WorldCat Identities

Epstein, Charles L.

Works: 16 works in 70 publications in 1 language and 1,886 library holdings
Roles: Author
Classifications: RC78.7.D53, 515
Publication Timeline
Most widely held works by Charles L Epstein
Introduction to the mathematics of medical imaging by Charles L Epstein( Book )

25 editions published between 2003 and 2008 in English and held by 352 WorldCat member libraries worldwide

"At the heart of every medical imaging technology is a sophisticated mathematical model of the measurement process and an algorithm to reconstruct an image from the measured data. This book provides a firm foundation in the mathematical tools used to model the measurements and derive the reconstruction algorithms used in most imaging modalities in current use. In the process, it also covers many important analytic concepts, as well as techniques used in Fourier analysis, integral equations, sampling theory, and noise analysis." "This text uses X-ray computed tomography as a "pedagogical machine" to illustrate important ideas and incorporates extensive discussions of background material making the more advanced mathematical topics accessible to readers with a less formal mathematical education. The mathematical concepts are illuminated with over 200 illustrations and numerous exercises." "New to the second edition are a chapter on magnetic resonance imaging (MRI), a revised section on the relationship between the continuum and discrete Fourier transforms, a new section on Grangreat's formula, an improved description of the gridding method, and a new section on noise analysis in MRI." "The book is appropriate for one- or two-semester courses at the advanced undergraduate or beginning graduate level on the mathematical foundations of modern medical imaging technologies. The text assumes an understanding of calculus, linear algebra, and basic mathematical analysis."--Jacket
The spectral theory of geometrically periodic hyperbolic 3-manifolds by Charles L Epstein( Book )

15 editions published in 1985 in English and Undetermined and held by 237 WorldCat member libraries worldwide

Degenerate diffusion operators arising in population biology by Charles L Epstein( Book )

12 editions published in 2013 in English and held by 231 WorldCat member libraries worldwide

"This book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics, mathematical finance, and economics. The results discussed in this book prove the uniqueness of the solution to the Martingale problem and therefore the existence of the associated Markov process. Charles Epstein and Rafe Mazzeo use an "integral kernel method" to develop mathematical foundations for the study of such degenerate elliptic operators and the stochastic processes they define. The precise nature of the degeneracies of the principal symbol for these operators leads to solutions of the parabolic and elliptic problems that display novel regularity properties. Dually, the adjoint operator allows for rather dramatic singularities, such as measures supported on high codimensional strata of the boundary. Epstein and Mazzeo establish the uniqueness, existence, and sharp regularity properties for solutions to the homogeneous and inhomogeneous heat equations, as well as a complete analysis of the resolvent operator acting on Hèolder spaces. They show that the semigroups defined by these operators have holomorphic extensions to the right half-plane. Epstein and Mazzeo also demonstrate precise asymptotic results for the long-time behavior of solutions to both the forward and backward Kolmogorov equations."--
Cornerstones( )

in English and held by 4 WorldCat member libraries worldwide

A relative index on the space of embeddable CR-structures by Charles L Epstein( Book )

3 editions published in 1995 in English and held by 3 WorldCat member libraries worldwide

- Gulf-war aftermath. Building up to a construction bonanza.ʹ- A new world order for oil( )

1 edition published in 1991 in English and held by 3 WorldCat member libraries worldwide

The first of these two articles deals with the task of rebuilding Kuwait after the Gulf War with Iraq. The size and award of contracts to Western companies and the issue of war reparations are discussed. The second article examines the implications for world oil markets of the war in the Gulf and its aftermath and discusses the measures for reducing oil consumption and dependance from OPEC oil.--SCAD summary
A stable manifold theorem for the curve shortening equation by Charles L Epstein( Book )

1 edition published in 1986 in English and held by 2 WorldCat member libraries worldwide

Genomic imprinting a lasting memory of your parents( Visual )

1 edition published in 1992 in English and held by 1 WorldCat member library worldwide

Advanced real analysis by Anthony W Knapp( Book )

3 editions published in 2005 in English and held by 1 WorldCat member library worldwide

Advanced€Real Analysis systematically develops the concepts and tools that are vital to every mathematician, whether pure or applied, aspiring or established. This work presents a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics. Key topics and features: . Early chapters treat the fundamentals of real variables, the theory of Fourier series for the Riemann integral, and the theoretical underpinnings of multivariable calculus and differential equations . Subsequent chapters develop measure theory, point-set topology, Fourier series for the Lebesgue integral, and the basics of Banach and Hilbert spaces . Later chapters provide a higher-level view of the interaction between real analysis and algebra, including functional analysis, partial differential equations, and further topics in Fourier analysis . Throughout the text are problems that develop and illuminate aspects of the theory of probability . Includes many examples and hundreds of problems, and a chapter gives hints or complete solutions for most of the problems It requires of the reader only familiarity with some linear algebra and real variable theory, a few weeks' worth of group theory, and an acquaintance with proofs. Because it focuses on what every young mathematician needs to know about real analysis, this book is ideal both as a course text and for self-study, especially for graduate students preparing for qualifying examinations. Its scope and unique approach will appeal to instructors and professors in nearly all areas of pure mathematics, as well as applied mathematicians working in analytic areas such as statistics, math physics, and applied differential equations. Indeed, the clarity and breadth of Advanced Real Analysis make it a welcome addition to the personal library of every mathematician. TOC:Preface * Theory of calculus in one real variable * Metric spaces * Theory of differential calculus in several variables * Theory of ordinary differential equations and systems * Riemann integration in several variables * Abstract measure theory and Lebesgue measure * Measure theory for Euclidean space * Fourier transform in R^N * L^p spaces * Further topics in abstract measure theory * Topological spaces * Integration on locally compact spaces * Haar measure * Hilbert and Banach spaces * Distributions and their application to PDEs * References * Index
Magnetic resonance imaging of short-T₂ tissues with applications for quantifying cortical bone water and myelin by Cheng Li( Book )

1 edition published in 2014 in English and held by 1 WorldCat member library worldwide

The human body contains a variety of tissue species with short T₂ ranging from a few microseconds to hundreds of microseconds. Detection and quantification of these short- T₂ species is of considerable clinical and scientific interest. Cortical bone water and myelin are two of the most important tissue constituents. Quantification of cortical bone water concentration allows for indirect estimation of bone pore volume and noninvasive assessment of bone quality. Myelin is essential for the proper functioning of the central nervous system (CNS). Direct assessment of myelin would reveal CNS abnormalities and enhance our understanding of neurological diseases. However, conventional MRI with echo times of several milliseconds or longer is unable to detect these short-lived MR signals. Recent advances in MRI technology and hardware have enabled development of a number of short- T₂ imaging techniques, key among which are ultra-short echo time (UTE) imaging, zero echo time (ZTE) imaging, and sweep imaging with Fourier transform (SWIFT). While these pulse sequences are able to detect short- T₂ species, they still suffer from signal interference between different T₂ tissue constituents, image artifacts and excessive scan time. These are primary technical hurdles for application to whole-body clinical scanners. In this thesis research, new MRI techniques for improving short- T₂ tissue imaging have been developed to address these challenges with a focus on direct detection and quantification of cortical bone water and myelin on a clinical MRI scanner. The first focus of this research was to optimize long- T₂ suppression in UTE imaging. Saturation and adiabatic RF pulses were designed to achieve maximum long- T₂ suppression while maximizing the signal from short- T₂ species. The imaging protocols were optimized by Bloch equation simulations and were validated using phantom and in vivo experiments. The results show excellent short- T₂ contrast with these optimized pulse sequences. The problem of blurring artifacts resulting from the inhomogeneous excitation profile of the rectangular pulses in ZTE imaging was addressed. The proposed approach involves quadratic phase-modulated RF excitation and iterative solution of an inverse problem formulated from the signal model of ZTE imaging and is shown to effectively remove the image artifacts. Subsequently image acquisition efficiency was improved in order to attain clinically-feasible scan times. To accelerate the acquisition speed in UTE and ZTE imaging, compressed sensing was applied with a hybrid 3D UTE sequence. Further, the pulse sequence and reconstruction procedure were modified to enable anisotropic field-of-view shape conforming to the geometry of the elongated imaged object. These enhanced acquisition techniques were applied to the detection and quantification of cortical bone water. A new biomarker, the suppression ratio (a ratio image derived from two UTE images, one without and the other with long- T₂ suppression), was conceived as a surrogate measure of cortical bone porosity. Experimental data suggest the suppression ratio may be a more direct measure of porosity than previously measured total bone water concentration. Lastly, the feasibility of directly detecting and quantifying spatially-resolved myelin concentration with a clinical imager was explored, both theoretically and experimentally. Bloch equation simulations were conducted to investigate the intrinsic image resolution and the fraction of detectable myelin signal under current scanner hardware constraints. The feasibility of quantitative ZTE imaging of myelin extract and lamb spinal cord at 3T was demonstrated. The technological advances achieved in this dissertation research may facilitate translation of short- T₂ MRI methods from the laboratory to the clinic
CT CISM team response to Newtown, CT - December 14, 2012 by Charles L Epstein( )

1 edition published in 2013 in English and held by 1 WorldCat member library worldwide

The spectral theory of geometrically periodic hyperbolic 3-manyfolds by Charles L Epstein( )

1 edition published in 1983 in English and held by 1 WorldCat member library worldwide

Gulf-war aftermath : building up to a construction bonanza( )

1 edition published in 1991 in English and held by 1 WorldCat member library worldwide

Degenerate Diffusion Operators Arising in Population Biology (Annals of Mathematics Studies) by Charles L Epstein( Book )

1 edition published in 2013 in Undetermined and held by 1 WorldCat member library worldwide

Mathematics of medical imaging by Charles L Epstein( Book )

1 edition published in 2003 in English and held by 1 WorldCat member library worldwide

Seizures and pseudo-seizures( Visual )

1 edition published in 1992 in English and held by 0 WorldCat member libraries worldwide

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The spectral theory of geometrically periodic hyperbolic 3-manifolds
Alternative Names
Charles Epstein Amerikaans wiskundige

Charles Epstein mathématicien américain, a professé à l'université de Pennsylvanie, Philadelphie.

Epstein, C. 1957-

Epstein, C. L. 1957-

Epstein, Charles 1957-

چارلز اپستاین

English (68)

The spectral theory of geometrically periodic hyperbolic 3-manifoldsMathematics of medical imaging