Mathematical physics

Ten years have passed since the publication of the first English edition.

This text takes advantage of recent developments in the theory of path integration to provide an improved treatment of quantization of systems that either have no constraints or instead involve constraints with demonstratively improved procedures.

According to Drinfeld, a quantum group is the same as a Hopf algebra.

An Introduction to Tensors and Group Theory for Physicists provides both an intuitive and rigorous approach to tensors and groups and their role in theoretical physics and applied mathematics.

Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball focuses on spherical problems as they occur in the geosciences and medical imaging.

This volume comprises a carefully selected collection of articles emerging from and pertinent to the 2010 CFL-80 conference in Rio de Janeiro, celebrating the 80th anniversary of the Courant-Friedrichs-Lewy (CFL) condition.

The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics.

Broadly organized around the applications of Fourier analysis, Methods of Applied Mathematics with a MATLAB Overview covers both classical applications in partial differential equations and boundary value problems, as well as the concepts and methods associated to the Laplace, Fourier, and discrete transforms.

Arnold Sommerfeld's "e;Mathematische Theorie der Diffraction"e; marks a milestone in optical theory, full of insights that are still relevant today.

Advances in technology over the last 25 years have created a situation in which workers in diverse areas of computerscience and engineering have found it neces- sary to increase their knowledge of related fields in order to make further progress.

An outgrowth of The Seventh International Conference on Integral Methods in Science and Engineering, this book focuses on applications of integration-based analytic and numerical techniques.

Scientia Gratiii Scientiae It is now thirteen years since the first book that discusses transfinite graphs and elec- trical networks appeared [50].

This second edition of Generalized Functions has been strengthened in many ways.

Many partial differential equations (PDEs) that arise in physics can be viewed as infinite-dimensional Hamiltonian systems.

Quantization of physical systems requires a correct definition of quantum-mechanical observables, such as the Hamiltonian, momentum, etc.

Direct involvement with the subject area of the present work dates from my years with NASA at its Electronics Research Center (ERC) in Cambridge, M- sachusetts, in the 1960s.

Thesubjectofthisbookisthemodelingofcomplex systemsinthelife sciences constituted by a large number of interacting entities called active particles.

In modern theoretical physics, gauge field theories are of great importance since they keep internal symmetries and account for phenomena such as spontaneous symmetry breaking, the quantum Hall effect, charge fractionalization, superconductivity and supergravity.

Differential geometry, in the classical sense, is developed through the theory of smooth manifolds.

Fuchsian reduction is a method for representing solutions of nonlinear PDEs near singularities.

Conformal groups play a key role in geometry and spin structures.

Integral transforms, such as the Laplace and Fourier transforms, have been major tools in mathematics for at least two centuries.

This textbook is an introduction to the theory and applications of finite tight frames, an area that has developed rapidly in the last decade.

The Theory of the Top.

Classical mechanics is a chief example of the scientific method organizing a "e;complex"e;collection of information into theoretically rigorous, unifying principles; in this sense, mechanics represents one of the highest forms of mathematical modeling.

Steady progress in recent years has been made in understanding the special mathematical features of certain exactly solvable models in statistical mechanics and quantum field theory, including the scaling limits of the 2-D Ising (lattice) model, and more generally, a class of 2-D quantum fields known as holonomic fields.

The second in a series of three volumes surveying the theory of theta functions, this volume gives emphasis to the special properties of the theta functions associated with compact Riemann surfaces and how they lead to solutions of the Korteweg-de-Vries equations as well as other non-linear differential equations of mathematical physics.

Molecular Gas Dynamics originates from lectures and seminars delivered by the author at various universities and institutions worldwide.

TheTheory of the Top attained its great fame from both its monum- tal scope and its outstanding authors.

This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics- such as algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics- and in theoretical physics such as quantum field theory and string theory.

Riemannian Topology and Geometric Structures on Manifolds results from a similarly entitled conference held at the University of New Mexico in Albuquerque.

Algebra, Arithmetic, and Geometry: In Honor of Yu.

One of the most fundamental and active areas in mathematics, the theory of partial differential equations (PDEs) is essential in the modeling of natural phenomena.

More than ten years have passed since the book of F.

One of the most creative mathematicians of our times, Vladimir Drinfeld received the Fields Medal in 1990 for his groundbreaking contributions to the Langlands program and to the theory of quantum groups.

Hideki Omori is widely recognized as one of the world's most creative and original mathematicians.

This collection of original articles and surveys treats the linear and nonlinear aspects of the theory of partial differential equations.

This book is an elementary introduction to some ideas and techniques that have revolutionized enumerative geometry: stable maps and quantum cohomology.

This monograph presents a comprehensive treatment of important new ideas on Dirac operators and Dirac cohomology.

One of the key issues related to superfluidity is the existence of vortices.

Differential geometry, in the classical sense, is developed through the theory of smooth manifolds.

Homogenization is a method for modeling processes in microinhomogeneous media, which are encountered in radiophysics, filtration theory, rheology, elasticity theory, and other domains of mechanics, physics, and technology.

A tribute to the vision and legacy of Israel Moiseevich Gelfand, the invited papers in this volume reflect the unity of mathematics as a whole, with particular emphasis on the many connections among the fields of geometry, physics, and representation theory.

Ever since the analogy between number fields and function fields was discovered, it has been a source of inspiration for new ideas, and a long history has not in any way detracted from the appeal of the subject.

Themainobjectiveofthisbookistogiveacollectionofcriteriaavailablein the spectral theory of selfadjoint operators, and to identify the spectrum and its components in the Lebesgue decomposition.