The theory of travelling waves described by parabolic equations and systems is a rapidly developing branch of modern mathematics. This book presents a general picture of current results about wave solutions of parabolic systems, their existence, stability, and bifurcations. With introductory material accessible to non-mathematicians and a nearly complete bibliography of about 500 references, this book is an excellent resource on the subject.
This book is devoted to a systematic analysis of asymptotic behavior of distributions of various typical functionals of Gaussian random variables and fields. The text begins with an extended introduction, which explains fundamental ideas and sketches the basic methods fully presented later in the book. Good approximate formulas and sharp estimates of the remainders are obtained for a large class of Gaussian and similar processes. The author devotes special attention to the development of asymptotic analysis methods, emphasizing the method of comparison, the double-sum method and the method of moments. The author has added an extended introduction and has significantly revised the text for this translation, particularly the material on the double-sum method.
Beginning algebraic geometers are well served by Uneno's inviting introduction to the language of schemes. Grothendieck's schemes and Zariski's emphasis on algebra and rigor are primary sources for this introduction to a rich mathematical subject. Ueno's book is a self-contained text suitable for an introductory course on algebraic geometry.
This book investigates the distributions of functionals defined on the sample paths of stochastic processes. It contains systematic exposition and applications of three general research methods developed by the authors. (i) The method of stratifications is used to study the problem of absolute continuity of distribution for different classes of functionals under very mild smoothness assumptions. It can be used also for evaluation of the distribution density of the functional. (ii) The method of differential operators is based on the abstract formalism of differential calculus and proves to be a powerful tool for the investigation of the smoothness properties of the distributions. (iii) The s...
If we had to formulate in one sentence what this book is about, it might be "How partial differential equations can help to understand heat explosion, tumor growth or evolution of biological species". These and many other applications are described by reaction-diffusion equations. The theory of reaction-diffusion equations appeared in the first half of the last century. In the present time, it is widely used in population dynamics, chemical physics, biomedical modelling. The purpose of this book is to present the mathematical theory of reaction-diffusion equations in the context of their numerous applications. We will go from the general mathematical theory to specific equations and then to their applications. Existence, stability and bifurcations of solutions will be studied for bounded domains and in the case of travelling waves. The classical theory of reaction-diffusion equations and new topics such as nonlocal equations and multi-scale models in biology will be considered.
This comprehensive chronological reference work lists the results of men’s chess competitions all over the world—individual and team matches, 1956 through 1960. Entries record location and, when available, the group that sponsored the event. First and last names of players are included whenever possible and are standardized for easy reference. Compiled from contemporary sources such as newspapers, periodicals, tournament records and match books, this work contains 1,390 tournament crosstables and 142 match scores. It is indexed by events and by players.
Despite the great strides in nonlinear dynamics over the past 40 years, applying nonlinear dynamics to polymeric systems has not received much attention. This book addresses this absence by covering present theory, modeling, and experiments of nonlinear dynamics in polymeric systems. Oscillating chemical reactions, propagating fronts, far-from equilibrium pattern formation, Turing structures, and chaos are but some of the exotic phenomena discussed in this book. The book is divided into six sections. The first section introduces nonlinear dynamics and shows how polymeric systems exhibit comparable phenomena. The second section addresses phenomena in gels in which mechanical effects can be important. Coupling gels and chemistry allow some new phenomena and potentially useful devices. The third section reviews frontal polymerization and includes chapters on new chemistry and new modeling. The fourth section focuses on interfacial systems, including polymer-like surfactant systems, laser excited systems, and dewetting phenomena. Phase separation is discussed in the fifth section. Finally, oscillating reactions-the prototypical nonlinear chemical dynamical systems-close the book.
Nano-science and nano-technology are rapidly developing scientific and technological areas that deal with physical, chemical and biological processes that occur on nano-meter scale – one millionth of a millimeter. Self-organization and pattern formation play crucial role on nano-scales and promise new, effective routes to control various nano-scales processes. This book contains lecture notes written by the lecturers of the NATO Advanced Study Institute "Self-Assembly, Pattern Formation and Growth Phenomena in Nano-Systems" that took place in St Etienne de Tinee, France, in the fall 2004. They give examples of self-organization phenomena on micro- and nano-scale as well as examples of the ...