The Integrals of Lebesgue, Denjoy, Perron, and Henstock

Author: Russell A. Gordon

Publisher: American Mathematical Soc.

ISBN: 0821838059

Category: Mathematics

Page: 395

View: 4902

Provides an elementary, self-contained presentation of the integration processes developed by Lebesgue, Denjoy, Perron, and Henstock. The Lebesgue integral and its essential properties are first developed in detail. The other three integrals are all generalizations of the Lebesgue integral that satisfy the ideal version of the Fundamental Theorem of Calculus. The Denjoy, Perron, and Henstock integrals are each developed fully and carefully from their corresponding definitions. The last part of the book is devoted to integration processes which satisfy a theorem analogous to the Fundamental Theorem, in which F is approximately differentiable. This part of this book is preceded by a detailed study of the approximate derivative and ends with some open questions. Contains over 230 exercises (with solutions) that illustrate and expand the material in the text.
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Mathematics Almost Everywhere: In Memory Of Solomon Marcus

Author: Bellow Alexandra,Calude Cristian S,Zamfirescu Tudor

Publisher: World Scientific

ISBN: 9813237325

Category: Computers

Page: 252

View: 7318

The book is a collection of original papers, research and surveys, dedicated to the memory of the Romanian mathematician Solomon Marcus (1925-2016). Marcus published many papers and books in mathematical analysis, theoretical computer science, mathematical linguistics, poetics, theory of literature, semiotics, and several other fields less strongly connected to mathematics, like cultural anthropology, biology, history and philosophy of science, education. He exemplified an unimaginable richness of ideas. This volume intends to emphasize the mathematical fields in which Solomon Marcus worked, and demonstrate -- as he also did -- the interconnection between them. The authors who contribute to this volume are well-known experts in their fields. Most of them knew Solomon Marcus well, some even owed him for his decisive impulses for their careers and general development. With articles in so diverse areas, the volume will attract readers who would like to diversify their own knowledge or find unexpected connections with other topics. Contents: Logic, Complexity and Algebra: On Bases of Many-Valued Truth Functions (A Salomaa) Quasiperiods of Infinite Words (L Staiger) Early Romanian Contributions to Algebra and Polynomials (D Ştefănescu) Distributed Compression through the Lens of Algorithmic Information Theory: A Primer (M Zimand) Integrals, Operators, AF Algebras, Proof Mining and Monotone Nonexpansive Mappings: Monotonically Controlled Integrals (T Ball, D Preiss) Fine Properties of Duality Mappings (G Dincă) Primitive Ideal Spaces of Postliminal AF Algebras (A Lazar) An Application of Proof Miningto the Proximal Point Algorithm in CAT(0) Spaces (L Leuştean, A Sipoş) Generic Well-posedness of the Fixed Point Problem for Monotone Nonexpansive Mappings (S Reich, A J Zaslavski) Linguistics, Computer Science and Physics: Analytical Linguistics and Formal Grammars: Contributions of Solomon Marcus and Their Further Developments (M Burgin) A Contagious Creativity (Gh Păun) Entanglement through Path Identification (K Svozil) Solomon Marcus in Context: Memories about Solomon Marcus (A Bruckner) Memories With and About My Uncle (M Marcus) Index Readership: Graduate students and researchers. Keywords: Discrete Mathematics;Mathematical Analysis;Complexity Theory;Proof Mining;Mathematical Biology;Formal Languages;Theoretical Mechanics;Mathematical Linguistics;Theoretical PhysicsReview: Key Features: New results in a variety of mathematical areas including operator theory, measure theory, real and functional analysis, computable algebra, formal languages, proof mining in nonlinear analysis, theoretical mechanics, mathematical logic, and topical surveys in mathematical linguistics, complexity theory and computational biology The authors, coming from various parts of the world, are well-known experts in the areas of their contributions Interconnections between results and domains will make the volume not only informative, but also attractive and unique
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Trends in African Diaspora Mathematics Research

Author: Toka Diagana

Publisher: Nova Publishers

ISBN: 9781600213311

Category: Mathematics

Page: 173

View: 6542

The African Diaspora presents mathematical research of highest rank. It offers a forum for mathematical research with some emphasis on the contributions of all African mathematicians and the rich connections between all African universities and those of other continents. This includes the Denjoy integral, equivalent cohomology, semi-linear equations, rational approximants, automorphic solutions and characterisations of mulitvariate exponential families.
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Functional Analysis and the Feynman Operator Calculus

Author: Tepper Gill,Woodford Zachary

Publisher: Springer

ISBN: 331927595X

Category: Mathematics

Page: 354

View: 5129

This book provides the mathematical foundations for Feynman's operator calculus and for the Feynman path integral formulation of quantum mechanics as a natural extension of analysis and functional analysis to the infinite-dimensional setting. In one application, the results are used to prove the last two remaining conjectures of Freeman Dyson for quantum electrodynamics. In another application, the results are used to unify methods and weaken domain requirements for non-autonomous evolution equations. Other applications include a general theory of Lebesgue measure on Banach spaces with a Schauder basis and a new approach to the structure theory of operators on uniformly convex Banach spaces. This book is intended for advanced graduate students and researchers.
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The Kurzweil-Henstock Integral and Its Differential

A Unified Theory of Integration on R and Rn

Author: Solomon Leader

Publisher: CRC Press

ISBN: 9780824705350

Category: Mathematics

Page: 276

View: 2442

A comprehensive review of the Kurzweil-Henstock integration process on the real line and in higher dimensions. It seeks to provide a unified theory of integration that highlights Riemann-Stieljes and Lebesgue integrals as well as integrals of elementary calculus. The author presents practical applications of the definitions and theorems in each section as well as appended sets of exercises.
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Combined Membership List (American Mathematical Society)

Author: American Mathematical Society

Publisher: N.A

ISBN: N.A

Category: Mathematicians

Page: N.A

View: 2091

Lists for 19 include the Mathematical Association of America, and 1955- also the Society for Industrial and Applied Mathematics.
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SCMJ

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 6199

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Mathematical Analysis and Applications

International Conference on Mathematical Analysis and Applications, Craiova, Romania, 23-24 September 2005

Author: V. Rădulescu,Constantin Niculescu (P.)

Publisher: Amer Inst of Physics

ISBN: 9780735403284

Category: Mathematics

Page: 167

View: 6959

In these proceedings from the conference in September 2005, participants describe their work at the interface between mathematical physics, numerical analysis, optimal control and calculus of variations. Papers include work in nonlinear analysis and partial differential equations as well as classical mathematical analysis and dynamical systems. Ind
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Real Analysis

A First Course

Author: Russell A. Gordon

Publisher: Addison-Wesley

ISBN: 9780201832105

Category: Mathematics

Page: 303

View: 6470

This text provides the theory behind single variable calculus, including the standard topics on sequences, continuity, differentiation, integration and infinite series. It takes a rigorous approach to the subject, building up student confidence with exercises.
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Discussiones Mathematicae

Differential inclusions, control and optimization

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Control theory

Page: N.A

View: 1657

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Integral

An Easy Approach After Kurzweil and Henstock

Author: Lee Peng Yee,Rudolf Vyborny

Publisher: Cambridge University Press

ISBN: 9780521779685

Category: Mathematics

Page: 311

View: 5652

Textbook on the theory of integration. Suitable for beginning graduate and final year undergraduate students.
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The American Mathematical Monthly

The Official Journal of the Mathematical Association of America

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematicians

Page: N.A

View: 8472

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Subject Guide to Books in Print

An Index to the Publishers' Trade List Annual

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 4025

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