Chapter 9 Of Ramanujan S Second Notebook Infinite Series Identities Transformations And Evaluations
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Chapter 9 Of Ramanujan S Second Notebook Infinite Series Identities Transformations And Evaluations
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Author : Bruce C. Berndt
language : en
Publisher: American Mathematical Soc.
Release Date : 1983
Chapter 9 Of Ramanujan S Second Notebook Infinite Series Identities Transformations And Evaluations written by Bruce C. Berndt and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.
Chapter 9 Of Ramanujan S Second Notebook
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Author : Bruce C. Berndt
language : en
Publisher:
Release Date : 1983
Chapter 9 Of Ramanujan S Second Notebook written by Bruce C. Berndt and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.
Number Theory
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Author : Krishnaswami Alladi
language : en
Publisher: Springer
Release Date : 2006-11-14
Number Theory written by Krishnaswami Alladi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Analytic And Combinatorial Number Theory The Legacy Of Ramanujan Contributions In Honor Of Bruce C Berndt
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Author : George E Andrews
language : en
Publisher: World Scientific
Release Date : 2024-08-19
Analytic And Combinatorial Number Theory The Legacy Of Ramanujan Contributions In Honor Of Bruce C Berndt written by George E Andrews and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-19 with Mathematics categories.
This volume reflects the contributions stemming from the conference Analytic and Combinatorial Number Theory: The Legacy of Ramanujan which took place at the University of Illinois at Urbana-Champaign on June 6-9, 2019. The conference included 26 plenary talks, 71 contributed talks, and 170 participants. As was the case for the conference, this book is in honor of Bruce C Berndt and in celebration of his mathematics and his 80th birthday.Along with a number of papers previously appearing in Special Issues of the International Journal of Number Theory, the book collects together a few more papers, a biography of Bruce by Atul Dixit and Ae Ja Yee, a preface by George Andrews, a gallery of photos from the conference, a number of speeches from the conference banquet, the conference poster, a list of Bruce's publications at the time this volume was created, and a list of the talks from the conference.
Infinite Algebraic Extensions Of Finite Fields
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Author : Joel V. Brawley
language : en
Publisher: American Mathematical Soc.
Release Date : 1989
Infinite Algebraic Extensions Of Finite Fields written by Joel V. Brawley and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
Over the last several decades there has been a renewed interest in finite field theory, partly as a result of important applications in a number of diverse areas such as electronic communications, coding theory, combinatorics, designs, finite geometries, cryptography, and other portions of discrete mathematics. In addition, a number of recent books have been devoted to the subject. Despite the resurgence in interest, it is not widely known that many results concerning finite fields have natural generalizations to abritrary algebraic extensions of finite fields. The purpose of this book is to describe these generalizations. After an introductory chapter surveying pertinent results about finite fields, the book describes the lattice structure of fields between the finite field $GF(q)$ and its algebraic closure $\Gamma (q)$. The authors introduce a notion, due to Steinitz, of an extended positive integer $N$ which includes each ordinary positive integer $n$ as a special case. With the aid of these Steinitz numbers, the algebraic extensions of $GF(q)$ are represented by symbols of the form $GF(q^N)$. When $N$ is an ordinary integer $n$, this notation agrees with the usual notation $GF(q^n)$ for a dimension $n$ extension of $GF(q)$. The authors then show that many of the finite field results concerning $GF(q^n)$ are also true for $GF(q^N)$. One chapter is devoted to giving explicit algorithms for computing in several of the infinite fields $GF(q^N)$ using the notion of an explicit basis for $GF(q^N)$ over $GF(q)$. Another chapter considers polynomials and polynomial-like functions on $GF(q^N)$ and contains a description of several classes of permutation polynomials, including the $q$-polynomials and the Dickson polynomials. Also included is a brief chapter describing two of many potential applications. Aimed at the level of a beginning graduate student or advanced undergraduate, this book could serve well as a supplementary text for a course in finite field theory.
The Connection Between Infinite Dimensional And Finite Dimensional Dynamical Systems
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Author : Basil Nicolaenko
language : en
Publisher: American Mathematical Soc.
Release Date : 1989
The Connection Between Infinite Dimensional And Finite Dimensional Dynamical Systems written by Basil Nicolaenko and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
The last few years have seen a number of major developments demonstrating that the long-term behavior of solutions of a very large class of partial differential equations possesses a striking resemblance to the behavior of solutions of finite dimensional dynamical systems, or ordinary differential equations. The first of these advances was the discovery that a dissipative PDE has a compact, global attractor with finite Hausdorff and fractal dimensions. More recently, it was shown that some of these PDEs possess a finite dimensional inertial manifold-that is, an invariant manifold containing the attractor and exponentially attractive trajectories. With the improved understanding of the exact connection between finite dimensional dynamical systems and various classes of dissipative PDEs, it is now realistic to hope that the wealth of studies of such topics as bifurcations of finite vector fields and ``strange'' fractal attractors can be brought to bear on various mathematical models, including continuum flows. Surprisingly, a number of distributed systems from continuum mechanics have been found to exhibit the same nontrivial dynamic behavior as observed in low-dimensional dynamical systems. As a natural consequence of these observations, a new direction of research has arisen: detection and analysis of finite dimensional dynamical characteristics of infinite-dimensional systems. This book represents the proceedings of an AMS-IMS-SIAM Summer Research Conference, held in July, 1987 at the University of Colorado at Boulder. Bringing together mathematicians and physicists, the conference provided a forum for presentations on the latest developments in the field and fostered lively interactions on open questions and future directions. With contributions from some of the top experts, these proceedings will provide readers with an overview of this vital area of research.
Differential Analysis In Infinite Dimensional Spaces
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Author : Kondagunta Sundaresan
language : en
Publisher: American Mathematical Soc.
Release Date : 1986
Differential Analysis In Infinite Dimensional Spaces written by Kondagunta Sundaresan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
Focuses on developments made in the field of differential analysis in infinite dimensional spaces. This work covers a range of topics including gauge theories, polar subsets, approximation theory, group analysis of partial differential equations, inequalities and actions on infinite groups.
The Lefschetz Centennial Conference Part Ii Proceedings On Algebraic Topology
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Author :
language : en
Publisher: American Mathematical Soc.
Release Date : 1987
The Lefschetz Centennial Conference Part Ii Proceedings On Algebraic Topology written by and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Algebraic geometry categories.
Every Planar Map Is Four Colorable
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Author : Kenneth I. Appel
language : en
Publisher: American Mathematical Soc.
Release Date : 1989
Every Planar Map Is Four Colorable written by Kenneth I. Appel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
In this volume, the authors present their 1972 proof of the celebrated Four Color Theorem in a detailed but self-contained exposition accessible to a general mathematical audience. An emended version of the authors' proof of the theorem, the book contains the full text of the supplements and checklists, which originally appeared on microfiche. The thiry-page introduction, intended for nonspecialists, provides some historical background of the theorem and details of the authors' proof. In addition, the authors have added an appendix which treats in much greater detail the argument for situations in which reducible configurations are immersed rather than embedded in triangulations. This result leads to a proof that four coloring can be accomplished in polynomial time.
Recent Developments In Geometry
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Author : Robert Everist Greene
language : en
Publisher: American Mathematical Soc.
Release Date : 1989
Recent Developments In Geometry written by Robert Everist Greene and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
This volume is the outgrowth of a Special Session on Geometry, held at the November 1987 meeting of the AMS at the University of California at Los Angeles. The unusually well-attended session attracted more than sixty participants and featured over forty addresses by some of the day's outstanding geometers. By common consent, it was decided that the papers to be collected in the present volume should be surveys of relatively broad areas of geometry, rather than detailed presentations of new research results. A comprehensive survey of the field is beyond the scope of a volume such as this. Nonetheless, the editors have sought to provide all geometers, whatever their specialties, with some insight into recent developments in a variety of topics in this active area of research.