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Author: Werner Balser
Publisher: Springer
ISBN: 3540485945
Category : Mathematics
Languages : en
Pages : 117
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Book Description
Multisummability is a method which, for certain formal power series with radius of convergence equal to zero, produces an analytic function having the formal series as its asymptotic expansion. This book presents the theory of multisummabi- lity, and as an application, contains a proof of the fact that all formal power series solutions of non-linear meromorphic ODE are multisummable. It will be of use to graduate students and researchers in mathematics and theoretical physics, and especially to those who encounter formal power series to (physical) equations with rapidly, but regularly, growing coefficients.
Author: Werner Balser
Publisher: Springer
ISBN: 3540485945
Category : Mathematics
Languages : en
Pages : 117
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Book Description
Multisummability is a method which, for certain formal power series with radius of convergence equal to zero, produces an analytic function having the formal series as its asymptotic expansion. This book presents the theory of multisummabi- lity, and as an application, contains a proof of the fact that all formal power series solutions of non-linear meromorphic ODE are multisummable. It will be of use to graduate students and researchers in mathematics and theoretical physics, and especially to those who encounter formal power series to (physical) equations with rapidly, but regularly, growing coefficients.
Author: Barry Simon
Publisher: Cambridge University Press
ISBN: 1139497596
Category : Mathematics
Languages : en
Pages : 357
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Book Description
Convexity is important in theoretical aspects of mathematics and also for economists and physicists. In this monograph the author provides a comprehensive insight into convex sets and functions including the infinite-dimensional case and emphasizing the analytic point of view. Chapter one introduces the reader to the basic definitions and ideas that play central roles throughout the book. The rest of the book is divided into four parts: convexity and topology on infinite-dimensional spaces; Loewner's theorem; extreme points of convex sets and related issues, including the Krein–Milman theorem and Choquet theory; and a discussion of convexity and inequalities. The connections between disparate topics are clearly explained, giving the reader a thorough understanding of how convexity is useful as an analytic tool. A final chapter overviews the subject's history and explores further some of the themes mentioned earlier. This is an excellent resource for anyone interested in this central topic.
Author: Karen J. Maroda
Publisher: Routledge
ISBN: 1135060843
Category : Psychology
Languages : en
Pages : 206
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Book Description
Seduction, Surrender, and Transformation demonstrates how interpersonal psychoanalysis obliges analysts to engage their patients with genuine emotional responsiveness, so that not only the patient but the analyst too is open to ongoing transformation through the analytic experience. In so doing, the analyst moves from the position of an "interpreting observer" to that of an "active participant and facilitator" whose affective communications enable the patient to acquire basic self-trust along with self-knowledge. Drawing on the current literature on affect, Maroda argues that psychological change occurs through affect-laden interpersonal processes. Given that most patients in psychotherapy have problems with affect management, the completing of cycles of affective communication between therapist and patient becomes a vitally important aspect of the therapeutic enterprise. Through emotionally open responses to their patients and careful use of patient-prompted self-disclosures, analysts can facilitate affect regulation responsibly and constructively, with the emphasis always remaining on the patients' experience. Moments of mutual surrender - the honest emotional giving over of patient to analyst and analyst to patient - epitomize the emotionally intense interpersonal experiences that lead to enduring intrapsychic change. Maroda's work is profoundly personal. She does not hesitate to share with the reader how her own personality affects her thinking and her work. Indeed, she believes her theoretical and clinical preferences are emblematic of the way in which the analyst's subjectivity necessarily shapes theory choice and practice preferences in general. Seduction, Surrender, and Transfomation is not only a powerful brief for emotional honesty in the analytic relationship but also a model of the personal openness that, according to Maroda, psychoanalysis demands of all its practitioners.
Author: Frank Stenger
Publisher: Springer Science & Business Media
ISBN: 1461227062
Category : Mathematics
Languages : en
Pages : 580
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Book Description
Many mathematicians, scientists, and engineers are familiar with the Fast Fourier Transform, a method based upon the Discrete Fourier Transform. Perhaps not so many mathematicians, scientists, and engineers recognize that the Discrete Fourier Transform is one of a family of symbolic formulae called Sinc methods. Sinc methods are based upon the Sinc function, a wavelet-like function replete with identities which yield approximations to all classes of computational problems. Such problems include problems over finite, semi-infinite, or infinite domains, problems with singularities, and boundary layer problems. Written by the principle authority on the subject, this book introduces Sinc methods to the world of computation. It serves as an excellent research sourcebook as well as a textbook which uses analytic functions to derive Sinc methods for the advanced numerical analysis and applied approximation theory classrooms. Problem sections and historical notes are included.
Author: John Ben Hough
Publisher: American Mathematical Soc.
ISBN: 0821843737
Category : Mathematics
Languages : en
Pages : 170
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Book Description
Examines in some depth two important classes of point processes, determinantal processes and 'Gaussian zeros', i.e., zeros of random analytic functions with Gaussian coefficients. This title presents a primer on modern techniques on the interface of probability and analysis.
Author: Robin Pemantle
Publisher: Cambridge University Press
ISBN: 1107031575
Category : Mathematics
Languages : en
Pages : 395
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Book Description
Aimed at graduate students and researchers in enumerative combinatorics, this book is the first to treat the analytic aspects of combinatorial enumeration from a multivariate perspective.
Author: KRANTZ
Publisher: Birkhäuser
ISBN: 3034876440
Category : Science
Languages : en
Pages : 190
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Book Description
The subject of real analytic functions is one of the oldest in mathe matical analysis. Today it is encountered early in ones mathematical training: the first taste usually comes in calculus. While most work ing mathematicians use real analytic functions from time to time in their work, the vast lore of real analytic functions remains obscure and buried in the literature. It is remarkable that the most accessible treatment of Puiseux's theorem is in Lefschetz's quite old Algebraic Geometry, that the clearest discussion of resolution of singularities for real analytic manifolds is in a book review by Michael Atiyah, that there is no comprehensive discussion in print of the embedding prob lem for real analytic manifolds. We have had occasion in our collaborative research to become ac quainted with both the history and the scope of the theory of real analytic functions. It seems both appropriate and timely for us to gather together this information in a single volume. The material presented here is of three kinds. The elementary topics, covered in Chapter 1, are presented in great detail. Even results like a real ana lytic inverse function theorem are difficult to find in the literature, and we take pains here to present such topics carefully. Topics of middling difficulty, such as separate real analyticity, Puiseux series, the FBI transform, and related ideas (Chapters 2-4), are covered thoroughly but rather more briskly.
Author:
Publisher:
ISBN:
Category : Public health
Languages : en
Pages : 100
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Book Description
Author: Hermann Weyl
Publisher: Princeton University Press
ISBN: 1400882281
Category : Mathematics
Languages : en
Pages : 269
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Book Description
The description for this book, Meromorphic Functions and Analytic Curves. (AM-12), will be forthcoming.
Author: Jian-Ke Lu
Publisher: World Scientific
ISBN: 9789810210205
Category : Mathematics
Languages : en
Pages : 484
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Book Description
This book deals with boundary value problems for analytic functions with applications to singular integral equations. New and simpler proofs of certain classical results such as the Plemelj formula, the Privalov theorem and the Poincar-Bertrand formula are given. Nearly one third of this book contains the author's original works, most of which have not been published in English before and, hence, were previously unknown to most readers in the world.It consists of 7 chapters together with an appendix: Chapter I describes the basic knowledge on Cauchy-type integrals and Cauchy principal value integrals; Chapters II and III study, respectively, fundamental boundary value problems and their applications to singular integral equations for closed contours; Chapters IV and V discuss the same problems for curves with nodes (including open arcs); Chaper VI deals with similar problems for systems of functions; Chapter VII is concerned with some miscellaneous problems and the Appendix contains some basic results on Fredholm integral equations. In most sections, there are carefully selected sets of exercises, some of which supplement the text of the sections; answers/hints are also given for some of these exercises.For graduate students or seniors, all the 7 chapters can be used for a full year course, while the first 3 chapters may be used for a one-semester course.
