Kategoria BISAC: Mathematics >> Discrete Mathematics

Performance optimization is vital in the design and operation of modern engineering systems, including communications, manufacturing, robotics, and logistics. Most engineering systems are too complicated to model, or the system parameters cannot be easily identified, so learning techniques have to be applied. This book provides a unified framework based on a sensitivity point of view. It also introduces new approaches and proposes new research topics within this sensitivity-based framework. This new perspective on a popular topic is presented by a well respected expert in the field.

Our civilization employs increasingly complex human-made systems, such as large-scale electric power grids, air traffic control systems, manufacturing plants and supply chains, the Internet and other communication networks. Performance evaluation of these systems is accomplished by using simulation models rather than experiment with the real systems. However, these systems operate and evolve in time via human-made rules of operation which are difficult to describe and capture by succinct mathematical models. And while simulation models are often used for design validation and other...

Discrete mathematics is quickly becoming one of the most important areas of mathematical research, with applications to cryptography, linear programming, coding theory and the theory of computing. This book is aimed at undergraduate mathematics and computer science students interested in developing a feeling for what mathematics is all about, where mathematics can be helpful, and what kinds of questions mathematicians work on. The authors discuss a number of selected results and methods of discrete mathematics, mostly from the areas of combinatorics and graph theory, with a little number...

This book presents what in our opinion constitutes the basis of the theory of the mu-calculus, considered as an algebraic system rather than a logic. We have wished to present the subject in a unified way, and in a form as general as possible. Therefore, our emphasis is on the generality of the fixed-point notation, and on the connections between mu-calculus, games, and automata, which we also explain in an algebraic way.

This book should be accessible for graduate or advanced undergraduate students both in mathematics and computer science. We have designed this book especially for...

Key Features:

- Complete state of the art of the importance of triangular norms in various mathematical fields
- 16 self-contained chapters with extensive bibliographies cover both the...

The modern theory of algebras of binary relations, reformulated by Tarski as an abstract, algebraic, equational theory of relation algebras, has considerable mathematical significance, with applications in various fields: e.g., in computer science---databases, specification theory, AI---and in anthropology, economics, physics, and philosophical logic.

This comprehensive treatment of the theory of relation algebras and the calculus of relations is the first devoted to a systematic development of the subject.

• Presents historical milestones from a modern...

The book will provide powerful resource for all researchers using Mathematics as well as for mathematicians themselves. In the time when over-specialization and terminology fences isolate researchers, this Dictionary try to be "centripedal" and "oikoumeni," providing some access and altitude of vision but without taking the route of scientific vulgarisation. This attempted balance is the main philosophy...

The book is meant to serve two purposes. The first and more obvious one is to present state of the art results in algebraic research into residuated structures related to substructural logics. The second, less obvious but equally important, is to provide a reasonably gentle introduction to algebraic logic. At the beginning, the second objective is predominant. Thus, in the first few chapters the reader will find a primer of universal algebra for logicians, a crash course in nonclassical logics for algebraists, an introduction to residuated structures, an outline of Gentzen-style calculi as...

Quantum logic is a heterogeneous field of research ranging from investigations which may be termed logical in the traditional sense to studies focusing on structures which are on the border between algebra and logic. For the latter structures the term quantum structures...

Combinatorial Problems and Exercises was first published in 1979. This revised edition has the same basic structure but has been brought up to date with a series of exercises...

As the applicability of cellular automata broadens and technology advances, there is a need for a concise, yet thorough, resource that lays the foundation of key cellularautomata rules and applications. In recent years, Stephen Wolfram's A New Kind of Science has brought the modeling power that lies in cellular automata to the attentionof the scientific world, and now, Cellular Automata: A Discrete View of the World presents all the depth, analysis, and applicability of the classic Wolfram text in a straightforward,...