springer basel springer basel jun 2016 (6 Ergebnisse)

Buch. Zustand: Neu. Neuware -This book presents applications of hypercomplex analysis to boundary value and initial-boundary value problems from various areas of mathematical physics. Given that quaternion and Clifford analysis offer natural and intelligent ways to enter into higher dimensions, it starts with quaternion and Clifford versions of complex function theory including series expansions with Appell polynomials, as well as Taylor and Laurent series. Several necessary function spaces are introduced, and an operator calculus based on modifications of the Dirac, Cauchy-Fueter, and Teodorescu operators and different decompositions of quaternion Hilbert spaces are proved. Finally, hypercomplex Fourier transforms are studied in detail.All this is then applied to first-order partial differential equations such as the Maxwell equations, the Carleman-Bers-Vekua system, the Schrödinger equation, and the Beltrami equation. The higher-order equations start with Riccati-type equations. Further topicsinclude spatial fluid flow problems, image and multi-channel processing, image diffusion, linear scale invariant filtering, and others. One of the highlights is the derivation of the three-dimensional Kolosov-Mushkelishvili formulas in linear elasticity.Throughout the book the authors endeavor to present historical references and important personalities. The book is intended for a wide audience in the mathematical and engineering sciences and is accessible to readers with a basic grasp of real, complex, and functional analysis.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 408 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -The main focus of this monograph is to offer a comprehensive presentation of known and new results on various generalizations of CS-modules and CS-rings. Extending (or CS) modules are generalizations of injective (and also semisimple or uniform) modules. While the theory of CS-modules is well documented in monographs and textbooks, results on generalized forms of the CS property as well as dual notions are far less present in the literature.With their work the authors provide a solid background to module theory, accessible to anyone familiar with basic abstract algebra. The focus of the book is on direct sums of CS-modules and classes of modules related to CS-modules, such as relative (injective) ejective modules, (quasi) continuous modules, and lifting modules. In particular, matrix CS-rings are studied and clear proofs of fundamental decomposition results on CS-modules over commutative domains are given, thus complementing existing monographs in this area.Open problems round out the work and establish the basis for further developments in the field. The main text is complemented by a wealth of examples and exercises.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 392 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -Das vorliegende Lehrbuch möchte seine Leser auf knappem Raum nachhaltig fürdie Eleganz und Geschlossenheit der Funktionentheorie und ihre Wirkungsmächtigkeitbegeistern. Funktionentheoretische, d.h. komplex-analytische Methoden leisten nämlichetwas fast Magisches: kompakte Darstellung von Formeln vertieftes Verständnis von Funktionsverhalten einfache Berechnung von Grenzwerten eleganter Zugang zu Geometrie und Topologie der EbeneDie Analysis im Komplexen macht vieles also tatsächlich sehr viel unaufwändiger alsim Reellen: ¿Funktionentheorie spart Rechnungen¿.Das Buch eignet sich für Studierende der Mathematik ab dem zweiten Studienjahrund kommt mit einem Minimum an topologischen Begriffen aus. Der äußerst ökonomischeAufbau des Stoffs betont Konzepte und Ideen; konsequent wird daher begrifflichenBeweisen gegenüber solchen mit vielen Rechnungen der Vorzug gegeben. Zahlreicheinteressante Beispiele, Anwendungen und 230 Übungsaufgaben beleuchten die Kraftder eingeführten Methoden. Trotz der Kürze des Buchs reicht der Stoff bis zumRiemann¿schen Abbildungssatz, zur Theorie normaler Familien (auf Grundlage desextrem effektiven Reskalierungslemmas von Zalcman) und zu den¿elementaren¿Beweisen der Picard¿schen Sätze.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 164 pp. Deutsch.

Taschenbuch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -In dieser konzisen und zielgerichteten Einführung wird die Eleganz und Geschlossenheit der Funktionentheorie vorgeführt. So lassen sich mit den komplex-analytischen Methoden u. a. Formeln kompakt darstellen und Grenzwerte einfach berechnen - Funktionentheorie spart Rechnungen. Zahlreiche interessante Beispiele, Anwendungen und 170 Übungsaufgaben zeigen die Effizienz der Methoden. Trotz der Kürze des Buchs reicht der Stoff bis zum Riemann'schen Abbildungssatz. Das zugehörige Elektronisches Buch enthält computergestützte Rechnungen und historische Informationen. 164 pp. Deutsch.

Buch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book presents applications of hypercomplex analysis to boundary value and initial-boundary value problems from various areas of mathematical physics. Given that quaternion and Clifford analysis offer natural and intelligent ways to enter into higher dimensions, it starts with quaternion and Clifford versions of complex function theory including series expansions with Appell polynomials, as well as Taylor and Laurent series. Several necessary function spaces are introduced, and an operator calculus based on modifications of the Dirac, Cauchy-Fueter, and Teodorescu operators and different decompositions of quaternion Hilbert spaces are proved. Finally, hypercomplex Fourier transforms are studied in detail. All this is then applied to first-order partial differential equations such as the Maxwell equations, the Carleman-Bers-Vekua system, the Schrödinger equation, and the Beltrami equation. The higher-order equations start with Riccati-type equations. Further topics include spatial fluid flow problems, image and multi-channel processing, image diffusion, linear scale invariant filtering, and others. One of the highlights is the derivation of the three-dimensional Kolosov-Mushkelishvili formulas in linear elasticity.Throughout the book the authors endeavor to present historical references and important personalities. The book is intended for a wide audience in the mathematical and engineering sciences and is accessible to readers with a basic grasp of real, complex, and functional analysis. 408 pp. Englisch.

Taschenbuch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -The main focus of this monograph is to offer a comprehensive presentation of known and new results on various generalizations of CS-modules and CS-rings.Extending (or CS) modules are generalizations of injective (and also semisimple or uniform) modules. While the theory of CS-modules is well documented in monographs and textbooks, results on generalized forms of the CS property as well as dual notions are far less present in the literature.With their work the authors provide a solid background to module theory, accessible to anyone familiar with basic abstract algebra. The focus of the book is on direct sums of CS-modules and classes of modules related to CS-modules, such as relative (injective) ejective modules, (quasi) continuous modules, and lifting modules. In particular, matrix CS-rings are studied and clear proofs of fundamental decomposition results on CS-modules over commutative domains are given, thus complementing existing monographs in this area.Open problems round out the work and establish the basis for further developments in the field. The main text is complemented by a wealth of examples and exercises. 392 pp. Englisch.