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    The Mathematics of Medical Imaging: A Beginner’s Guide

    Posted By: AvaxGenius
    The Mathematics of Medical Imaging: A Beginner’s Guide

    The Mathematics of Medical Imaging: A Beginner’s Guide by Timothy G. Feeman
    English | PDF (True) | 2010 | 150 Pages | ISBN : 0387927115 | 6.1 MB

    In 1979, the Nobel Prize for Medicine and Physiology was awarded jointly to Allan McLeod Cormack and Godfrey Newbold Houns eld, the two pioneering scienti- engineers primarily responsible for the development, in the 1960s and early 1970s, of computerized axial tomography, popularly known as the CAT or CT scan. In his papers [13], Cormack, then a Professor at Tufts University, in Massachusetts, dev- oped certain mathematical algorithms that, he envisioned, could be used to create an image from X-ray data. Working completely independently of Cormack and at about the same time, Houns eld, a research scientist at EMI Central Research Laboratories in the United Kingdom, designed the rst operational CT scanner as well as the rst commercially available model. (See [22] and [23]. ) Since 1980, the number of CT scans performed each year in the United States has risen from about 3 million to over 67 million. What few people who have had CT scans probably realize is that the fundamental problem behind this procedure is essentially mathematical: If we know the values of the integral of a two- or three-dimensional fu- tion along all possible cross-sections, then how can we reconstruct the function itself? This particular example of what is known as an inverse problem was studied by Johann Radon, an Austrian mathematician, in the early part of the twentieth century.

    Convex Functional Analysis

    Posted By: AvaxGenius
    Convex Functional Analysis

    Convex Functional Analysis by Andrew J. Kurdila , Michael Zabarankin
    English | PDF (True) | 2005 | 238 Pages | ISBN : 3764321989 | 1.9 MB

    Overview of Book This book evolved over a period of years as the authors taught classes in var- tional calculus and applied functional analysis to graduatestudents in engineering and mathematics. The book has likewise been in?uenced by the authors’ research programs that have relied on the application of functional analytic principles to problems in variational calculus, mechanics and control theory. One of the most di?cult tasks in preparing to utilize functional, convex, and set-valued analysis in practical problems in engineering and physics is the inti- dating number of de?nitions, lemmas, theorems and propositions that constitute thefoundationsoffunctionalanalysis. Itcannotbeoveremphasizedthatfunctional analysis can be a powerful tool for analyzing practical problems in mechanics and physics. However, many academicians and researchers spend their lifetime stu- ing abstract mathematics. It is a demanding ?eld that requires discipline and devotion. It is a trite analogy that mathematics can be viewed as a pyramid of knowledge, that builds layer upon layer as more mathematical structure is put in place. The di?culty lies in the fact that an engineer or scientist typically would like to start somewhere “above the base” of the pyramid. Engineers and scientists are not as concerned, generally speaking, with the subtleties of deriving theorems axiomatically. Rather, they are interested in gaining a working knowledge of the applicability of the theory to their ?eld of interest.

    Selected Topics On Generalized Integration

    Posted By: hill0
    Selected Topics On Generalized Integration

    Selected Topics On Generalized Integration
    English | 2025 | ISBN: 9819812194 | 316 Pages | PDF (True) | 5 MB

    Applied Nonlinear Analysis

    Posted By: AvaxGenius
    Applied Nonlinear Analysis

    Applied Nonlinear Analysis by Adélia Sequeira, Hugo Beirão Veiga, Juha Hans Videman
    English | PDF | 2002 | 569 Pages | ISBN : 1475782543 | 13.7 MB

    This book is meant as a present to honor Professor on the th occasion of his 70 birthday. It collects refereed contributions from sixty-one mathematicians from eleven countries. They cover many different areas of research related to the work of Professor including Navier-Stokes equations, nonlinear elasticity, non-Newtonian fluids, regularity of solutions of parabolic and elliptic problems, operator theory and numerical methods. The realization of this book could not have been made possible without the generous support of Centro de Matemática Aplicada (CMA/IST) and Fundação Calouste Gulbenkian. Special thanks are due to Dr. Ulrych for the careful preparation of the final version of this book. Last but not least, we wish to express our gratitude to Dr. for her invaluable assistance from the very beginning. This project could not have been successfully concluded without her enthusiasm and loving care for her father. On behalf of the editors ADÉLIA SEQUEIRA v honored by the Order of Meritof the Czech Republic by Václav Havel, President of the Czech Republic, on the October 28, 1998, Professor Emeritus of Mathematics at the Charles University in Prague, Presidential Research Professor at the Northern Illinois University and Doctor Honoris Causa at the Technical University of Dresden, has been enriching the Czech and world mathematics with his new ideas in the areas of partial differential equations, nonlinear functional analysis and applications of the both disciplines in continuum mechanics and hydrodynamics for more than forty years.

    Recent Advances in Mathematical Analysis: Celebrating the 70th Anniversary of Francesco Altomare (Trends in Mathematics)

    Posted By: Free butterfly
    Recent Advances in Mathematical Analysis: Celebrating the 70th Anniversary of Francesco Altomare (Trends in Mathematics)

    Recent Advances in Mathematical Analysis: Celebrating the 70th Anniversary of Francesco Altomare (Trends in Mathematics) by Anna Maria Candela, Mirella Cappelletti Montano, Elisabetta Mangino
    English | May 19, 2023 | ISBN: 3031200209 | 481 pages | MOBI | 78 Mb

    Matrix and Operator Equations and Applications (Mathematics Online First Collections)

    Posted By: Free butterfly
    Matrix and Operator Equations and Applications (Mathematics Online First Collections)

    Matrix and Operator Equations and Applications (Mathematics Online First Collections) by Mohammad Sal Moslehian
    English | July 30, 2023 | ISBN: 303125385X | 775 pages | MOBI | 106 Mb

    Dynamical Entropy in Operator Algebras

    Posted By: AvaxGenius
    Dynamical Entropy in Operator Algebras

    Dynamical Entropy in Operator Algebras by Sergey Neshveyev , Erling Størmer
    English | PDF (True | 2006 | 294 Pages | ISBN : 3540346708 | 2.6 MB

    During the last 30 years there have been several attempts at extending the notion of entropy to noncommutative dynamical systems. The authors present in the book the two most successful approaches to the extensions of measure entropy and topological entropy to the noncommutative setting and analyze in detail the main models in the theory.

    The Fourfold Way in Real Analysis: An Alternative to the Metaplectic Representation

    Posted By: AvaxGenius
    The Fourfold Way in Real Analysis: An Alternative to the Metaplectic Representation

    The Fourfold Way in Real Analysis: An Alternative to the Metaplectic Representation by André Unterberger
    English | PDF (True) | 2006 | 228 Pages | ISBN : 3764375442 | 2.4 MB

    The fourfold way starts with the consideration of entire functions of one variable satisfying specific estimates at infinity, both on the real line and the pure imaginary line. A major part of classical analysis, mainly that which deals with Fourier analysis and related concepts, can then be given a parameter-dependent analogue. The parameter is some real number modulo 2, the classical case being obtained when it is an integer. The space L2(R) has to give way to a pseudo-Hilbert space, on which a new translation-invariant integral still exists. All this extends to the n-dimensional case, and in the alternative to the metaplectic representation so obtained, it is the space of Lagrangian subspaces of R2n that plays the usual role of the complex Siegel domain. In fourfold analysis, the spectrum of the harmonic oscillator can be an arbitrary class modulo the integers.

    Partial Differential Operators and Mathematical Physics

    Posted By: AvaxGenius
    Partial Differential Operators and Mathematical Physics

    Partial Differential Operators and Mathematical Physics: International Conference in Holzhau, Germany, July 3–9, 1994 by Michael Demuth, Bert-Wolfgang Schulze
    English | PDF | 1995 | 422 Pages | ISBN : 3764352086 | 33.7 MB

    This volume contains the proceedings of the International Conference on "Par­ tial Differential Equations" held in HolzhaujErzgebirge, Germany, July 3~9, 1994. The conference was sponsored by the Max-Planck-Gesellschaft, the Deutsche For­ schungsgemeinschaft, the Land Brandenburg and the Freistaat Sachsen. It was initiated by the Max-Planck-Research Group "Partielle Differential­ gleichungen und Komplexe Analysis" at the University of Potsdam as one of the annual meetings of the research group. This conference is part of a series begun by the former Karl-Weierstraf3-Institute of Mathematics in Berlin, with the confer­ ences in Ludwigsfelde 1976, Reinhardsbrunn 1985, Holzhau 1988 (proceedings in the Teubner Texte zur Mathematik 112, Teubner-Verlag 1989), Breitenbrunn 1990 (proceedings in the Teubner Texte zur Mathematik 131, Teubner-Verlag 1992), and Lambrecht 1991 (proceedings in Operator Theory: Advances and Applications, Vol. 57, Birkhiiuser Verlag 1992); subsequent conferences took place in Potsdam in 1992 and 1993 under the auspices of the Max-Planck-Research Group "Partielle Differentialgleichungen und Komplexe Analysis" at the University of Potsdam. It was the intention of the organizers to bring together specialists from differ­ ent areas of modern analysis, geometry and mathematical physics to discuss not only recent progress in the respective disciplines but also to encourage interaction between these fields. The scientific advisory board of the Holzhau conference consisted of S. Al­ beverio (Bochum), L. Boutet de Monvel (Paris), M. Demuth (Clausthal), P. Gilkey (Eugene), B. Gramsch (Mainz), B. Helffer (Paris), S.T. Kuroda (Tokyo), B.-W. Schulze (Potsdam).

    Levy Processes, Integral Equations, Statistical Physics: Connections and Interactions

    Posted By: AvaxGenius
    Levy Processes, Integral Equations, Statistical Physics: Connections and Interactions

    Levy Processes, Integral Equations, Statistical Physics: Connections and Interactions by Lev A. Sakhnovich
    English | PDF (True) | 2012 | 246 Pages | ISBN : 3034803559 | 2 MB

    In a number of famous works, M. Kac showed that various methods of probability theory can be fruitfully applied to important problems of analysis. The interconnection between probability and analysis also plays a central role in the present book. However, our approach is mainly based on the application of analysis methods (the method of operator identities, integral equations theory, dual systems, integrable equations) to probability theory (Levy processes, M. Kac's problems, the principle of imperceptibility of the boundary, signal theory). The essential part of the book is dedicated to problems of statistical physics (classical and quantum cases). We consider the corresponding statistical problems (Gibbs-type formulas, non-extensive statistical mechanics, Boltzmann equation) from the game point of view (the game between energy and entropy). One chapter is dedicated to the construction of special examples instead of existence theorems (D. Larson's theorem, Ringrose's hypothesis, the Kadison-Singer and Gohberg-Krein questions). We also investigate the Bezoutiant operator. In this context, we do not make the assumption that the Bezoutiant operator is normally solvable, allowing us to investigate the special classes of the entire functions.

    The Legacy of Niels Henrik Abel

    Posted By: AvaxGenius
    The Legacy of Niels Henrik Abel

    The Legacy of Niels Henrik Abel: The Abel Bicentennial, Oslo, 2002 by Olav Arnfinn Laudal, Ragni Piene
    English | PDF | 2004 | 784 Pages | ISBN : 3540438262 | 5.3 MB

    This book contains a series of research papers on subjects related to the work of Niels Henrik Abel, written by some of the foremost specialists in their fields. Some of the authors have been specifically invited to present papers, discussing the influence of Abel in a mathematical-historical context. Others have submitted papers presented at the Abel Bicentennial Conference, Oslo June 3-8, 2002. The idea behind the book has been to produce a text covering a substantial part of the legacy of Abel, as perceived at the beginning of the 21st century.

    Complex Convexity and Analytic Functionals

    Posted By: AvaxGenius
    Complex Convexity and Analytic Functionals

    Complex Convexity and Analytic Functionals by Mats Andersson , Ragnar Sigurdsson , Mikael Passare
    English | PDF (True) | 2004 | 172 Pages | ISBN : 3764324201 | 17.8 MB

    A set in complex Euclidean space is called C-convex if all its intersections with complex lines are contractible, and it is said to be linearly convex if its complement is a union of complex hyperplanes. These notions are intermediates between ordinary geometric convexity and pseudoconvexity. Their importance was first manifested in the pioneering work of André Martineau from about forty years ago. Since then a large number of new related results have been obtained by many different mathematicians. The present book puts the modern theory of complex linear convexity on a solid footing, and gives a thorough and up-to-date survey of its current status. Applications include the Fantappié transformation of analytic functionals, integral representation formulas, polynomial interpolation, and solutions to linear partial differential equations.

    Nigel J. Kalton Selecta: Volume 2 (Repost)

    Posted By: AvaxGenius
    Nigel J. Kalton Selecta: Volume 2 (Repost)

    Nigel J. Kalton Selecta: Volume 2 by Fritz Gesztesy, Gilles Godefroy, Loukas Grafakos, Igor Verbitsky
    English | PDF (True | 2016 | 778 Pages | ISBN : 3319187988 | 262.5 MB

    This is the second part of a two volume anthology comprising a selection of 49 articles that illustrate the depth, breadth and scope of Nigel Kalton’s research. Each article is accompanied by comments from an expert on the respective topic, which serves to situate the article in its proper context, to successfully link past, present and hopefully future developments of the theory and to help readers grasp the extent of Kalton’s accomplishments. Kalton’s work represents a bridge to the mathematics of tomorrow, and this book will help readers to cross it.

    Different Faces of Geometry

    Posted By: AvaxGenius
    Different Faces of Geometry

    Different Faces of Geometry by Simon Donaldson, Yakov Eliashberg, Mikhael Gromov
    English | PDF | 2004 | 424 Pages | ISBN : 0306486571 | 71.6 MB

    Different Faces of Geometry - edited by the world renowned geometers S. Donaldson, Ya. Eliashberg, and M. Gromov - presents the current state, new results, original ideas and open questions from the following important topics in modern geometry:

    Fourier Analysis and Convexity

    Posted By: AvaxGenius
    Fourier Analysis and Convexity

    Fourier Analysis and Convexity by Luca Brandolini, Leonardo Colzani, Giancarlo Travaglini, Alex Iosevich
    English | PDF (True) | 2004 | 274 Pages | ISBN : 0817632638 | 21.9 MB

    Over the course of the last century, the systematic exploration of the relationship between Fourier analysis and other branches of mathematics has lead to important advances in geometry, number theory, and analysis, stimulated in part by Hurwitz’s proof of the isoperimetric inequality using Fourier series.