Название: Nonstandard analysis for the working mathematician ISBN: 9401773262 ISBN-13(EAN): 9789401773263 Издательство: Springer Рейтинг: Цена: 13974.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: it is often used as a `secret weapon` by those who know the technique.This book illuminates the subject with some of the most striking applications in analysis, topology, functional analysis, probability and stochastic analysis, as well as applications in economics and combinatorial number theory.
Inequalities for polynomials and their derivatives are very important in many areas of mathematics, as well as in other computational and applied sciences; in particular they play a fundamental role in approximation theory. Here, not only Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials, but also ones for trigonometric polynomials and related functions, are treated in an integrated and comprehensive style in different metrics, both on general classes of polynomials and on important restrictive classes of polynomials. Primarily for graduate and PhD students, this book is useful for any researchers exploring problems which require derivative estimates. It is particularly useful for those studying inverse problems in approximation theory.
Автор: Nicholson, Neil R., Название: A transition to proof : ISBN: 0367201577 ISBN-13(EAN): 9780367201579 Издательство: Taylor&Francis Рейтинг: Цена: 14086.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The fundamental tool of theoretical mathematics is mathematical proof. Any claim or justification a mathematician makes must be proven. This book is designed for a reader who wants to learn what exactly a mathematical proof is, how they are constructed, and how to go about writing one.
Автор: A.B. Kharazishvili Название: Applications of Point Set Theory in Real Analysis ISBN: 0792349792 ISBN-13(EAN): 9780792349792 Издательство: Springer Рейтинг: Цена: 13275.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The main goal of this book is to demonstrate the usefulness of set-theoretical methods in various questions of real analysis and classical measure theory. It includes: similarities and differences between measure and category; and three aspects of the measure extension problem.
Описание: This book develops the theory of multivariable analysis, building on the single variable foundations established in the companion volume, Real Analysis: Foundations and Functions of One Variable.
Автор: Rajarama Mohan Jena, Snehashish Chakraverty, Subrat Kumar Jena Название: Time-Fractional Order Biological Systems with Uncertain Parameters ISBN: 1681737493 ISBN-13(EAN): 9781681737492 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 8593.00 р. Наличие на складе: Нет в наличии.
Описание: The subject of fractional calculus has gained considerable popularity and importance during the past three decades, mainly due to its validated applications in various fields of science and engineering. It is a generalization of ordinary differentiation and integration to arbitrary (non-integer) order. The fractional derivative has been used in various physical problems, such as frequency-dependent damping behavior of structures, biological systems, motion of a plate in a Newtonian fluid, ����λ��μ controller for the control of dynamical systems, and so on. It is challenging to obtain the solution (both analytical and numerical) of related nonlinear partial differential equations of fractional order. So for the last few decades, a great deal of attention has been directed towards the solution for these kind of problems. Different methods have been developed by other researchers to analyze the above problems with respect to crisp (exact) parameters.
However, in real-life applications such as for biological problems, it is not always possible to get exact values of the associated parameters due to errors in measurements/experiments, observations, and many other errors. Therefore, the associated parameters and variables may be considered uncertain. Here, the uncertainties are considered interval/fuzzy. Therefore, the development of appropriate efficient methods and their use in solving the mentioned uncertain problems are the recent challenge.
In view of the above, this book is a new attempt to rigorously present a variety of fuzzy (and interval) time-fractional dynamical models with respect to different biological systems using computationally efficient method. The authors believe this book will be helpful to undergraduates, graduates, researchers, industry, faculties, and others throughout the globe.
Автор: Rajarama Mohan Jena, Snehashish Chakraverty, Subrat Kumar Jena Название: Time-Fractional Order Biological Systems with Uncertain Parameters ISBN: 1681737515 ISBN-13(EAN): 9781681737515 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 11365.00 р. Наличие на складе: Нет в наличии.
Описание: The subject of fractional calculus has gained considerable popularity and importance during the past three decades, mainly due to its validated applications in various fields of science and engineering. It is a generalization of ordinary differentiation and integration to arbitrary (non-integer) order. The fractional derivative has been used in various physical problems, such as frequency-dependent damping behavior of structures, biological systems, motion of a plate in a Newtonian fluid, ����λ��μ controller for the control of dynamical systems, and so on. It is challenging to obtain the solution (both analytical and numerical) of related nonlinear partial differential equations of fractional order. So for the last few decades, a great deal of attention has been directed towards the solution for these kind of problems. Different methods have been developed by other researchers to analyze the above problems with respect to crisp (exact) parameters.
However, in real-life applications such as for biological problems, it is not always possible to get exact values of the associated parameters due to errors in measurements/experiments, observations, and many other errors. Therefore, the associated parameters and variables may be considered uncertain. Here, the uncertainties are considered interval/fuzzy. Therefore, the development of appropriate efficient methods and their use in solving the mentioned uncertain problems are the recent challenge.
In view of the above, this book is a new attempt to rigorously present a variety of fuzzy (and interval) time-fractional dynamical models with respect to different biological systems using computationally efficient method. The authors believe this book will be helpful to undergraduates, graduates, researchers, industry, faculties, and others throughout the globe.
Автор: Carlson, Robert Название: A Concrete Introduction to Real Analysis ISBN: 1032476435 ISBN-13(EAN): 9781032476438 Издательство: Taylor&Francis Рейтинг: Цена: 7195.00 р. Наличие на складе: Нет в наличии.
Автор: Loya Paul Название: Amazing and Aesthetic Aspects of Analysis ISBN: 1493992457 ISBN-13(EAN): 9781493992454 Издательство: Springer Рейтинг: Цена: 7965.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Preface.- Some of the most beautiful formul in the world.- Part 1. Some standard curriculum.- 1. Very naive set theory, functions, and proofs.- 2. Numbers, numbers, and more numbers.- 3. Infinite sequences of real and complex numbers.- 4. Limits, continuity, and elementary functions.- 5. Some of the most beautiful formul in the world I-III.- Part 2. Extracurricular activities.- 6. Advanced theory of infinite series.- 7. More on the infinite: Products and partial fractions.- 8. Infinite continued fractions.- Bibliography.- Index.
Автор: Alps Название: A.P. Morse`s Set Theory and Analysis ISBN: 3031053540 ISBN-13(EAN): 9783031053542 Издательство: Springer Рейтинг: Цена: 19564.00 р. Наличие на складе: Поставка под заказ.
Описание: This volume explores A.P. Morse’s (1911-1984) development of a formal language for writing mathematics, his application of that language in set theory and mathematical analysis, and his unique perspective on mathematics. The editor brings together a variety of Morse’s works in this compilation, including Morse's book A Theory of Sets, Second Edition (1986), in addition to material from another of Morse’s publications, Web Derivatives, and notes for a course on analysis from the early 1950's. Because Morse provided very little in the way of explanation in his written works, the editor’s commentary serves to outline Morse’s goals, give informal explanations of Morse’s formal language, and compare Morse’s often unique approaches to more traditional approaches. Minor corrections to Morse’s previously published works have also been incorporated into the text, including some updated axioms, theorems, and definitions. The editor’s introduction thoroughly details the corrections and changes made and provides readers with valuable insight on Morse’s methods. A.P. Morse’s Set Theory and Analysis will appeal to graduate students and researchers interested in set theory and analysis who also have an interest in logic. Readers with a particular interest in Morse’s unique perspective and in the history of mathematics will also find this book to be of interest.
Описание: This book gives a detailed treatment of functional interpretations of arithmetic, analysis, and set theory. The subject goes back to G del's Dialectica interpretation of Heyting arithmetic which replaces nested quantification by higher type operations and thus reduces the consistency problem for arithmetic to the problem of computability of primitive recursive functionals of finite types. Regular functional interpretations, in particular the Dialectica interpretation and its generalization to finite types, the Diller-Nahm interpretation, are studied on Heyting as well as Peano arithmetic in finite types and extended to functional interpretations of constructive as well as classical systems of analysis and set theory. Kreisel's modified realization and Troelstra's hybrids of it are presented as interpretations of Heyting arithmetic and extended to constructive set theory, both in finite types. They serve as background for the construction of hybrids of the Diller-Nahm interpretation of Heyting arithmetic and constructive set theory, again in finite types. All these functional interpretations yield relative consistency results and closure under relevant rules of the theories in question as well as axiomatic characterizations of the functional translations.
Описание: Uncertainty is an inseparable component of almost every measurement and occurrence when dealing with real-world problems.
Finding solutions to real-life problems in an uncertain environment is a difficult and challenging task. As such, this book addresses the solution of uncertain static and dynamic problems based on affine arithmetic approaches. Affine arithmetic is one of the recent developments designed to handle such uncertainties in a different manner which may be useful for overcoming the dependency problem and may compute better enclosures of the solutions. Further, uncertain static and dynamic problems turn into interval and/or fuzzy linear/nonlinear systems of equations and eigenvalue problems, respectively. Accordingly, this book includes newly developed efficient methods to handle the said problems based on the affine and interval/fuzzy approach. Various illustrative examples concerning static and dynamic problems of structures have been investigated in order to show the reliability and efficacy of the developed approaches.
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