Название: Associative Algebraic Geometry
Автор: Arvid Siqveland
Издательство: World Scientific Publishing
Год: 2023
Страниц: 420
Язык: английский
Формат: pdf (true)
Размер: 10.7 MB

Classical Deformation Theory is used for determining the completions of local rings of an eventual moduli space. When a moduli variety exists, the main result explored in the book is that the local ring in a closed point can be explicitly computed as an algebraization of the pro-representing hull, called the local formal moduli, of the deformation functor for the corresponding closed point. The book gives explicit computational methods and includes the most necessary prerequisites for understanding associative algebraic geometry. It focuses on the meaning and the place of deformation theory, resulting in a complete theory applicable to moduli theory. It answers the question 'why moduli theory', and gives examples in mathematical physics by looking at the universe as a moduli of molecules, thereby giving a meaning to most noncommutative theories. The book contains the first explicit definition of a noncommutative scheme, not necessarily covered by commutative rings. This definition does not contradict any previous abstract definitions of noncommutative algebraic geometry, but sheds interesting light on other theories, which is left for further investigation.

Название: Perfect and Amicable Numbers, 1st Edition
Автор: Elena Deza
Издательство: World Scientific Publishing
Серия: Selected Chapters of Number Theory: Special Numbers
Год: 2023
Страниц: 462
Язык: английский
Формат: pdf (true)
Размер: 15.6 MB

Special numbers, among integers, are an important part of number theory, general mathematics, and several applied areas (such as cryptography). While the “names” of some of them (Fermat numbers, Mersenne numbers, Fibonacci numbers, Catalan numbers, Bernoulli numbers, Stirling numbers, etc.) are known to every mathematician, actual information on them is often scattered in the special literature. There are only few books which systematically present their history and properties while giving the main proofs. This book contains a detailed presentation on the theory of two classes of special numbers, perfect numbers, and amicable numbers, as well as some of their generalizations. It also gives a large list of their properties, facts and theorems with full proofs. Perfect and amicable numbers, as well as most classes of special numbers, have many interesting properties, including numerous modern and classical applications as well as a long history connected with the names of famous mathematicians. The theory of perfect and amicable numbers is a part of pure Arithmetic, and in particular a part of Divisibility Theory and the Theory of Arithmetical Functions.

Название: Simplifying Statistics for Graduate Students: Making the Use of Data Simple and User-Friendly
Автор: Susan Rovezzi Carroll, David J. Carroll
Издательство: Rowman & Littlefield Publishers
Год: 2023
Страниц: 135
Язык: английский
Формат: pdf (true), epub
Размер: 10.2 MB

One of the greatest barriers to completing a graduate thesis or a doctoral dissertation is statistics. Oftentimes, the journey through graduate school is gratifying when the content courses in the chosen field of study are undertaken. Conversely, the statistics courses are met with trepidation. Many graduate students feel lost when it comes to dealing with data. Simplifying Statistics for Grad Students:Making the Use of Data Simple and User-Friendly is intended to help graduate students move through the barriers that seem formidable but are not. While this book is not a statistics text and does not purport to be such, it introduces graduate students to basic statistical concepts in an easy-to-comprehend manner. It is also a handbook that they can refer back to time and time again. Expertise with data is expected of graduate students. Simplifying Statistics for Grad Students is an antidote for the research and statistics blues.

Название: A Course on Hopf Algebras
Автор: Rinat Kashaev
Издательство: Springer
Год: 2023
Страниц: 173
Язык: английский
Формат: pdf (true), epub
Размер: 14.2 MB

Starting with a reformulation of the definition of a group in terms of structural maps as motivation for the definition of a Hopf algebra, the book introduces the related algebraic notions: algebras, coalgebras, bialgebras, convolution algebras, modules, comodules. Next, Drinfel'd's quantum double construction is achieved through the important notion of the restricted (or finite) dual of a Hopf algebra, which allows one to work purely algebraically, without completions. As a result, in applications to knot theory, to any Hopf algebra with invertible antipode one can associate a universal invariant of long knots. These constructions are elucidated in detailed analyses of a few examples of Hopf algebras.

Название: Concrete Abstractions: Formalizing and Analyzing Discrete Theories and Algorithms with the RISCAL Model Checker
Автор: Wolfgang Schreiner
Издательство: Springer
Год: 2023
Страниц: 278
Язык: английский
Формат: pdf (true)
Размер: 10.1 MB

This book demonstrates how to formally model various mathematical domains (including algorithms operating in these domains) in a way that makes them amenable to a fully automatic analysis by computer software.The presented domains are typically investigated in discrete mathematics, logic, algebra, and Computer Science; they are modeled in a formal language based on first-order logic which is sufficiently rich to express the core entities in whose correctness we are interested: mathematical theorems and algorithmic specifications. This formal language is the language of RISCAL, a “mathematical model checker” by which the validity of all formulas and the correctness of all algorithms can be automatically decided. The RISCAL software is freely available; all formal contents presented in the book are given in the form of specification files by which the reader may interact with the software while studying the corresponding book material. The goal of this book is to demonstrate how we can formally model various mathematical domains (including algorithms operating in these domains) in a way that makes them amenable to a fully automatic analysis by computer software.

Название: Fibonacci Cubes with Applications and Variations
Автор: Omer Egecioglu, Sandi Klavzar, Michel Mollard
Издательство: World Scientific Publishing
Год: 2023
Страниц: 303
Язык: английский
Формат: pdf (true)
Размер: 14.6 MB

Fibonacci Cubes have been an extremely popular area of research since the 1990s. This unique compendium features the state of research into Fibonacci Cubes. It expands the knowledge in graph theoretic and combinatorial properties of Fibonacci Cubes and their variants. By highlighting various approaches with numerous examples, it provides a fundamental source for further research in the field. This useful reference text surely benefits advanced students in Computer Science and mathematics and serves as an archival record of the current state of the field. Readership: Researchers, professionals, academics and graduate students in theoretical Computer Science, graph theory and combinatorics.

Название: Simulink 5/6/7: Самоучитель
Автор: Дьяконов В.П.
Издательство: М.: ДMK-Прecc
Год: 2008
Cтраниц: 784
Формат: pdf
Размер: 11 мб
Язык: русский

Самоучитель по новейшим реализациям пакета визуального блочного имитационного моделирования Simulink 5/6/7 матричной системы MATLAB R2006/2007. Подробно описаны библиотека блоков Simulink, методика подготовки диаграмм моделей, их редактирование, настройка и запуск на исполнение. Дано описание наиболее важных пакетов расширения Simulink инструментального ящика Blockset, в том числе SimPowerSystems, SimMechanics, Aerospace, Stateflow, Signal Processing, Telecommunication, Video and Image Processing и др.

Название: Прикладной системный анализ
Автор: Тарасенко Ф.П.
Издательство: М.: КНОРУС
Год: 2004, 2010, 2015 (три издания в одном архиве)
Cтраниц: 224
Формат: pdf, djvu
Размер: 13 мб
Язык: русский

В основу пособия положен курс лекций, читаемый автором в Томском государственном университете по новой дисциплине — прикладному системному анализу. Содержится описание созданной в последние десятилетия теоретиками и практиками системного анализа технологии решения проблем реальной жизни.

Название: Graph Theory and Mobile Communications
Автор: Masakazu Sengoku
Издательство: World Scientific Publishing
Серия: Advanced Series in Electrical and Computer Engineering
Год: 2023
Страниц: 409
Язык: английский
Формат: pdf (true)
Размер: 25.9 MB

This comprehensive compendium discusses the basics of graph theory to its application, focusing on the application of graph theory to mobile communications. A mobile communication connects a mobile terminal and a base station wirelessly, and the base station enables communications all over the world via a wired and satellite communication system. This means that the mobile communication system includes wire and wireless technologies, and also hardware such as analog electric circuits, digital circuits and a software part such as computer algorithms. There are various systems having a network structure. For example, the Internet, a communication network, an electrical network, a road network, a traffic network, a human network, and so forth. The field of studying this network structure is called graph theory. In this book, we will discuss from the basics of graph theory to its application and in particular, we will focus on the application of graph theory to mobile communications.

Название: Understanding the Physics of Toys: Principles, Theory and Exercises
Автор: S. Rajasekar, R. Velusamy
Издательство: World Scientific Publishing
Год: 2023
Страниц: 471
Язык: английский
Формат: pdf (true)
Размер: 13.0 MB

Demonstrating many fundamental concepts of physics and engineering through the working principles of popular science toys is inexpensive, quickly reaching the senses and inspiring a better learning. The systematic way of setting theoretical model equations for the toys provides a remarkable experience in constructing model equations for physical and engineering systems. Given that most science toys are based on the principles of physics, and to cater to the needs of graduate and master-level programme students in physics and engineering, the present book covers more than 40 wide ranging popular toys. For each toy various features are presented including history, construction, working principle, theoretical model, a solved problem and 5–10 exercises.