By: Peter C. Schulze

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Obstacles to Environmental Progress

By: Peter C. Schulze

Why, when so many people understand the severity of environmental problems, is progress so slow and sustainability such a distant goal? What gets in the way? Perhaps you have immediately thought of several barriers. In Obstacles to Environmental Progress, Peter Schulze identifies 18 practical obstacles that routinely and predictably hinder U.S. progress on existing environmental problems. The obstacles apply to problems small and large and, in most cases, regardless of whether an issue is controversial. Though the book focuses on the U.S., most of the obstacles pertain elsewhere as well. The obstacles fall into three categories: scientific challenges to anticipating and detecting problems; political and economic factors that interfere with responding; and obstacles to effective responses. While all the obstacles are predictable and common, they have not been systematically studied as related phenomena, perhaps because they span a wide range of academic disciplines. In practice, they often arise as surprises that are then addressed in an ad hoc manner. Might they be better understood and thus more readily anticipated and overcome or avoided? The book seeks to hasten environmental progress by forewarning and thus forearming those who are striving or will soon be striving for environmental progress, and by drawing scholarly attention to the obstacles as a set of related phenomena to systematically understand and more quickly overcome. Praise for Obstacles to Environmental Projects ‘I have never come across another book that gives students such an accessible and helpful guide to the broad scope of the challenges facing an environmentally sound and sustainable future.’ – Al Wurth, Lehigh University

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378

Publisher

UCL Press

Published Date

ISBN 10

180008207X

ISBN 13

9781800082076

Advances in Imaging and Electron Physics

By: Peter W. Hawkes

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Advances in Imaging and Electron Physics

By: Peter W. Hawkes

Advances in Imaging and Electron Physics merges two long-running serials-Advances in Electronics and Electron Physics and Advances in Optical and Electron Microscopy. This series features extended articles on the physics of electron devices (especially semiconductor devices), particle optics at high and low energies, microlithography, image science and digital image processing, electromagnetic wave propagation, electron microscopy, and the computing methods used in all these domains. Includes grey systems and grey information Discusses Phase diversity Recent developments in the imaging of magnetic domains Explores stochastic deconvolution over groups

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327

Publisher

Elsevier

Published Date

ISBN 10

0080462782

ISBN 13

9780080462783

Grid Homology for Knots and Links

By: Peter S. Ozsváth,András I. Stipsicz,Zoltán Szabó

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Grid Homology for Knots and Links

By: Peter S. Ozsváth,András I. Stipsicz,Zoltán Szabó

Knot theory is a classical area of low-dimensional topology, directly connected with the theory of three-manifolds and smooth four-manifold topology. In recent years, the subject has undergone transformative changes thanks to its connections with a number of other mathematical disciplines, including gauge theory; representation theory and categorification; contact geometry; and the theory of pseudo-holomorphic curves. Starting from the combinatorial point of view on knots using their grid diagrams, this book serves as an introduction to knot theory, specifically as it relates to some of the above developments. After a brief overview of the background material in the subject, the book gives a self-contained treatment of knot Floer homology from the point of view of grid diagrams. Applications include computations of the unknotting number and slice genus of torus knots (asked first in the 1960s and settled in the 1990s), and tools to study variants of knot theory in the presence of a contact structure. Additional topics are presented to prepare readers for further study in holomorphic methods in low-dimensional topology, especially Heegaard Floer homology. The book could serve as a textbook for an advanced undergraduate or part of a graduate course in knot theory. Standard background material is sketched in the text and the appendices.

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Page Count

423

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470417375

ISBN 13

9781470417376

Stochastic Resonance

By: Samuel Herrmann, Peter Imkeller,Ilya Pavlyukevich, Dierk Peithmann

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Stochastic Resonance

By: Samuel Herrmann, Peter Imkeller,Ilya Pavlyukevich, Dierk Peithmann

Stochastic resonance is a phenomenon arising in a wide spectrum of areas in the sciences ranging from physics through neuroscience to chemistry and biology. This book presents a mathematical approach to stochastic resonance which is based on a large deviations principle (LDP) for randomly perturbed dynamical systems with a weak inhomogeneity given by an exogenous periodicity of small frequency. Resonance, the optimal tuning between period length and noise amplitude, is explained by optimizing the LDP's rate function. The authors show that not all physical measures of tuning quality are robust with respect to dimension reduction. They propose measures of tuning quality based on exponential transition rates explained by large deviations techniques and show that these measures are robust. The book sheds some light on the shortcomings and strengths of different concepts used in the theory and applications of stochastic resonance without attempting to give a comprehensive overview of the many facets of stochastic resonance in the various areas of sciences. It is intended for researchers and graduate students in mathematics and the sciences interested in stochastic dynamics who wish to understand the conceptual background of stochastic resonance.

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Page Count

209

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470410494

ISBN 13

9781470410490

Analysis of Hydrodynamic Models

By: Peter Constantin

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Analysis of Hydrodynamic Models

By: Peter Constantin

Analysis of Hydrodynamic Models presents a concise treatment of a number of partial differential equations of hydrodynamic origin, including the incompressible Euler equations, SQG, Boussinesq, incompressible porous medium, and Oldroyd-B. The author?s approach is based on properties of the particle trajectory maps and on analysis of the back-and-forth passage between the Lagrangian and the Eulerian descriptions. This concise, unified approach brings readers up to date on current open problems. This book is intended for graduate students and junior researchers in mathematics.

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SIAM

Published Date

ISBN 10

1611974798

ISBN 13

9781611974799

Introduction to Quantum Graphs

By: Gregory Berkolaiko,Peter Kuchment

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Introduction to Quantum Graphs

By: Gregory Berkolaiko,Peter Kuchment

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Page Count

291

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821892118

ISBN 13

9780821892114

Liouville-Riemann-Roch Theorems on Abelian Coverings

By: Minh Kha,Peter Kuchment

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Liouville-Riemann-Roch Theorems on Abelian Coverings

By: Minh Kha,Peter Kuchment

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Springer Nature

Published Date

ISBN 10

3030674282

ISBN 13

9783030674281

Voronezh Winter Mathematical Schools

Dedicated to Selim Krein

By: Peter Kuchment

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Voronezh Winter Mathematical Schools

Dedicated to Selim Krein

By: Peter Kuchment

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Page Count

308

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821809768

ISBN 13

9780821809761

Waves in Periodic and Random Media

Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Waves in Periodic and Random Media, June 22-28, 2002, Mount Holyoke College, South Hadley, MA

By: Peter Kuchment

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Waves in Periodic and Random Media

Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Waves in Periodic and Random Media, June 22-28, 2002, Mount Holyoke College, South Hadley, MA

By: Peter Kuchment

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232

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821832867

ISBN 13

9780821832868

Tomography, Impedance Imaging, and Integral Geometry

1993 AMS-SIAM Summer Seminar on the Mathematics of Tomography, Impedance Imaging, and Integral Geometry, June 7-18, 1993, Mount Holyoke College, Massachusetts

By: Eric Todd Quinto,Margaret Cheney,Peter Kuchment,American Mathematical Society

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Tomography, Impedance Imaging, and Integral Geometry

1993 AMS-SIAM Summer Seminar on the Mathematics of Tomography, Impedance Imaging, and Integral Geometry, June 7-18, 1993, Mount Holyoke College, Massachusetts

By: Eric Todd Quinto,Margaret Cheney,Peter Kuchment,American Mathematical Society

One of the most exciting features of tomography is the strong relationship between high-level pure mathematics (such as harmonic analysis, partial differential equations, microlocal analysis, and group theory) and applications to medical imaging, impedance imaging, radiotherapy, and industrial nondestructive evaluation. This book contains the refereed proceedings of the AMS-SIAM Summer Seminar on Tomography, Impedance Imaging, and Integral Geometry, held at Mount Holyoke College in June 1993. A number of common themes are found among the papers. Group theory is fundamental both to tomographic sampling theorems and to pure Radon transforms. Microlocal and Fourier analysis are important for research in all three fields. Differential equations and integral geometric techniques are useful in impedance imaging. In short, a common body of mathematics can be used to solve dramatically different problems in pure and applied mathematics. Radon transforms can be used to model impedance imaging problems. These proceedings include exciting results in all three fields represented at the conference.

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Page Count

300

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821896997

ISBN 13

9780821896990

Book's by Peter Kuchment

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