Algebra and Applications 2

This book is part of Algebra and Geometry, a subject within the SCIENCES collection published by ISTE and Wiley, and the first of three volumes specifically focusing on algebra and its applications. Algebra and Applications 1 centers on non-associative algebras and includes an introduction to derived categories. The chapters are written by recognized experts in the field, providing insight into new trends, as well as a comprehensive introduction to the theory.

The book incorporates self-contained surveys with the main results, applications and perspectives. The chapters in this volume cover a wide variety of algebraic structures and their related topics. Jordan superalgebras, Lie algebras, composition algebras, graded division algebras, non-associative C*– algebras, H*-algebras, Krichever-Novikov type algebras, preLie algebras and related structures, geometric structures on 3-Lie algebras and derived categories are all explored. Algebra and Applications 1 is of great interest to graduate students and researchers.

Each chapter combines some of the features of both a graduate level textbook and of research level surveys.

Praise for the first edition «This book is clearly written and presents a large number of examples illustrating the theory . . . there is no other book of comparable content available. Because of its detailed coverage of applications generally neglected in the literature, it is a desirable if not essential addition to undergraduate mathematics and computer science libraries.» –CHOICE As a cornerstone of mathematical science, the importance of modern algebra and discrete structures to many areas of science and technology is apparent and growing–with extensive use in computing science, physics, chemistry, and data communications as well as in areas of mathematics such as combinatorics. Blending the theoretical with the practical in the instruction of modern algebra, Modern Algebra with Applications, Second Edition provides interesting and important applications of this subject–effectively holding your interest and creating a more seamless method of instruction. Incorporating the applications of modern algebra throughout its authoritative treatment of the subject, this book covers the full complement of group, ring, and field theory typically contained in a standard modern algebra course. Numerous examples are included in each chapter, and answers to odd-numbered exercises are appended in the back of the text. Chapter topics include: Boolean Algebras Polynomial and Euclidean Rings Groups Quotient Rings Quotient Groups Field Extensions Symmetry Groups in Three Dimensions Latin Squares P?lya—Burnside Method of Enumeration Geometrical Constructions Monoids and Machines Error-Correcting Codes Rings and Fields In addition to improvements in exposition, this fully updated Second Edition also contains new material on order of an element and cyclic groups, more details about the lattice of divisors of an integer, and new historical notes. Filled with in-depth insights and over 600 exercises of varying difficulty, Modern Algebra with Applications, Second Edition can help anyone appreciate and understand this subject.

A coherent and integrated account of the leading UML 2 semantics work and the practical applications of UML semantics development With contributions from leading experts in the field, the book begins with an introduction to UML and goes on to offer in-depth and up-to-date coverage of: The role of semantics Considerations and rationale for a UML system model Definition of the UML system model UML descriptive semantics Axiomatic semantics of UML class diagrams The object constraint language Axiomatic semantics of state machines A coalgebraic semantic framework for reasoning about interaction designs Semantics of activity diagrams Verification of UML models State invariants Model transformation specification and verification Additionally, readers are provided with expert guidance on how to resolve semantic problems and a section on applications of UML semantics with model analysis. UML 2 Semantics and Applications is an ideal resource for researchers and tool-builders working in UML, among others. It is also an excellent textbook for postgraduate teaching and research.

Explore the main algebraic structures and number systems that play a central role across the field of mathematics Algebra and number theory are two powerful branches of modern mathematics at the forefront of current mathematical research, and each plays an increasingly significant role in different branches of mathematics, from geometry and topology to computing and communications. Based on the authors' extensive experience within the field, Algebra and Number Theory has an innovative approach that integrates three disciplines—linear algebra, abstract algebra, and number theory—into one comprehensive and fluid presentation, facilitating a deeper understanding of the topic and improving readers' retention of the main concepts. The book begins with an introduction to the elements of set theory. Next, the authors discuss matrices, determinants, and elements of field theory, including preliminary information related to integers and complex numbers. Subsequent chapters explore key ideas relating to linear algebra such as vector spaces, linear mapping, and bilinear forms. The book explores the development of the main ideas of algebraic structures and concludes with applications of algebraic ideas to number theory. Interesting applications are provided throughout to demonstrate the relevance of the discussed concepts. In addition, chapter exercises allow readers to test their comprehension of the presented material. Algebra and Number Theory is an excellent book for courses on linear algebra, abstract algebra, and number theory at the upper-undergraduate level. It is also a valuable reference for researchers working in different fields of mathematics, computer science, and engineering as well as for individuals preparing for a career in mathematics education.

This book concerns the use of dioid algebra as (max, +) algebra to treat the synchronization of tasks expressed by the maximum of the ends of the tasks conditioning the beginning of another task – a criterion of linear programming. A classical example is the departure time of a train which should wait for the arrival of other trains in order to allow for the changeover of passengers. The content focuses on the modeling of a class of dynamic systems usually called “discrete event systems” where the timing of the events is crucial. Events are viewed as sudden changes in a process which is, essentially, a man-made system, such as automated manufacturing lines or transportation systems. Its main advantage is its formalism which allows us to clearly describe complex notions and the possibilities to transpose theoretical results between dioids and practical applications.

Refrigeration Systems and Applications, 2nd edition offers a comprehensive treatise that addresses real-life technical and operational problems, enabling the reader to gain an understanding of the fundamental principles and the practical applications of refrigeration technology. New and unique analysis techniques (including exergy as a potential tool), models, correlations, procedures and applications are covered, and recent developments in the field are included – many of which are taken from the author's own research activities in this area. The book also includes some discussion of global warming issues and its potential solutions. Enables the reader to gain an understanding of the fundamental principles and the practical applications of refrigeration technologies. Discusses crucial industrial technical and operational problems, as well as new performance improvement techniques and tools for better design and analysis. Includes fundamental aspects of thermodynamics, fluid flow, and heat transfer; refrigerants; refrigeration cycles and systems; advanced refrigeration cycles and systems, including some novel applications; heat pumps; heat pipes; and many more. Provides easy to follow explanations, numerous new chapter-end problems and worked-out examples as learning aids for students and instructors. Refrigeration is extensively used in a variety of thermal engineering applications ranging from the cooling of electronic devices to food cooling processes. Its wide-ranging implications and applications mean that this industry plays a key role in national and international economies, and it continues to be an area of active research and development. Refrigeration Systems and Applications, 2nd edition forms a useful reference source for graduate and postgraduate students and researchers in academia and as well as practicing engineers working in this important field who are interested in refrigeration systems and applications and the methods and analysis tools for their analysis, design and performance improvement.

This book provides a pedagogical and comprehensive introduction to graph theory and its applications. It contains all the standard basic material and develops significant topics and applications, such as: colorings and the timetabling problem, matchings and the optimal assignment problem, and Hamiltonian cycles and the traveling salesman problem, to name but a few. Exercises at various levels are given at the end of each chapter, and a final chapter presents a few general problems with hints for solutions, thus providing the reader with the opportunity to test and refine their knowledge on the subject. An appendix outlines the basis of computational complexity theory, in particular the definition of NP-completeness, which is essential for algorithmic applications.

Plates: Theories and Applications provides a comprehensive introduction to plate structures, covering classical theory and applications. It considers plate structures in several forms, starting from the simple uniform, thin, homogeneous metallic structure to more efficient and durable alternatives involving features such as variable-thickness, lamination, sandwich construction, fiber reinforcement, functional gradation, and moderately-thick to very-thick geometry. Different theoretical models are then discussed for analysis and design purposes starting from the classical thin plate theory to alternatives obtained by incorporation of appropriate complicating effects or by using fundamentally different assumptions. Plates: Theories and Applications alsocovers the latest developments on the topic.

The definitive text/reference for students, researchers and practicing engineers This book provides comprehensive coverage on refrigeration systems and applications, ranging from the fundamental principles of thermodynamics to food cooling applications for a wide range of sectoral utilizations. Energy and exergy analyses as well as performance assessments through energy and exergy efficiencies and energetic and exergetic coefficients of performance are explored, and numerous analysis techniques, models, correlations and procedures are introduced with examples and case studies. There are specific sections allocated to environmental impact assessment and sustainable development studies. Also featured are discussions of important recent developments in the field, including those stemming from the author’s pioneering research. Refrigeration is a uniquely positioned multi-disciplinary field encompassing mechanical, chemical, industrial and food engineering, as well as chemistry. Its wide-ranging applications mean that the industry plays a key role in national and international economies. And it continues to be an area of active research, much of it focusing on making the technology as environmentally friendly and sustainable as possible without compromising cost efficiency and effectiveness. This substantially updated and revised edition of the classic text/reference now features two new chapters devoted to renewable-energy-based integrated refrigeration systems and environmental impact/sustainability assessment. All examples and chapter-end problems have been updated as have conversion factors and the thermophysical properties of an array of materials. Provides a solid foundation in the fundamental principles and the practical applications of refrigeration technologies Examines fundamental aspects of thermodynamics, refrigerants, as well as energy and exergy analyses and energy and exergy based performance assessment criteria and approaches Introduces environmental impact assessment methods and sustainability evaluation of refrigeration systems and applications Covers basic and advanced (and hence integrated) refrigeration cycles and systems, as well as a range of novel applications Discusses crucial industrial, technical and operational problems, as well as new performance improvement techniques and tools for better design and analysis Features clear explanations, numerous chapter-end problems and worked-out examples Refrigeration Systems and Applications, Third Edition is an indispensable working resource for researchers and practitioners in the areas of Refrigeration and Air Conditioning. It is also an ideal textbook for graduate and senior undergraduate students in mechanical, chemical, biochemical, industrial and food engineering disciplines.