Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The main goal of this book is to introduce readers to functional analysis methods, in particular, time dependent analysis, for reliability models. Understanding the concept of reliability is of key importance - schedule delays, inconvenience, customer dissatisfaction, and loss of prestige and even weakening of national security are common examples of results that are caused by unreliability of systems and individuals. The book begins with an introduction to C0-semigroup theory. Then, after a brief history of reliability theory, methods that study the well-posedness, the asymptotic behaviors of solutions and reliability indices for varied reliability models are presented. Finally, further research problems are explored. Functional Analysis Methods for Reliability Models is an excellent reference for graduate students and researchers in operations research, applied mathematics and systems engineering.

Functional analysis --- functies (wiskunde)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This is the second of a two-volume work presenting a comprehensive exposition of extension results for maps between different geometric objects and of extension-trace results for smooth functions on subsets with no a priori differential structure (Whitney problems). The account covers the development of the area from the initial classical works of the first half of the 20th century to the flourishing period of the last decade. Seemingly very specific, these problems have been from the very beginning a powerful source of ideas, concepts and methods that essentially influenced and in some cases even transformed considerable areas of analysis. Aside from the material linked by the aforementioned problems the work is also unified by the geometric analysis approach used in the proofs of basic results. This requires a variety of geometric tools from convex and combinatorial geometry to geometry of metric space theory to Riemannian and Coarse geometry and more. The necessary facts are presented mostly with detailed proofs to make the book accessible to a wide audience.

Functional analysis --- functies (wiskunde)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

E' un testo adatto per una prima esposizione della teoria delle funzioni di singola variabile complessa. Esso si rivolge a studenti di Fisica, Matematica e Ingegneria che abbiano acquisito le nozioni fondamentali dell'Analisi Matematica reale. L'esigenza di una nuova pubblicazione nasce dall'idea di effettuare una selezione di argomenti, ritenuti fondamentali, con le seguenti finalita': i) ottenere un'esposizione sistematica e autoconsistente in circa 60 ore di lezione, ii) fornire le basi per le principali sucessive applicazioni nel campo della Fisica Teorica, iii) mantenere il rigore matematico onde favorire la maturazione scientifica dello studente e prepararlo per la lettura di testi avanzati, iv) accompagnare l'enunciato dei teoremi e le loro dimostrazioni con esempi pratici. A corredo della trattazione teorica, vengono proposti oltre 200 esercizi tutti corredati di soluzione dettagliata. Il loro svolgimento costituisce una parte imprescindibile per l'acquisizione della materia.

Functional analysis --- functies (wiskunde)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The main theme of this book is the relation between the global structure of Banach spaces and the various types of generalized "coordinate systems" - or "bases" - they possess. This subject is not new and has been investigated since the inception of the study of Banach spaces. In this book, the authors systematically investigate the concepts of Markushevich bases, fundamental systems, total systems and their variants. The material naturally splits into the case of separable Banach spaces, as is treated in the first two chapters, and the nonseparable case, which is covered in the remainder of the book. This book contains new results, and a substantial portion of this material has never before appeared in book form. The book will be of interest to both researchers and graduate students. Topics covered in this book include: - Biorthogonal Systems in Separable Banach Spaces - Universality and Szlenk Index - Weak Topologies and Renormings - Biorthogonal Systems in Nonseparable Spaces - Transfinite Sequence Spaces - Applications Petr Hájek is Professor of Mathematics at the Mathematical Institute of the Academy of Sciences of the Czech Republic. Vicente Montesinos is Professor of Mathematics at the Polytechnic University of Valencia, Spain. Jon Vanderwerff is Professor of Mathematics at La Sierra University, in Riverside, California. Václav Zizler is Professor of Mathematics at the Mathematical Institute of the Academy of Sciences of the Czech Republic.

Functional analysis --- functies (wiskunde)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The guiding principle of this presentation of ``Classical Complex Analysis'' is to proceed as quickly as possible to the central results while using a small number of notions and concepts from other fields. Thus the prerequisites for understanding this book are minimal; only elementary facts of calculus and algebra are required. The first four chapters cover the essential core of complex analysis: - differentiation in C (including elementary facts about conformal mappings) - integration in C (including complex line integrals, Cauchy's Integral Theorem, and the Integral Formulas) - sequences and series of analytic functions, (isolated) singularities, Laurent series, calculus of residues - construction of analytic functions: the gamma function, Weierstrass' Factorization Theorem, Mittag-Leffler Partial Fraction Decomposition, and -as a particular highlight- the Riemann Mapping Theorem, which characterizes the simply connected domains in C. Further topics included are: - the theory of elliptic functions based on the model of K. Weierstrass (with an excursions to older approaches due to N.H. Abel and C.G.J. Jacobi using theta series) - an introduction to the theory of elliptic modular functions and elliptic modular forms - the use of complex analysis to obtain number theoretical results - a proof of the Prime Number Theorem with a weak form of the error term. The book is especially suited for graduated students in mathematics and advanced undergraduated students in mathematics and other sciences. Motivating introductions, more than four hundred exercises of all levels of difficulty with hints or solutions, historical annotations, and over 120 figures make the overall presentation very attractive. The structure of the text, including abstracts beginning each chapter and highlighting of the main results, makes this book very appropriate for self-guided study and an indispensable aid in preparing for tests. This English edition is based on the fourth forthcoming German edition.

Functional analysis --- functies (wiskunde)