Multidimensional Residue Theory And Applications

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Multidimensional Residue Theory and Applications

Author : Alekos Vidras
Publisher : American Mathematical Society
ISBN 13 : 1470471124
Total Pages : 556 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Multidimensional Residue Theory and Applications by : Alekos Vidras

Download or read book Multidimensional Residue Theory and Applications written by Alekos Vidras and published by American Mathematical Society. This book was released on 2023-10-18 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: Residue theory is an active area of complex analysis with connections and applications to fields as diverse as partial differential and integral equations, computer algebra, arithmetic or diophantine geometry, and mathematical physics. Multidimensional Residue Theory and Applications defines and studies multidimensional residues via analytic continuation for holomorphic bundle-valued current maps. This point of view offers versatility and flexibility to the tools and constructions proposed, allowing these residues to be defined and studied outside the classical case of complete intersection. The book goes on to show how these residues are algebraic in nature, and how they relate and apply to a wide range of situations, most notably to membership problems, such as the Briançon–Skoda theorem and Hilbert's Nullstellensatz, to arithmetic intersection theory and to tropical geometry. This book will supersede the existing literature in this area, which dates back more than three decades. It will be appreciated by mathematicians and graduate students in multivariate complex analysis. But thanks to the gentle treatment of the one-dimensional case in Chapter 1 and the rich background material in the appendices, it may also be read by specialists in arithmetic, diophantine, or tropical geometry, as well as in mathematical physics or computer algebra.

Applications of Group Theory in Cryptography

Author : Delaram Kahrobaei
Publisher : American Mathematical Society
ISBN 13 : 1470474697
Total Pages : 162 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Applications of Group Theory in Cryptography by : Delaram Kahrobaei

Download or read book Applications of Group Theory in Cryptography written by Delaram Kahrobaei and published by American Mathematical Society. This book was released on 2024-03-25 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as a comprehensive treatment of group-based cryptography accessible to both mathematicians and computer scientists, with emphasis on the most recent developments in the area. To make it accessible to a broad range of readers, the authors started with a treatment of elementary topics in group theory, combinatorics, and complexity theory, as well as providing an overview of classical public-key cryptography. Then some algorithmic problems arising in group theory are presented, and cryptosystems based on these problems and their respective cryptanalyses are described. The book also provides an introduction to ideas in quantum cryptanalysis, especially with respect to the goal of post-quantum group-based cryptography as a candidate for quantum-resistant cryptography. The final part of the book provides a description of various classes of groups and their suitability as platforms for group-based cryptography. The book is a monograph addressed to graduate students and researchers in both mathematics and computer science.

From Fourier Analysis and Number Theory to Radon Transforms and Geometry

Author : Hershel M. Farkas
Publisher : Springer Science & Business Media
ISBN 13 : 1461440742
Total Pages : 567 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis From Fourier Analysis and Number Theory to Radon Transforms and Geometry by : Hershel M. Farkas

Download or read book From Fourier Analysis and Number Theory to Radon Transforms and Geometry written by Hershel M. Farkas and published by Springer Science & Business Media. This book was released on 2012-09-18 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: A memorial conference for Leon Ehrenpreis was held at Temple University, November 15-16, 2010. In the spirit of Ehrenpreis’s contribution to mathematics, the papers in this volume, written by prominent mathematicians, represent the wide breadth of subjects that Ehrenpreis traversed in his career, including partial differential equations, combinatorics, number theory, complex analysis and a bit of applied mathematics. With the exception of one survey article, the papers in this volume are all new results in the various fields in which Ehrenpreis worked . There are papers in pure analysis, papers in number theory, papers in what may be called applied mathematics such as population biology and parallel refractors and papers in partial differential equations. The mature mathematician will find new mathematics and the advanced graduate student will find many new ideas to explore.A biographical sketch of Leon Ehrenpreis by his daughter, a professional journalist, enhances the memorial tribute and gives the reader a glimpse into the life and career of a great mathematician.

Integral Representations and Residues in Multidimensional Complex Analysis

Author : Lev Abramovich Aĭzenberg
Publisher : American Mathematical Soc.
ISBN 13 : 0821815504
Total Pages : 296 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Integral Representations and Residues in Multidimensional Complex Analysis by : Lev Abramovich Aĭzenberg

Download or read book Integral Representations and Residues in Multidimensional Complex Analysis written by Lev Abramovich Aĭzenberg and published by American Mathematical Soc.. This book was released on 1983 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with integral representations of holomorphic functions of several complex variables, the multidimensional logarithmic residue, and the theory of multidimensional residues. Applications are given to implicit function theory, systems of nonlinear equations, computation of the multiplicity of a zero of a mapping, and computation of combinatorial sums in closed form. Certain applications in multidimensional complex analysis are considered. The monograph is intended for specialists in theoretical and applied mathematics and theoretical physics, and for postgraduate and graduate students interested in multidimensional complex analysis or its applications.

Bimonoidal Categories, $E_n$-Monoidal Categories, and Algebraic $K$-Theory

Author : Donald Yau
Publisher : American Mathematical Society
ISBN 13 : 1470478102
Total Pages : 439 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Bimonoidal Categories, $E_n$-Monoidal Categories, and Algebraic $K$-Theory by : Donald Yau

Download or read book Bimonoidal Categories, $E_n$-Monoidal Categories, and Algebraic $K$-Theory written by Donald Yau and published by American Mathematical Society. This book was released on 2024-10-11 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bimonoidal categories are categorical analogues of rings without additive inverses. They have been actively studied in category theory, homotopy theory, and algebraic $K$-theory since around 1970. There is an abundance of new applications and questions of bimonoidal categories in mathematics and other sciences. The three books published by the AMS in the Mathematical Surveys and Monographs series under the title Bimonoidal Categories, $E_n$-Monoidal Categories, and Algebraic $K$-Theory (Volume I: Symmetric Bimonoidal Categories and Monoidal Bicategories, Volume II: Braided Bimonoidal Categories with Applications?this book, and Volume III: From Categories to Structured Ring Spectra) provide a unified treatment of bimonoidal and higher ring-like categories, their connection with algebraic $K$-theory and homotopy theory, and applications to quantum groups and topological quantum computation. With ample background material, extensive coverage, detailed presentation of both well-known and new theorems, and a list of open questions, this work is a user-friendly resource for beginners and experts alike. Part 1 of this book studies braided bimonoidal categories, with applications to quantum groups and topological quantum computation. It is proved that the categories of modules over a braided bialgebra, of Fibonacci anyons, and of Ising anyons form braided bimonoidal categories. Two coherence theorems for braided bimonoidal categories are proved, confirming the Blass-Gurevich Conjecture. The rest of this part discusses braided analogues of Baez's Conjecture and the monoidal bicategorical matrix construction in Volume I: Symmetric Bimonoidal Categories and Monoidal Bicategories. Part 2 studies ring and bipermutative categories in the sense of Elmendorf-Mandell, braided ring categories, and $E_n$-monoidal categories, which combine $n$-fold monoidal categories with ring categories.

Iwasawa Theory and Its Perspective, Volume 2

Author : Tadashi Ochiai
Publisher : American Mathematical Society
ISBN 13 : 1470456737
Total Pages : 228 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Iwasawa Theory and Its Perspective, Volume 2 by : Tadashi Ochiai

Download or read book Iwasawa Theory and Its Perspective, Volume 2 written by Tadashi Ochiai and published by American Mathematical Society. This book was released on 2024-04-25 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iwasawa theory began in the late 1950s with a series of papers by Kenkichi Iwasawa on ideal class groups in the cyclotomic tower of number fields and their relation to $p$-adic $L$-functions. The theory was later generalized by putting it in the context of elliptic curves and modular forms. The main motivation for writing this book was the need for a total perspective of Iwasawa theory that includes the new trends of generalized Iwasawa theory. Another motivation is to update the classical theory for class groups, taking into account the changed point of view on Iwasawa theory. The goal of this second part of the three-part publication is to explain various aspects of the cyclotomic Iwasawa theory of $p$-adic Galois representations.

Bimonoidal Categories, $E_n$-Monoidal Categories, and Algebraic $K$-Theory

Author : Niles Johnson
Publisher : American Mathematical Society
ISBN 13 : 1470478110
Total Pages : 633 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Bimonoidal Categories, $E_n$-Monoidal Categories, and Algebraic $K$-Theory by : Niles Johnson

Download or read book Bimonoidal Categories, $E_n$-Monoidal Categories, and Algebraic $K$-Theory written by Niles Johnson and published by American Mathematical Society. This book was released on 2024-10-23 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bimonoidal categories are categorical analogues of rings without additive inverses. They have been actively studied in category theory, homotopy theory, and algebraic $K$-theory since around 1970. There is an abundance of new applications and questions of bimonoidal categories in mathematics and other sciences. The three books published by the AMS in the Mathematical Surveys and Monographs series under the title Bimonoidal Categories, $E_n$-Monoidal Categories, and Algebraic $K$-Theory (Volume I: Symmetric Bimonoidal Categories and Monoidal Bicategories, Volume II: Braided Bimonoidal Categories with Applications, and Volume III: From Categories to Structured Ring Spectra?this book) provide a unified treatment of bimonoidal and higher ring-like categories, their connection with algebraic $K$-theory and homotopy theory, and applications to quantum groups and topological quantum computation. With ample background material, extensive coverage, detailed presentation of both well-known and new theorems, and a list of open questions, this work is a user-friendly resource for beginners and experts alike. Part 1 of this book is a detailed study of enriched monoidal categories, pointed diagram categories, and enriched multicategories. Using this machinery, Part 2 discusses the rich interconnection between the higher ring-like categories, homotopy theory, and algebraic $K$-theory. Starting with a chapter on homotopy theory background, the first half of Part 2 constructs the Segal $K$-theory functor and the Elmendorf-Mandell $K$-theory multifunctor from permutative categories to symmetric spectra. For the latter, the detailed treatment here includes identification and correction of some subtle errors concerning its extended domain. The second half applies the $K$-theory multifunctor to small ring, bipermutative, braided ring, and $E_n$-monoidal categories to obtain, respectively, strict ring, $E_{infty}$-, $E_2$-, and $E_n$-symmetric spectra.

The Double Mellin-Barnes Type Integrals and Their Applications to Convolution Theory

Author : Thanh Hai Nguyen
Publisher : World Scientific
ISBN 13 : 9789810206901
Total Pages : 318 pages
Book Rating : 4.2/5 (69 download)

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Book Synopsis The Double Mellin-Barnes Type Integrals and Their Applications to Convolution Theory by : Thanh Hai Nguyen

Download or read book The Double Mellin-Barnes Type Integrals and Their Applications to Convolution Theory written by Thanh Hai Nguyen and published by World Scientific. This book was released on 1992 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents new results in the theory of the double Mellin-Barnes integrals popularly known as the general H-function of two variables.A general integral convolution is constructed by the authors and it contains Laplace convolution as a particular case and possesses a factorization property for one-dimensional H-transform. Many examples of convolutions for classical integral transforms are obtained and they can be applied for the evaluation of series and integrals.

The Double Mellin-barnes Type Integrals And Their Application To Convolution Theory

Author : Semyon B Yakubovich
Publisher : World Scientific
ISBN 13 : 9814506141
Total Pages : 308 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis The Double Mellin-barnes Type Integrals And Their Application To Convolution Theory by : Semyon B Yakubovich

Download or read book The Double Mellin-barnes Type Integrals And Their Application To Convolution Theory written by Semyon B Yakubovich and published by World Scientific. This book was released on 1992-05-26 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents new results in the theory of the double Mellin-Barnes integrals popularly known as the general H-function of two variables.A general integral convolution is constructed by the authors and it contains Laplace convolution as a particular case and possesses a factorization property for one-dimensional H-transform. Many examples of convolutions for classical integral transforms are obtained and they can be applied for the evaluation of series and integrals.

The Mathematical Legacy of Leon Ehrenpreis

Author : Irene Sabadini
Publisher : Springer Science & Business Media
ISBN 13 : 8847019478
Total Pages : 391 pages
Book Rating : 4.8/5 (47 download)

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Book Synopsis The Mathematical Legacy of Leon Ehrenpreis by : Irene Sabadini

Download or read book The Mathematical Legacy of Leon Ehrenpreis written by Irene Sabadini and published by Springer Science & Business Media. This book was released on 2012-04-23 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leon Ehrenpreis has been one of the leading mathematicians in the twentieth century. His contributions to the theory of partial differential equations were part of the golden era of PDEs, and led him to what is maybe his most important contribution, the Fundamental Principle, which he announced in 1960, and fully demonstrated in 1970. His most recent work, on the other hand, focused on a novel and far reaching understanding of the Radon transform, and offered new insights in integral geometry. Leon Ehrenpreis died in 2010, and this volume collects writings in his honor by a cadre of distinguished mathematicians, many of which were his collaborators.

Trees of Hyperbolic Spaces

Author : Michael Kapovich
Publisher : American Mathematical Society
ISBN 13 : 1470474255
Total Pages : 295 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Trees of Hyperbolic Spaces by : Michael Kapovich

Download or read book Trees of Hyperbolic Spaces written by Michael Kapovich and published by American Mathematical Society. This book was released on 2024-08-15 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an alternative proof of the Bestvina?Feighn combination theorem for trees of hyperbolic spaces and describes uniform quasigeodesics in such spaces. As one of the applications of their description of uniform quasigeodesics, the authors prove the existence of Cannon?Thurston maps for inclusion maps of total spaces of subtrees of hyperbolic spaces and of relatively hyperbolic spaces. They also analyze the structure of Cannon?Thurston laminations in this setting. Furthermore, some group-theoretic applications of these results are discussed. This book also contains background material on coarse geometry and geometric group theory.

Several Complex Variables II

Author : G.M. Khenkin
Publisher : Springer Science & Business Media
ISBN 13 : 3642578829
Total Pages : 267 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Several Complex Variables II by : G.M. Khenkin

Download or read book Several Complex Variables II written by G.M. Khenkin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: Plurisubharmonic functions playa major role in the theory of functions of several complex variables. The extensiveness of plurisubharmonic functions, the simplicity of their definition together with the richness of their properties and. most importantly, their close connection with holomorphic functions have assured plurisubharmonic functions a lasting place in multidimensional complex analysis. (Pluri)subharmonic functions first made their appearance in the works of Hartogs at the beginning of the century. They figure in an essential way, for example, in the proof of the famous theorem of Hartogs (1906) on joint holomorphicity. Defined at first on the complex plane IC, the class of subharmonic functions became thereafter one of the most fundamental tools in the investigation of analytic functions of one or several variables. The theory of subharmonic functions was developed and generalized in various directions: subharmonic functions in Euclidean space IRn, plurisubharmonic functions in complex space en and others. Subharmonic functions and the foundations ofthe associated classical poten tial theory are sufficiently well exposed in the literature, and so we introduce here only a few fundamental results which we require. More detailed expositions can be found in the monographs of Privalov (1937), Brelot (1961), and Landkof (1966). See also Brelot (1972), where a history of the development of the theory of subharmonic functions is given.

Multidimensional Systems Theory and Applications

Author : N.K. Bose
Publisher : Springer
ISBN 13 : 9401702756
Total Pages : 282 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Multidimensional Systems Theory and Applications by : N.K. Bose

Download or read book Multidimensional Systems Theory and Applications written by N.K. Bose and published by Springer. This book was released on 2013-12-20 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Second Edition of this book includes an abundance of examples to illustrate advanced concepts and brings out in a text book setting the algorithms for bivariate polynomial matrix factorization results that form the basis of two-dimensional systems theory. Algorithms and their implementation using symbolic algebra are emphasized.

Discrete-Time Dynamics of Structured Populations and Homogeneous Order-Preserving Operators

Author : Horst R. Thieme
Publisher : American Mathematical Society
ISBN 13 : 1470474654
Total Pages : 357 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Discrete-Time Dynamics of Structured Populations and Homogeneous Order-Preserving Operators by : Horst R. Thieme

Download or read book Discrete-Time Dynamics of Structured Populations and Homogeneous Order-Preserving Operators written by Horst R. Thieme and published by American Mathematical Society. This book was released on 2024-05-07 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fundamental question in the theory of discrete and continuous-time population models concerns the conditions for the extinction or persistence of populations – a question that is addressed mathematically by persistence theory. For some time, it has been recognized that if the dynamics of a structured population are mathematically captured by continuous or discrete semiflows and if these semiflows have first-order approximations, the spectral radii of certain bounded linear positive operators (better known as basic reproduction numbers) act as thresholds between population extinction and persistence. This book combines the theory of discrete-time dynamical systems with applications to population dynamics with an emphasis on spatial structure. The inclusion of two sexes that must mate to produce offspring leads to the study of operators that are (positively) homogeneous (of degree one) and order-preserving rather than linear and positive. While this book offers an introduction to ordered normed vector spaces, some background in real and functional analysis (including some measure theory for a few chapters) will be helpful. The appendix and selected exercises provide a primer about basic concepts and about relevant topics one may not find in every analysis textbook.

Automorphic Forms Beyond $mathrm {GL}_2$

$Download Automorphic Forms Beyond $mathrm {GL}_2$ PDF Online Free$

Author : Ellen Elizabeth Eischen
Publisher : American Mathematical Society
ISBN 13 : 1470474921
Total Pages : 199 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Automorphic Forms Beyond $mathrm {GL}_2$ by : Ellen Elizabeth Eischen

Download or read book Automorphic Forms Beyond $mathrm {GL}_2$ written by Ellen Elizabeth Eischen and published by American Mathematical Society. This book was released on 2024-03-26 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Langlands program has been a very active and central field in mathematics ever since its conception over 50 years ago. It connects number theory, representation theory and arithmetic geometry, and other fields in a profound way. There are nevertheless very few expository accounts beyond the GL(2) case. This book features expository accounts of several topics on automorphic forms on higher rank groups, including rationality questions on unitary group, theta lifts and their applications to Arthur's conjectures, quaternionic modular forms, and automorphic forms over functions fields and their applications to inverse Galois problems. It is based on the lecture notes prepared for the twenty-fifth Arizona Winter School on “Automorphic Forms beyond GL(2)”, held March 5–9, 2022, at the University of Arizona in Tucson. The speakers were Ellen Eischen, Wee Teck Gan, Aaron Pollack, and Zhiwei Yun. The exposition of the book is in a style accessible to students entering the field. Advanced graduate students as well as researchers will find this a valuable introduction to various important and very active research areas.

Residuated Structures in Algebra and Logic

Author : George Metcalfe
Publisher : American Mathematical Society
ISBN 13 : 1470469855
Total Pages : 282 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Residuated Structures in Algebra and Logic by : George Metcalfe

Download or read book Residuated Structures in Algebra and Logic written by George Metcalfe and published by American Mathematical Society. This book was released on 2023-11-06 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to residuated structures, viewed as a common thread binding together algebra and logic. The framework includes well-studied structures from classical abstract algebra such as lattice-ordered groups and ideals of rings, as well as structures serving as algebraic semantics for substructural and other non-classical logics. Crucially, classes of these structures are studied both algebraically, yielding a rich structure theory along the lines of Conrad's program for lattice-ordered groups, and algorithmically, via analytic sequent or hypersequent calculi. These perspectives are related using a natural notion of equivalence for consequence relations that provides a bridge offering benefits to both sides. Algorithmic methods are used to establish properties like decidability, amalgamation, and generation by subclasses, while new insights into logical systems are obtained by studying associated classes of structures. The book is designed to serve the purposes of novices and experts alike. The first three chapters provide a gentle introduction to the subject, while subsequent chapters provide a state-of-the-art account of recent developments in the field.

Solving Polynomial Equations

Author : Alicia Dickenstein
Publisher : Springer Science & Business Media
ISBN 13 : 3540243267
Total Pages : 433 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Solving Polynomial Equations by : Alicia Dickenstein

Download or read book Solving Polynomial Equations written by Alicia Dickenstein and published by Springer Science & Business Media. This book was released on 2005-04-27 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a general introduction to modern mathematical aspects in computing with multivariate polynomials and in solving algebraic systems. It presents the state of the art in several symbolic, numeric, and symbolic-numeric techniques, including effective and algorithmic methods in algebraic geometry and computational algebra, complexity issues, and applications ranging from statistics and geometric modelling to robotics and vision. Graduate students, as well as researchers in related areas, will find an excellent introduction to currently interesting topics. These cover Groebner and border bases, multivariate resultants, residues, primary decomposition, multivariate polynomial factorization, homotopy continuation, complexity issues, and their applications.