This brief provides an elementary introduction to the theory of piecewise differentiable functions with an emphasis on differentiable equations. In the first chapter, two sample problems are used to motivate the study of this theory. The presentation is then developed using two basic tools for the analysis of piecewise differentiable...

This graduate-level, course-based text is devoted to the 3+1 formalism of general relativity, which also constitutes the theoretical foundations of numerical relativity. The book starts by establishing the mathematical background (differential geometry, hypersurfaces embedded in space-time, foliation of space-time by a family of space-like...

Finite-state devices, which include finite-state automata, graphs, and finite-state transducers, are in wide use in many areas of computer science. Recently, there has been a resurgence of the use of finite-state devices in all aspects of computational linguistics, including dictionary encoding, text processing, and speech processing. This...

This book covers combinatorial data structures and algorithms, algebraic issues in geometric computing, approximation of curves and surfaces, and computational topology. Each chapter fully details and provides a tutorial introduction to important concepts and results. The focus is on methods which are both well founded mathematically and...

Computational complexity, originated from the interactions between computer science and numerical optimization, is one of the major theories that have revolutionized the approach to solving optimization problems and to analyzing their intrinsic difficulty. This volume is a collection of articles on recent complexity developments in numerical...

This book presents a comprehensive review of key distributed graph algorithms for computer network applications, with a particular emphasis on practical implementation. Topics and features: introduces a range of fundamental graph algorithms, covering spanning trees, graph traversal algorithms, routing algorithms, and self-stabilization;...

This state-of-the-art textbook examines four research directions in harmonic analysis and features some of the latest applications in the field, including cosmic microwave background analysis, human cortex image denoising, and wireless communication. The work is the first one that combines spline theory (from a numerical or...

Approximation methods are of vital importance in many challenging applications from computational science and engineering. This book collects papers from world experts in a broad variety of relevant applications of approximation theory, including pattern recognition and machine learning, multiscale modelling of fluid flow, metrology,...

The ultimate goal of computers is to help humans to solve problems. The solutions for such problems are typically programmed by experts, and the computers need only to follow the specified steps to solve the problem. However, the solution of some problems may be too difficult to be explicitly programmed. In such difficult cases,...

Fuzzy Sets have been...