Strange Functions In Real Analysis Second Edition
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Strange Functions In Real Analysis Second Edition
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Author : Alexander Kharazishvili
language : en
Publisher: CRC Press
Release Date : 2005-12-20
Strange Functions In Real Analysis Second Edition written by Alexander Kharazishvili and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-20 with Mathematics categories.
Weierstrass and Blancmange nowhere differentiable functions, Lebesgue integrable functions with everywhere divergent Fourier series, and various nonintegrable Lebesgue measurable functions. While dubbed strange or "pathological," these functions are ubiquitous throughout mathematics and play an important role in analysis, not only as counterexamples of seemingly true and natural statements, but also to stimulate and inspire the further development of real analysis. Strange Functions in Real Analysis explores a number of important examples and constructions of pathological functions. After introducing the basic concepts, the author begins with Cantor and Peano-type functions, then moves to functions whose constructions require essentially noneffective methods. These include functions without the Baire property, functions associated with a Hamel basis of the real line, and Sierpinski-Zygmund functions that are discontinuous on each subset of the real line having the cardinality continuum. Finally, he considers examples of functions whose existence cannot be established without the help of additional set-theoretical axioms and demonstrates that their existence follows from certain set-theoretical hypotheses, such as the Continuum Hypothesis.
Strange Functions In Real Analysis
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Author : A.B. Kharazishvili
language : en
Publisher:
Release Date : 2006
Strange Functions In Real Analysis written by A.B. Kharazishvili and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
Topological Vector Spaces
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Author : Lawrence Narici
language : en
Publisher: CRC Press
Release Date : 2010-07-26
Topological Vector Spaces written by Lawrence Narici and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-26 with Mathematics categories.
With many new concrete examples and historical notes, Topological Vector Spaces, Second Edition provides one of the most thorough and up-to-date treatments of the Hahn-Banach theorem. This edition explores the theorem's connection with the axiom of choice, discusses the uniqueness of Hahn-Banach extensions, and includes an entirely new chapter on v
Frontiers In Interpolation And Approximation
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Author : N. K. Govil
language : en
Publisher: CRC Press
Release Date : 2006-07-20
Frontiers In Interpolation And Approximation written by N. K. Govil and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-20 with Mathematics categories.
Dedicated to the well-respected research mathematician Ambikeshwar Sharma, Frontiers in Interpolation and Approximation explores approximation theory, interpolation theory, and classical analysis. Written by authoritative international mathematicians, this book presents many important results in classical analysis, wavelets, and interpolati
Classes Of Modules
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Author : John Dauns
language : en
Publisher: CRC Press
Release Date : 2006-06-19
Classes Of Modules written by John Dauns and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-19 with Mathematics categories.
Because traditional ring theory places restrictive hypotheses on all submodules of a module, its results apply only to small classes of already well understood examples. Often, modules with infinite Goldie dimension have finite-type dimension, making them amenable to use with type dimension, but not Goldie dimension. By working with natural classes
Geometric Function Theory In One And Higher Dimensions
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Author : Ian Graham
language : en
Publisher: CRC Press
Release Date : 2003-03-18
Geometric Function Theory In One And Higher Dimensions written by Ian Graham and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-18 with Mathematics categories.
This reference details valuable results that lead to improvements in existence theorems for the Loewner differential equation in higher dimensions, discusses the compactness of the analog of the Caratheodory class in several variables, and studies various classes of univalent mappings according to their geometrical definitions. It introduces the in
Introduction To The Mathematics Of Operations Research With Mathematica
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Author : Kevin J. Hastings
language : en
Publisher: CRC Press
Release Date : 2018-10-24
Introduction To The Mathematics Of Operations Research With Mathematica written by Kevin J. Hastings and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-24 with Business & Economics categories.
The breadth of information about operations research and the overwhelming size of previous sources on the subject make it a difficult topic for non-specialists to grasp. Fortunately, Introduction to the Mathematics of Operations Research with Mathematica®, Second Edition delivers a concise analysis that benefits professionals in operations research and related fields in statistics, management, applied mathematics, and finance. The second edition retains the character of the earlier version, while incorporating developments in the sphere of operations research, technology, and mathematics pedagogy. Covering the topics crucial to applied mathematics, it examines graph theory, linear programming, stochastic processes, and dynamic programming. This self-contained text includes an accompanying electronic version and a package of useful commands. The electronic version is in the form of Mathematica notebooks, enabling you to devise, edit, and execute/reexecute commands, increasing your level of comprehension and problem-solving. Mathematica sharpens the impact of this book by allowing you to conveniently carry out graph algorithms, experiment with large powers of adjacency matrices in order to check the path counting theorem and Markov chains, construct feasible regions of linear programming problems, and use the "dictionary" method to solve these problems. You can also create simulators for Markov chains, Poisson processes, and Brownian motions in Mathematica, increasing your understanding of the defining conditions of these processes. Among many other benefits, Mathematica also promotes recursive solutions for problems related to first passage times and absorption probabilities.
Direct Sum Decompositions Of Torsion Free Finite Rank Groups
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Author : Theodore G. Faticoni
language : en
Publisher: CRC Press
Release Date : 2007-03-28
Direct Sum Decompositions Of Torsion Free Finite Rank Groups written by Theodore G. Faticoni and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-03-28 with Mathematics categories.
With plenty of new material not found in other books, Direct Sum Decompositions of Torsion-Free Finite Rank Groups explores advanced topics in direct sum decompositions of abelian groups and their consequences. The book illustrates a new way of studying these groups while still honoring the rich history of unique direct sum decompositions of groups
Algorithmic Lie Theory For Solving Ordinary Differential Equations
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Author : Fritz Schwarz
language : en
Publisher: CRC Press
Release Date : 2007-10-02
Algorithmic Lie Theory For Solving Ordinary Differential Equations written by Fritz Schwarz and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-02 with Mathematics categories.
Despite the fact that Sophus Lie's theory was virtually the only systematic method for solving nonlinear ordinary differential equations (ODEs), it was rarely used for practical problems because of the massive amount of calculations involved. But with the advent of computer algebra programs, it became possible to apply Lie theory to concrete proble
Matrix Theory
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Author : Robert Piziak
language : en
Publisher: CRC Press
Release Date : 2007-02-22
Matrix Theory written by Robert Piziak and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-02-22 with Mathematics categories.
In 1990, the National Science Foundation recommended that every college mathematics curriculum should include a second course in linear algebra. In answer to this recommendation, Matrix Theory: From Generalized Inverses to Jordan Form provides the material for a second semester of linear algebra that probes introductory linear algebra concepts while also exploring topics not typically covered in a sophomore-level class. Tailoring the material to advanced undergraduate and beginning graduate students, the authors offer instructors flexibility in choosing topics from the book. The text first focuses on the central problem of linear algebra: solving systems of linear equations. It then discusses LU factorization, derives Sylvester's rank formula, introduces full-rank factorization, and describes generalized inverses. After discussions on norms, QR factorization, and orthogonality, the authors prove the important spectral theorem. They also highlight the primary decomposition theorem, Schur's triangularization theorem, singular value decomposition, and the Jordan canonical form theorem. The book concludes with a chapter on multilinear algebra. With this classroom-tested text students can delve into elementary linear algebra ideas at a deeper level and prepare for further study in matrix theory and abstract algebra.