Analysis In Positive Characteristic
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Analysis In Positive Characteristic
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Author : Anatoly N. Kochubei
language : en
Publisher: Cambridge University Press
Release Date : 2009-03-05
Analysis In Positive Characteristic written by Anatoly N. Kochubei and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-05 with Mathematics categories.
Devoted to counterparts of classical structures of mathematical analysis in analysis over local fields of positive characteristic, this book treats positive characteristic phenomena from an analytic viewpoint. Building on the basic objects introduced by L. Carlitz - such as the Carlitz factorials, exponential and logarithm, and the orthonormal system of Carlitz polynomials - the author develops a kind of differential and integral calculi. He also expands on the basics of an analytic theory of (Carlitz's) differential equations, providing a useful foundation for the study of various special functions. The differential calculus is extended to a type of Rota's umbral calculus, and an investigation is made of the corresponding rings of differential operators. A theory of quasi-holonomic modules over these rings, having some common features with holonomic modules in the sense of Bernstein, is also connected to some special functions in the spirit of Zeilberger's theory.
Wavelet Analysis On Local Fields Of Positive Characteristic
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Author : Biswaranjan Behera
language : en
Publisher: Springer Nature
Release Date : 2022-01-01
Wavelet Analysis On Local Fields Of Positive Characteristic written by Biswaranjan Behera and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-01 with Mathematics categories.
This book discusses the theory of wavelets on local fields of positive characteristic. The discussion starts with a thorough introduction to topological groups and local fields. It then provides a proof of the existence and uniqueness of Haar measures on locally compact groups. It later gives several examples of locally compact groups and describes their Haar measures. The book focuses on multiresolution analysis and wavelets on a local field of positive characteristic. It provides characterizations of various functions associated with wavelet analysis such as scaling functions, wavelets, MRA-wavelets and low-pass filters. Many other concepts which are discussed in details are biorthogonal wavelets, wavelet packets, affine and quasi-affine frames, MSF multiwavelets, multiwavelet sets, generalized scaling sets, scaling sets, unconditional basis properties of wavelets and shift invariant spaces.
Wavelet Analysis On Local Fields Of Positive Characteristic
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Author : Biswaranjan Behera
language : en
Publisher:
Release Date : 2021
Wavelet Analysis On Local Fields Of Positive Characteristic written by Biswaranjan Behera and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
This book discusses the theory of wavelets on local fields of positive characteristic. The discussion starts with a thorough introduction to topological groups and local fields. It then provides a proof of the existence and uniqueness of Haar measures on locally compact groups. It later gives several examples of locally compact groups and describes their Haar measures. The book focuses on multiresolution analysis and wavelets on a local field of positive characteristic. It provides characterizations of various functions associated with wavelet analysis such as scaling functions, wavelets, MRA-wavelets and low-pass filters. Many other concepts which are discussed in details are biorthogonal wavelets, wavelet packets, affine and quasi-affine frames, MSF multiwavelets, multiwavelet sets, generalized scaling sets, scaling sets, unconditional basis properties of wavelets and shift invariant spaces. .
Non Archimedean Analysis Over Function Fields With Positive Characteristic
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Author : Zifeng Yang
language : en
Publisher:
Release Date : 1999
Non Archimedean Analysis Over Function Fields With Positive Characteristic written by Zifeng Yang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.
Algebraic Surfaces In Positive Characteristics Purely Inseparable Phenomena In Curves And Surfaces
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Author : Masayoshi Miyanishi
language : en
Publisher: World Scientific
Release Date : 2020-06-29
Algebraic Surfaces In Positive Characteristics Purely Inseparable Phenomena In Curves And Surfaces written by Masayoshi Miyanishi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-29 with Mathematics categories.
Customarily, the framework of algebraic geometry has been worked over an algebraically closed field of characteristic zero, say, over the complex number field. However, over a field of positive characteristics, many unpredictable phenomena arise where analyses will lead to further developments.In the present book, we consider first the forms of the affine line or the additive group, classification of such forms and detailed analysis. The forms of the affine line considered over the function field of an algebraic curve define the algebraic surfaces with fibrations by curves with moving singularities. These fibrations are investigated via the Mordell-Weil groups, which are originally introduced for elliptic fibrations.This is the first book which explains the phenomena arising from purely inseparable coverings and Artin-Schreier coverings. In most cases, the base surfaces are rational, hence the covering surfaces are unirational. There exists a vast, unexplored world of unirational surfaces. In this book, we explain the Frobenius sandwiches as examples of unirational surfaces.Rational double points in positive characteristics are treated in detail with concrete computations. These kinds of computations are not found in current literature. Readers, by following the computations line after line, will not only understand the peculiar phenomena in positive characteristics, but also understand what are crucial in computations. This type of experience will lead the readers to find the unsolved problems by themselves.
Simple Lie Algebras Over Fields Of Positive Characteristic Structure Theory
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Author : Helmut Strade
language : en
Publisher: Walter de Gruyter
Release Date : 2004
Simple Lie Algebras Over Fields Of Positive Characteristic Structure Theory written by Helmut Strade and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
The problem of classifying the finite-dimensional simple Lie algebras over fields of characteristic p > 0 is a long-standing one. Work on this question during the last 45 years has been directed by the Kostrikin-Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p > 5 a finite-dimensional restricted simple Lie algebra is classical or of Cartan type. This conjecture was proved for p > 7 by Block and Wilson in 1988. The generalization of the Kostrikin-Shafarevich Conjecture for the general case of not necessarily restricted Lie algebras and p > 7 was announced in 1991 by Strade and Wilson and eventually proved by Strade in 1998. The final Block-Wilson-Strade-Premet Classification Theorem is a landmark result of modern mathematics and can be formulated as follows: Every finite-dimensional simple Lie algebra over an algebraically closed field of characteristic p > 3 is of classical, Cartan, or Melikian type. In the three-volume book, the author is assembling the proof of the Classification Theorem with explanations and references. The goal is a state-of-the-art account on the structure and classification theory of Lie algebras over fields of positive characteristic leading to the forefront of current research in this field. This first volume is devoted to preparing the ground for the classification work to be performed in the second and third volume. The concise presentation of the general theory underlying the subject matter and the presentation of classification results on a subclass of the simple Lie algebras for all odd primesmake this volume an invaluable source and reference for all research mathematicians and advanced graduate students in albegra.
The Analysis Of The Characteristic Concepts Of The Establishment And Development Of Ukrainian Society In The Context Of The Historical Scientific And Philosophical Approaches
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Author : Bogatchuk S., Mazylo I., Belkin I., Mangora V., Makarov Z.
language : en
Publisher: International Science Group
Release Date : 2022-09-30
The Analysis Of The Characteristic Concepts Of The Establishment And Development Of Ukrainian Society In The Context Of The Historical Scientific And Philosophical Approaches written by Bogatchuk S., Mazylo I., Belkin I., Mangora V., Makarov Z. and has been published by International Science Group this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-30 with History categories.
The collective monograph is devoted to the analysis of the characteristic concepts of the evolution of modern Ukrainian society. The research uses an interdisciplinary approach, which allows analyzing various aspects of the development of social processes in Ukraine and obtaining socially significant scientific results. Svitlana Bogatchuk investigates the problem of the development of the agricultural sector of the Podil region in the ХІХ th century. Focuses attention on highlighting the very process of reform and development of the main branches of agriculture during this period, such as: cultivation of wheat, rye, oats, buckwheat. Highlights the difficult socioeconomic situation that prompted the authorities to make a decision to reform the agrarian sector. Analyzes the development of the agrarian sector of the Podilsk region after the peasant reform - the abolition of serfdom in 1861. About 75% of its population was employed in agricultural production as evidence of the importance of agriculture in the Podilsk province. Capitalization of the country as a result of the peasant reform also affected the development of the agricultural sector of Ukraine, as well as Podillia. Therefore, in the study, the author provided the main characteristics of the development of the sugar industry, flour milling, viticulture, distilling, and others. In his analysis, Ihor Mazilo pays attention to the topic of railway transport in the German-Soviet war. The author emphasizes that railway transport became an object of strategic importance and provided communication between the front and the rear. Therefore, railway communications played one of the key roles during the last war and post-war reconstruction. Ihor Belkin reveals the content and analysis of the pedagogical experiment as an integral component of the modern educational process. In the content of his chapter, he pays considerable attention to the research and experimental work of students in the learning process. Describes the content of key tasks of experimental research. Emphasizes the theoretical and practical aspects of the readiness and effectiveness of the pedagogical experiment in the conditions of student training in the context of future specialists. The author pays considerable attention to one of the effective methods of the pedagogical experiment mechanism - the business game. Plays a practical-applied analysis ofthe game technology method. Describes the sequence of stages of the experiment and the analysis of its results. In the study of Volodymyr Manhora, a comparative characterization of the prevention of illegal trade in human organs and tissues in Ukraine and European countries was carried out. The concept of illegal trade in human organs and tissues is given. The history of the development of prevention of illegal trade in human organs and tissues is considered. Periodization of the legal regulation of state administration in the field of transplantation has been carried out. The specifics of the regulatory and legal regulation to prevent illegal trade in human organs and tissues in Ukraine and European countries have been determined. Based on his own research, the author came to the conclusion that in orderto regulate the fight against the illegal trade in human organs and tissuesin modern Ukraine, it is necessary to improve the legislative framework, provide for sufficient state funding, and also implement the best practices of European countries in regulating the transplantation of human tissues or organs. The section prepared by Zorislav Makarov focuses on the study of general features and historical changes in the rationality of academic thought of the Renaissance era. Emphasis is placed on the analysis of the worldview level of the relationship between Man, Nature and God in the period of the ХІV-ХVI th centuries. The observed creative reception of ancient and early Christian thought at this level, which was embodied in the original concepts of a number of humanistic studies and educational guidelines of the Reformation, gives grounds for concluding that the subject-object dichotomy, naturalistic principles of creativity, and the instrumental model of rationality were gradually separated for the modern development of philosophy and science. The content of the collective monograph corresponds to the research direction of the Department of History of Ukraine and Philosophy of the Vinnytsia National Agrarian University "Study of trends of socio-economic development and consolidation of Ukrainian society in the modern history of Ukraine". monograph used: historical-genetic method, statistical analysis, sociologist and pedagogical research.
Fourier Analysis On Number Fields
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Author : Dinakar Ramakrishnan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Fourier Analysis On Number Fields written by Dinakar Ramakrishnan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
A modern approach to number theory through a blending of complementary algebraic and analytic perspectives, emphasising harmonic analysis on topological groups. The main goal is to cover John Tates visionary thesis, giving virtually all of the necessary analytic details and topological preliminaries -- technical prerequisites that are often foreign to the typical, more algebraically inclined number theorist. While most of the existing treatments of Tates thesis are somewhat terse and less than complete, the intent here is to be more leisurely, more comprehensive, and more comprehensible. While the choice of objects and methods is naturally guided by specific mathematical goals, the approach is by no means narrow. In fact, the subject matter at hand is germane not only to budding number theorists, but also to students of harmonic analysis or the representation theory of Lie groups. The text addresses students who have taken a year of graduate-level course in algebra, analysis, and topology. Moreover, the work will act as a good reference for working mathematicians interested in any of these fields.
Solution And Characteristic Analysis Of Fractional Order Chaotic Systems
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Author : Kehui Sun
language : en
Publisher: Springer Nature
Release Date : 2022-09-04
Solution And Characteristic Analysis Of Fractional Order Chaotic Systems written by Kehui Sun and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-04 with Science categories.
This book highlights the solution algorithms and characteristic analysis methods of fractional-order chaotic systems. Fractal dimensions exist broadly in the study of nature and the development of science and technology. Fractional calculus has become a hot research area in nonlinear science. Fractional-order chaotic systems are an important part of fractional calculus. The book discusses the numerical solution algorithms and characteristic analysis of fractional-order chaotic systems and introduces the techniques to implement the systems with circuits. To facilitate a quick grasp, the authors present examples from their years of work in the appendix. Intended for graduate students and researchers interested in chaotic systems, the book helps one to build a theoretical and experimental foundation for the application of fractional-order chaotic systems.
Analysis Of Operators On Function Spaces
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Author : Alexandru Aleman
language : en
Publisher: Springer
Release Date : 2019-05-30
Analysis Of Operators On Function Spaces written by Alexandru Aleman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-30 with Mathematics categories.
This book contains both expository articles and original research in the areas of function theory and operator theory. The contributions include extended versions of some of the lectures by invited speakers at the conference in honor of the memory of Serguei Shimorin at the Mittag-Leffler Institute in the summer of 2018. The book is intended for all researchers in the fields of function theory, operator theory and complex analysis in one or several variables. The expository articles reflecting the current status of several well-established and very dynamical areas of research will be accessible and useful to advanced graduate students and young researchers in pure and applied mathematics, and also to engineers and physicists using complex analysis methods in their investigations.