This book is devoted exclusively to Lebesgue spaces and their direct derived spaces. Unique in its sole dedication, this book explores Lebesgue spaces, distribution functions and nonincreasing rearrangement. Moreover, it also deals with weak, Lorentz and the more recent variable exponent and grand Lebesgue spaces with considerable detail to the proofs. The book also touches on basic harmonic analysis in the aforementioned spaces. An appendix is given at the end of the book giving it a self-contained character. This work is ideal for teachers, graduate students and researchers.
This textbook on functional analysis offers a short and concise introduction to the subject. The book is designed in such a way as to provide a smooth transition between elementary and advanced topics and its modular structure allows for an easy assimilation of the content. Starting from a dedicated chapter on the axiom of choice, subsequent chapters cover Hilbert spaces, linear operators, functionals and duality, Fourier series, Fourier transform, the fixed point theorem, Baire categories, the uniform bounded principle, the open mapping theorem, the closed graph theorem, the Hahn–Banach theorem, adjoint operators, weak topologies and reflexivity, operators in Hilbert spaces, spectral theory of operators in Hilbert spaces, and compactness. Each chapter ends with workable problems. The book is suitable for graduate students, but also for advanced undergraduates, in mathematics and physics. Contents: List of Figures Basic Notation Choice Principles Hilbert Spaces Completeness, Completion and Dimension Linear Operators Functionals and Dual Spaces Fourier Series Fourier Transform Fixed Point Theorem Baire Category Theorem Uniform Boundedness Principle Open Mapping Theorem Closed Graph Theorem Hahn–Banach Theorem The Adjoint Operator Weak Topologies and Reflexivity Operators in Hilbert Spaces Spectral Theory of Operators on Hilbert Spaces Compactness Bibliography Index
Aimed primarily at undergraduate level university students, An Illustrative Introduction to Modern Analysis provides an accessible and lucid contemporary account of the fundamental principles of Mathematical Analysis. The themes treated include Metric Spaces, General Topology, Continuity, Completeness, Compactness, Measure Theory, Integration, Lebesgue Spaces, Hilbert Spaces, Banach Spaces, Linear Operators, Weak and Weak* Topologies. Suitable both for classroom use and independent reading, this book is ideal preparation for further study in research areas where a broad mathematical toolbox is required.
This textbook covers the main results and methods of real analysis in a single volume. Taking a progressive approach to equations and transformations, this book starts with the very foundations of real analysis (set theory, order, convergence, and measure theory) before presenting powerful results that can be applied to concrete problems. In addition to classical results of functional analysis, differential calculus and integration, Analysis discusses topics such as convex analysis, dissipative operators and semigroups which are often absent from classical treatises. Acknowledging that analysis has significantly contributed to the understanding and development of the present world, the book further elaborates on techniques which pervade modern civilization, including wavelets in information theory, the Radon transform in medical imaging and partial differential equations in various mechanical and physical phenomena. Advanced undergraduate and graduate students, engineers as well as practitioners wishing to familiarise themselves with concepts and applications of analysis will find this book useful. With its content split into several topics of interest, the book’s style and layout make it suitable for use in several courses, while its self-contained character makes it appropriate for self-study.
Bilipschitz and Coarse Embeddings into Banach Spaces
Author: Mikhail I. Ostrovskii
Publisher: Walter de Gruyter
Embeddings of discrete metric spaces into Banach spaces recently became an important tool in computer science and topology. The book will help readers to enter and to work in this very rapidly developing area having many important connections with different parts of mathematics and computer science. The purpose of the book is to present some of the most important techniques and results, mostly on bilipschitz and coarse embeddings. The topics include embeddability of locally finite metric spaces into Banach spaces is finitely determined, constructions of embeddings, distortion in terms of Poincaré inequalities, constructions of families of expanders and of families of graphs with unbounded girth and lower bounds on average degrees, Banach spaces which do not admit coarse embeddings of expanders, structure of metric spaces which are not coarsely embeddable into a Hilbert space, applications of Markov chains to embeddability problem, metric characterizations of properties of Banach spaces, and Lipschitz free spaces.
260 2 Crew Legalities and Crew Pairing Repair 264 3 Model and Mathematical Formulation 266 4 Solution Methodology 271 5 Computational Experiences 277 6 Conclusion 285 REFERENCES 286 10 THE USE OF OPTIMIZATION TO PERFORM AIR TRAFFIC FLOW MANAGEMENT Kenneth Lindsay, E. Andrew Boyd, George Booth, and Charles Harvey 287 1 Introduction 288 2 The Traffic Flow Management (TFM) Problem 289 3 Recent TFM Optimization Models 292 4 The Time Assignment Model (TAM) 302 5 Summary and Conclusions 307 REFERENCES 309 11 THE PROCESSES OF AIRLINE SYSTEM OPERATIONS CONTROL Seth C. Grandeau, Michael D. Clarke, and Dennis F.X. Mathaisel 312 1 Introduction 313 2 The Four Phases of Airline Schedule Development 315 The Airline Operations Control Center (OCC) 3 320 4 Analysis of Operational Problems 331 5 Areas For Improvement 352 6 Case Study: PT Garuda Indonesia Airlines 357 REFERENCES 368 12 THE COMPLEX CONFIGURATION MODEL Bruce W. Patty and Jim Diamond 370 1 Introduction 370 Problem Description 2 371 Problem Formulation 3 375 4 Model Implementation 379 ix Contents 383 5 Summary REFERENCES 383 13 INTEGRATED AIRLINE SCHEDULE PLANNING Cynthia Barnhart, Fang Lu, and Rajesh Shenoi 384 1 Introduction 385 2 Fleet Assignment and Crew Pairing Problems: Existing M- els and Algorithms 388 3 An Integrated Approximate Fleet Assignment and Crew Pa- ing Model 393 4 An Advanced Integrated Solution Approach 395 5 Case Study 396 6 Conclusions and Future Research Directions 399 REFERENCES 401 14 AIRLINE SCHEDULE PERTURBATION PROBLEM: LANDING AND TAKEOFF WITH
Author: Melvil Dewey,Frederick Leypoldt,Karl Brown,Bertine Emma Weston,Helen E Wessells
Includes, beginning Sept. 15, 1954 (and on the 15th of each month, Sept.-May) a special section: School library journal, ISSN 0000-0035, (called Juniorlibraries, 1954-May 1961). Issued also separately.
Besonderen Wert legt Rudin darauf, dem Leser die Zusammenhänge unterschiedlicher Bereiche der Analysis zu vermitteln und so die Grundlage für ein umfassenderes Verständnis zu schaffen. Das Werk zeichnet sich durch seine wissenschaftliche Prägnanz und Genauigkeit aus und hat damit die Entwicklung der modernen Analysis in nachhaltiger Art und Weise beeinflusst. Der "Baby-Rudin" gehört weltweit zu den beliebtesten Lehrbüchern der Analysis und ist in 13 Sprachen übersetzt. 1993 wurde es mit dem renommierten Steele Prize for Mathematical Exposition der American Mathematical Society ausgezeichnet. Übersetzt von Uwe Krieg.
Issues in Discovery, Experimental, and Laboratory Medicine: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Discovery, Experimental, and Laboratory Medicine. The editors have built Issues in Discovery, Experimental, and Laboratory Medicine: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Discovery, Experimental, and Laboratory Medicine in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Discovery, Experimental, and Laboratory Medicine: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.