Mathematical physics

The method of compensated compactness as a technique for studying hyperbolic conservation laws is of fundamental importance in many branches of applied mathematics.

Pure mathematicians have only recently begun a rigorous study of topological quantum field theories (TQFTs).

The theory of holomorphic functions of several complex variables emerged from the attempt to generalize the theory in one variable to the multidimensional situation.

This Research Note addresses several pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure set of zeroes of a general class of nonlinear operators.

Although the theory of well-posed Cauchy problems is reasonably understood, ill-posed problems-involved in a numerous mathematical models in physics, engineering, and finance- can be approached in a variety of ways.

Over the last twenty years, the growing availability of computing power has had an enormous impact on the classical fields of direct and inverse scattering.

The literature on the spectral analysis of second order elliptic differential operators contains a great deal of information on the spectral functions for explicitly known spectra.

Complex Lie groups have often been used as auxiliaries in the study of real Lie groups in areas such as differential geometry and representation theory.

This book introduces the class of dynamical systems called semiflows, which includes systems defined or modeled by certain types of differential evolution equations (DEEs).

The analysis and topology of elliptic operators on manifolds with singularities are much more complicated than in the smooth case and require completely new mathematical notions and theories.

This text advances the study of approximate solutions to partial differential equations by formulating a novel approach that employs Hermite interpolating polynomials and by supplying algorithms useful in applying this approach.

Stochastic differential equations in infinite dimensional spaces are motivated by the theory and analysis of stochastic processes and by applications such as stochastic control, population biology, and turbulence, where the analysis and control of such systems involves investigating their stability.

Covering both classical and quantum models, nonlinear integrable systems are of considerable theoretical and practical interest, with applications over a wide range of topics, including water waves, pin models, nonlinear optics, correlated electron systems, plasma physics, and reaction-diffusion processes.

Computing in Nonlinear Media and Automata Collectives presents an account of new ways to design massively parallel computing devices in advanced mathematical models, such as cellular automata and lattice swarms, from unconventional materials, including chemical solutions, bio-polymers, and excitable media.

Branes are solitonic configurations of a string theory that are represented by extended objects in a higher-dimensional space-time.

With a unique approach and presenting an array of new and intriguing topics, Mathematical Quantization offers a survey of operator algebras and related structures from the point of view that these objects are quantizations of classical mathematical structures.

Inverse boundary problems are a rapidly developing area of applied mathematics with applications throughout physics and the engineering sciences.

Over the last decade, statisticians have developed new statistical tools in the field of spatial point processes.

Although multifractals are rooted in probability, much of the related literature comes from the physics and mathematics arena.

This book is a comprehensive survey of the current state of knowledge about the dynamics and gravitational properties of cosmic strings treated in the idealized classical approximation as line singularities described by the Nambu-Goto action.

Differential geometry is an actively developing area of modern mathematics.

The propagation of curved, nonlinear wavefronts and shock fronts are very complex phenomena.

In response to unanswered difficulties in the generalized case of conditional expectation and to treat the topic in a well-deservedly thorough manner, M.

Since the 1960s, many researchers have extended topological degree theory to various non-compact type nonlinear mappings, and it has become a valuable tool in nonlinear analysis.

Despite remarkable developments in the field, a detailed treatment of non-Kerr law media has not been published.

A Theoretical Introduction to Numerical Analysis presents the general methodology and principles of numerical analysis, illustrating these concepts using numerical methods from real analysis, linear algebra, and differential equations.

Methods for Solving Mixed Boundary Value ProblemsAn up-to-date treatment of the subject, Mixed Boundary Value Problems focuses on boundary value problems when the boundary condition changes along a particular boundary.

Due to the increase in computational power and new discoveries in propagation phenomena for linear and nonlinear waves, the area of computational wave propagation has become more significant in recent years.

The study of random sets is a large and rapidly growing area with connections to many areas of mathematics and applications in widely varying disciplines, from economics and decision theory to biostatistics and image analysis.

As a relatively new area in mathematics, stochastic partial differential equations (PDEs) are still at a tender age and have not yet received much attention in the mathematical community.

Covering both theory and progressive experiments, Quantum Computing: From Linear Algebra to Physical Realizations explains how and why superposition and entanglement provide the enormous computational power in quantum computing.

Numerical Methods in Astrophysics: An Introduction outlines various fundamental numerical methods that can solve gravitational dynamics, hydrodynamics, and radiation transport equations.

One of the first books to thoroughly examine the subject, Quantum Computing Devices: Principles, Designs, and Analysis covers the essential components in the design of a "e;real"e; quantum computer.

Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators.

Although the current dynamical system approach offers several important insights into the turbulence problem, issues still remain that present challenges to conventional methodologies and concepts.

This book presents the author's research on automatic learning procedures for categorial grammars of natural languages.

How does gravity work?

Trends in Computational Nanomechanics reviews recent advances in analytical and computational modeling frameworks to describe the mechanics of materials on scales ranging from the atomistic, through the microstructure or transitional, and up to the continuum.

Although computational modeling and simulation of material deformation was initiated with the study of structurally simple materials and inert environments, there is an increasing demand for predictive simulation of more realistic material structure and physical conditions.

The aim of this book is to show that the probabilistic formalisms of classical statistical mechanics and quantum mechanics can be unified on the basis of a general contextual probabilistic model.

Recent interest in nanotechnology is challenging the community to analyse, develop and design nanometer to micrometer-sized devices for applications in new generations of computer, electronics, photonics and drug delivery systems.

The problem of counting the number of self-avoiding polygons on a square grid, - therbytheirperimeterortheirenclosedarea,is aproblemthatis soeasytostate that, at ?

There are many books on the use of numerical methods for solving engineering problems and for modeling of engineering artifacts.

This volume defends a novel approach to the philosophy of physics: it is the first book devoted to a comparative study of probability, causality, and propensity, and their various interrelations, within the context of contemporary physics -- particularly quantum and statistical physics.

How can environmental scientists and engineers use the increasing amount of available data to enhance our understanding of planet Earth, its systems and processes?

Without listing his works, all of which are highly notable both for the originality of the methods utilized as well as for the importance of the results achieved, we limit ourselves to the following: Inmodernnucleartheories, thecontributionmadebythisresearcher to the introduction of the forces called 'Majorana forces' is universally recognized as the one, among the most fundamental, that permits us to theoretically comprehend the reasons for nuclear stability.

Vibration problems dealing with advanced Mathematical and Numerical Techniques have extensive application in a wide class of problems in ae- nautics, aerodynamics, space science and technology, off-shore engineering and in the design of different structural components of high speed space crafts and nuclear reactors.