Maths for scientists

This book presents two new mathematical techniques: nonstandard logics and nonstandard metrics.

This book deals with a series of topics on the cutting edge of nonlinear science, striking a balance between theory and experiment.

This book provides a concise presentation of the major techniques for determining analytic approximations to the solutions of planar oscillatory dynamic systems.

This book introduces a comprehensive mathematical formulation of the three-dimensional ocean acoustic propagation problem by means of functional and operator splitting techniques in conjunction with rational function approximations.

About one and a half decades ago, Feigenbaum observed that bifurcations, from simple dynamics to complicated ones, in a family of folding mappings like quadratic polynomials follow a universal rule (Coullet and Tresser did some similar observation independently).

Quantum groups are a generalization of the classical Lie groups and Lie algebras and provide a natural extension of the concept of symmetry fundamental to physics.

Looking beyond the boundaries of various disciplines, the author demonstrates that symmetry is a fascinating phenomenon which provides endless stimulation and challenges.

Fuzzy sets and fuzzy logic are powerful mathematical tools for modeling and controlling uncertain systems in industry, humanity, and nature; they are facilitators for approximate reasoning in decision making in the absence of complete and precise information.

In this volume, a comprehensive review is given for path integration in two- and three-dimensional homogeneous spaces of constant curvature, including an enumeration of all coordinate systems which allow separation of variables in the Hamiltonian and in the path integral.

This book provides a unified exposition of local-stereological methods developed within the last 15 years.

This book covers a new niche in circular accelerator design, motivated by the promising industrial prospects of recent micromanufacturing methods - X-ray lithography, synchrotron radiation-based micromachining and microanalysis techniques.

Mathematical ecology is a subject which recently attracts attentions of many mathematicians and biologists.

This book deals with the qualitative theory of dynamical systems and is devoted to the study of flows and cascades in the vicinity of a smooth invariant manifold.

Time is considered as an independent entity which cannot be reduced to the concept of matter, space or field.

This book is devoted to the theory of infinite-order linear and nonlinear differential operators with several real arguments and their applications to problems of partial differential equations and numerical analysis.

This book is essentially devoted to complex properties (Phase plane structure and bifurcations) of two-dimensional noninvertible maps, i.

In this second edition, the following recent papers have been added: "e;Gauss Codes, Quantum Groups and Ribbon Hopf Algebras"e;, "e;Spin Networks, Topology and Discrete Physics"e;, "e;Link Polynomials and a Graphical Calculus"e; and "e;Knots Tangles and Electrical Networks"e;.

This is the first book which describes completely the nontraditional difference schemes which combine the ideas of Pade-type approximation and upwind differencing.

This volume is a compilation of works which, taken together, give a complete and consistent presentation of instanton calculus in non-Abelian gauge theories, as it exists now.

This book contains a systematic study of ecological communities of two or three interacting populations.

This book is the first monograph on a new powerful method discovered by the author for the study of nonlinear dynamical systems relying on reduction of nonlinear differential equations to the linear abstract Schrodinger-like equation in Hilbert space.

This is an analysis of multidimensional nonlinear dissipative Hamiltonian dynamical systems subjected to parametric and external stochastic excitations by the Fokker-Planck equation method.

W-symmetry is an extension of conformal symmetry in two dimensions.

The main purpose of this book is to provide a self-contained, complete and geometrically clear presentation of the recent results on global controllability and stabilization.

Geometrical notions and methods play an important role in both classical and quantum field theory, and a connection is a deep structure which apparently underlies the gauge-theoretical models in field theory and mechanics.

This book introduces a rapidly growing new research area - the study of dynamical properties of elementary fields.

In this book, bifurcational mechanisms of the development, structure and properties of chaotic attractors are investigated by numerical and physical experiments based on the methods of the modern theory of nonlinear oscillations.

This book deals with the bifurcation and chaotic aspects of damped and driven nonlinear oscillators.

Systems of strongly correlated electrons are at the heart of recent developments in condensed matter theory.

This volume contains selected papers of Dr Morikazu Toda.

This book, intended for students, researchers and engineers, is a collection of classic papers on photorefractive nonlinear optics.

This book is an introductory course to accelerator physics at the level of graduate students.

Chaos control has become a fast-developing interdisciplinary research field in recent years.

This book provides a comprehensive account, from first principles, of the methods of numerical quantum mechanics, beginning with formulations and fundamental postulates.

The book deals with biological, mathematical, descriptive, causal and systemic phyllotaxis.

This book is devoted to the frequency domain approach, for both regular and degenerate Hopf bifurcation analyses.

For almost two decades Prof.

Remote sounding of the atmosphere has proved to be a fruitful method of obtaining global information about the atmospheres of the earth and other planets.

This book is about "e;diamond"e;, a logic of paradox.

It now appears that the old argument about Lorentz vs Galileo relativity is passing into history.

This monograph surveys the role of some associative and non-associative algebras, remarkable by their ubiquitous appearance in contemporary theoretical physics, particularly in particle physics.

This book presents some recent mathematical developments about neutron transport equations.

This book summarizes results on the creation of a new theory of condensation which has an impact on consideration of some microscopic effects left aside in the usual nucleation theories.

Many branches of science and engineering involve applications of mathematical analysis.

This book provides a research-expository treatment of infinite-dimensional nonstationary stochastic processes or time series.

The book comprises a broad panorama of phenomena occurring in four major classes of radiophysical and mechanical systems - linear, nonlinear, parametric, and nonlinear-parametric.

Many advanced mathematical disciplines, such as dynamical systems, calculus of variations, differential geometry and the theory of Lie groups, have a common foundation in general topology and calculus in normed vector spaces.

This book aims to develop algorithms of shape-preserving spline approximation for curves/surfaces with automatic choice of the tension parameters.

The quantization of physical systems moving on group and symmetric spaces has been an area of active research over the past three decades.