Inequalities


Author: G. H. Hardy,J. E. Littlewood,G. Pólya
Publisher: Cambridge University Press
ISBN: 9780521358804
Category: Mathematics
Page: 324
View: 7543

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This classic of the mathematical literature forms a comprehensive study of the inequalities used throughout mathematics. First published in 1934, it presents clearly and lucidly both the statement and proof of all the standard inequalities of analysis. The authors were well-known for their powers of exposition and made this subject accessible to a wide audience of mathematicians.

Advances in Mathematical Inequalities and Applications


Author: Praveen Agarwal,Silvestru Sever Dragomir,Mohamed Jleli,Bessem Samet
Publisher: Springer
ISBN: 9811330131
Category: Mathematics
Page: 349
View: 6367

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This book is a collection of original research and survey articles on mathematical inequalities and their numerous applications in diverse areas of mathematics and engineering. It includes chapters on convexity and related concepts; inequalities for mean values, sums, functions, operators, functionals, integrals and their applications in various branches of mathematics and related sciences; fractional integral inequalities; and weighted type integral inequalities. It also presents their wide applications in biomathematics, boundary value problems, mechanics, queuing models, scattering, and geomechanics in a concise, but easily understandable way that makes the further ramifications and future directions clear. The broad scope and high quality of the contributions make this book highly attractive for graduates, postgraduates and researchers. All the contributing authors are leading international academics, scientists, researchers and scholars.

Eine Einladung in die Mathematik

Einblicke in aktuelle Forschung
Author: Dierk Schleicher,Malte Lackmann
Publisher: Springer-Verlag
ISBN: 3642257984
Category: Mathematics
Page: 228
View: 2679

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Diese Einladung zur Mathematik besteht aus 14 Beiträgen, viele davon von weltweit führenden Mathematikern geschrieben, die die Leser in spannende Aspekte aktueller mathematischer Forschung einführen. Die Artikel sind so vielfältig wie die Persönlichkeiten ihrer Autoren und zeigen, wie reich und lebendig die Mathematik als Forschungsgebiet ist. Das Buch richtet sich in erster Linie an interessierte Schüler und junge Studierende, die Mathematik aus der Schule oder von Wettbewerben kennen und die aktuelle Forschungsmathematik kennenlernen wollen. Zusammen mit einem Team junger "Testleser" haben die Herausgeber und Autoren in einem intensiven Bearbeitungsprozess die Texte für junge Leser verständlich gestaltet. Schüler, Lehrer, Mathematiker und alle Mathematik-Begeisterten werden in diesem vielseitigen und spannenden Buch genussvoll lesen.

Function Spaces and Inequalities

New Delhi, India, December 2015
Author: Pankaj Jain,Hans-Jürgen Schmeisser
Publisher: Springer
ISBN: 981106119X
Category: Mathematics
Page: 335
View: 7199

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This book features original research and survey articles on the topics of function spaces and inequalities. It focuses on (variable/grand/small) Lebesgue spaces, Orlicz spaces, Lorentz spaces, and Morrey spaces and deals with mapping properties of operators, (weighted) inequalities, pointwise multipliers and interpolation. Moreover, it considers Sobolev–Besov and Triebel–Lizorkin type smoothness spaces. The book includes papers by leading international researchers, presented at the International Conference on Function Spaces and Inequalities, held at the South Asian University, New Delhi, India, on 11–15 December 2015, which focused on recent developments in the theory of spaces with variable exponents. It also offers further investigations concerning Sobolev-type embeddings, discrete inequalities and harmonic analysis. Each chapter is dedicated to a specific topic and written by leading experts, providing an overview of the subject and stimulating future research.

Tapas in Experimental Mathematics

AMS Special Session on Experimental Mathematics, January 5, 2007, New Orleans, Louisiana
Author: Tewodros Amdeberhan,Victor H. Moll
Publisher: American Mathematical Soc.
ISBN: 0821843176
Category: Mathematics
Page: 292
View: 7429

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Experimental Mathematics is a recently structured field of Mathematics that uses a computer and advanced computing technology as tools to perform experiments such as analysis of examples, testing of new ideas, and the search of patterns. The development of a broad spectrum of mathematical software products such as MathematicaR and MapleTM has allowed mathematicians of diverse backgrounds and interests to make the computer an essential part of their daily working environment. This volume represents the AMS Special Session on Experimental Mathematics held in January 2007 in New Orleans. This gathering is part of an annual meeting of a growing number of scientists that have been labeled experimental mathematicians. The guiding principles of the field, some of which are included in the introduction to these proceedings, are similar to those of laboratory experiments in the physical and biological sciences.

Convex Functions and their Applications

A Contemporary Approach
Author: Constantin Niculescu,Lars-Erik Persson
Publisher: Springer Science & Business Media
ISBN: 9780387243009
Category: Mathematics
Page: 256
View: 5120

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Thorough introduction to an important area of mathematics Contains recent results Includes many exercises

Analytic Methods for Diophantine Equations and Diophantine Inequalities


Author: H. Davenport
Publisher: Cambridge University Press
ISBN: 9781139441230
Category: Mathematics
Page: N.A
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Harold Davenport was one of the truly great mathematicians of the twentieth century. Based on lectures he gave at the University of Michigan in the early 1960s, this book is concerned with the use of analytic methods in the study of integer solutions to Diophantine equations and Diophantine inequalities. It provides an excellent introduction to a timeless area of number theory that is still as widely researched today as it was when the book originally appeared. The three main themes of the book are Waring's problem and the representation of integers by diagonal forms, the solubility in integers of systems of forms in many variables, and the solubility in integers of diagonal inequalities. For the second edition of the book a comprehensive foreword has been added in which three prominent authorities describe the modern context and recent developments. A thorough bibliography has also been added.

The Geometry of Moduli Spaces of Sheaves

A Publication of the Max-Planck-Institut für Mathematik, Bonn
Author: Daniel Huybrechts,Manfred Lehn
Publisher: Vieweg+Teubner Verlag
ISBN: 9783663116257
Category: Technology & Engineering
Page: 270
View: 1195

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This book is intended to serve as an introduction to the theory of semistable sheaves and at the same time to provide a survey of recent research results on the geometry of moduli spaces. The first part introduces the basic concepts in the theory: Hilbert polynomial, slope, stability, Harder-Narasimhan filtration, Grothendieck's Quot-scheme. It presents detailed proofs of the Grauert-Mülich Theorem, the Bogomolov Inequality, the semistability of tensor products, and the boundedness of the family of semistable sheaves. It also gives a self-contained account of the construction of moduli spaces of semistable sheaves on a projective variety à la Gieseker, Maruyama, and Simpson. The second part presents some of the recent results of the geometry of moduli spaces of sheaves on an algebraic surface, following work of Mukai, O'Grady, Gieseker, Li and many others. In particular, moduli spaces of sheaves on K3 surfaces and determinant line bundles on the moduli spaces are treated in some detail. Other topics include the Serre correspondence, restriction of stable bundles to curves, symplectic structures, irreducibility and Kodaira-dimension of moduli spaces.

Erfahrung Mathematik


Author: P.J. Davis,R. Hersh
Publisher: Springer-Verlag
ISBN: 3034850409
Category: Science
Page: 466
View: 5035

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ie ältesten uns bekannten mathematischen Schriftta D feln stammen aus der Zeit um 2400 v. ehr. ; aber wir dürfen davon ausgehen, daß das Bedürfnis, Mathematik zu schaffen, ein Ausdruck der menschlichen Zivilisation an sich ist. In vier bis fünf Jahrtausenden hat sich ein gewalti ges System von Praktiken und Begriffen - die Mathematik herangebildet, die in vielfältiger Weise mit unserem Alltag verknüpft ist. Was ist Mathematik? Was bedeutet sie? Wo mit befaßt sie sich? Was sind ihre Methoden? Wie wird sie geschaffen und benützt? Wo ist ihr Platz in der Vielgestalt der menschlichen Erfahrung? Welchen Nutzen bringt sie? Was für Schaden richtet sie an? Welches Gewicht kommt ihr zu? Diese schwierigen Fragen werden noch zusätzlich kompliziert durch die Fülle des Materials und die weitver zweigten Querverbindungen, die es dem einzelnen verun möglichen, alles zu begreifen, geschweige denn, es in seiner Gesamtheit zu erfassen und zwischen den Deckeln eines normalen Buches unterzubringen. Um von dieser Material fülle nicht erdrückt zu werden, haben sich die Autoren für eine andere Betrachtungsweise entschieden. Die Mathema tik ist seit Tausenden von Jahren ein Feld menschlicher Ak tivität. In begrenztem Rahmen ist jeder von uns ein Mathe matiker und betreibt bewußt Mathematik, wenn er zum Beispiel auf dem Markt einkauft, Tapeten ausmißt oder ei nen Keramiktopf mit einem regelmäßigen Muster verziert. In bescheidenem Ausmaß versucht sich auch jeder von uns als mathematischer Denker. Schon mit dem Ausruf «Aber Zahlen lügen nicht!» befinden wir uns in der Gesellschaft von Plato oder Lakatos.

A Course of Pure Mathematics


Author: G. H. Hardy
Publisher: Cambridge University Press
ISBN: 1139643517
Category: Mathematics
Page: N.A
View: 1347

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There are few textbooks of mathematics as well-known as Hardy's Pure Mathematics. Since its publication in 1908, this classic book has inspired successive generations of budding mathematicians at the beginning of their undergraduate courses. In its pages, Hardy combines the enthusiasm of the missionary with the rigour of the purist in his exposition of the fundamental ideas of the differential and integral calculus, of the properties of infinite series and of other topics involving the notion of limit. Celebrating 100 years in print with Cambridge, this edition includes a Foreword by T. W. Körner, describing the huge influence the book has had on the teaching and development of mathematics worldwide. Hardy's presentation of mathematical analysis is as valid today as when first written: students will find that his economical and energetic style of presentation is one that modern authors rarely come close to.

Aspects of Sobolev-Type Inequalities


Author: L. Saloff-Coste
Publisher: Cambridge University Press
ISBN: 9780521006071
Category: Mathematics
Page: 190
View: 3435

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Focusing on Poincaré, Nash and other Sobolev-type inequalities and their applications to the Laplace and heat diffusion equations on Riemannian manifolds, this text is an advanced graduate book that will also suit researchers.