Developments in Reliable Computing

Sample

Vladimir S. Lerner

The Variation Principle In Informational Macrodynamics (VP) introduces the process' integral information measure, which has a distinctive difference from traditional information approaches that use an entropy function. The VP's minimax mathematical mechanisms formalize the regularities of the cooperative informational dynamics, connecting randomness and regularities, stochastic and determinism, reversibility and irreversibility, symmetry and nonsymmetry, stability and instability, regular and chaotic dynamics, thermodynamics and informational dynamics, time-reversible and time-irreversible processes, reveals the information dynamic mechanisms of evolution and development. The mathematical formalisms and methods, implemented in the forms of computer models, algorithms and programs, provide new general tools for Information Systems' Modeling in such areas as biology, intelligent systems, computer and information technology, including communications, data modeling and data management. Variation Principle In Informational Macrodynamics, with its examples and applications, will meet the needs of a professional audience composed of researchers and practitioners in industry, as well as graduate-level students in computer science, mathematics and engineering.

Sample

Alexandre Ern, Jean-Luc Guermond

This book presents the mathematical theory of finite elements, starting from basic results on approximation theory and finite element interpolation and building up to more recent research topics, such as and Discontinuous Galerkin, subgrid viscosity stabilization, and a posteriori error estimation. The body of the text is organized into three parts plus two appendices collecting the functional analysis results used in the book. The first part develops the theoretical basis for the finite element method and emphasizes the fundamental role of inf-sup conditions. The second party addresses various applications encompassing elliptic PDE's, mixed formulations, first-order PDEs, and the time-dependent versions of these problems. The third part covers implementation issues and should provide readers with most of the practical details needed to write or understand a finite element code. Written at the graduate level, the text contains numerous examples and exercises and is intended to serve as a graduate textbook. Depending on one's interests, several reading paths can be followed, emphasizing either theoretical results, numerical algorithms, code efficiency, or applications in the engineering sciences. The book will be useful to researchers and graduate students in mathematics, computer science and engineering.

Sample

Lars Gårding, Torbjörn Tambour

The aim of this book is to teach the reader the topics in algebra which are useful in the study of computer science. In a clear, concise style, the author present the basic algebraic structures, and their applications to such topics as the finite Fourier transform, coding, complexity, and automata theory. The book can also be read profitably as a course in applied algebra for mathematics students.

Sample

Jason Yust, Jonathan Wild, John Ashley Burgoyne

This book constitutes the thoroughly refereed proceedings of the Fourth International Conference on Mathematics and Computation in Music, MCM 2013, held in Montreal, Canada, in June 2013. The 18 papers presented were carefully reviewed and selected from numerous submissions. They are promoting the collaboration and exchange of ideas among researchers in music theory, mathematics, computer science, musicology, cognition and other related fields.