Hydrodynamic stability is of fundamental importance in the mechanics of fluids and is mainly concerned with the problem of the transition to turbulence.
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).
The Monte Carlo method is inherently parallel and the extensive and rapid development in parallel computers, computational clusters and grids has resulted in renewed and increasing interest in this method.
Soft computing is a new, emerging discipline rooted in a group of technologies that aim to exploit the tolerance for imprecision and uncertainty in achieving solutions to complex problems.
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.
Ever since fuzzy logic was introduced by Lotfi Zadeh in the mid-sixties and genetic algorithms by John Holland in the early seventies, these two fields widely been subjects of academic research the world over.
This book provides a systematic and self-consistent introduction to the nonlinear continuum mechanics of solids, from the main axioms to comprehensive aspects of the theory.
The interaction of acoustic fields with submerged elastic structures, both by propagation and scattering, is being investigated at various institutions and laboratories world-wide with ever-increasing sophistication of experiments and analysis.
This book is a thorough and self-contained treatise of martingales as a tool in stochastic analysis, stochastic integrals and stochastic differential equations.
The book is a collection of research and review articles in several areas of modern mathematics and mathematical physics published in the span of three decades.
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.
This monograph defines the notion of a "e;system"e; by reference to those systems which exhibit goal-oriented behavior and utilize the notion of decision making and controls.
The book is suitable for a lecture course on the theory of Brownian motion, being based on final year undergraduate lectures given at Trinity College, Dublin.
This is the first book which describes completely the nontraditional difference schemes which combine the ideas of Pade-type approximation and upwind differencing.
New Edition: Ocean Surface Waves: Their Physics and Prediction (3rd Edition)This book is intended as a handbook for professionals and researchers in the areas of Physical Oceanography, Ocean and Coastal Engineering and as a text for graduate students in these fields.
This book is an exposition of a new approach to the Navier-Stokes equations, using powerful techniques provided by nonstandard analysis, as developed by the authors.
The interaction of the environment with a moving body is called "e;localized"e; if it has been found or assumed that the force or/and thermal influence of the environment on each body surface point is independent and can be determined by the local geometrical and kinematical characteristics of this point as well as by the parameters of the environment and body-environment interactions which are the same for the whole surface of contact.
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.
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.
The question of the presence of various asymptotic properties of the solutions of ordinary differential equations arises when solving various practical problems.
This research monograph discusses newly developed mathematical models and methods that provide biologically meaningful inferences from data on cancer latency produced by follow-up and discrete surveillance studies.
This book is devoted to an analysis of the way that structures must enter into a serious study of any subject, and the term "e;structuralism"e; refers to the general method of approaching a subject from the viewpoint of structure.
This book provides a systematic and unified approach to the analysis, identification and optimal control of continuous-time dynamical systems via orthogonal polynomials such as Legendre, Laguerre, Hermite, Tchebycheff, Jacobi, Gegenbauer, and via orthogonal functions such as sine-cosine, block-pulse, and Walsh.
This book of lecture notes contains theoretical background material required for computer generation of random fields, which is of interest in various fields of applied mathematics.
This volume is a collection of research papers devoted to the study of relationships between knot theory and the foundations of mathematics, physics, chemistry, biology and psychology.
