Book Description
This collection contains papers by participants in the Seminar onMathematical Physics in Kharkov, Ukraine. The papers mainlyfocus on nontraditional problems of spectral theory, such as newtypes of inverse problems for one-dimensional differentialoperators, new classes of solutions to nonlinear differentialequations obtained using spectral methods, distribution ofeigenvalues of large random matrices, and related problems ofstatistical physics of disordered systems. In addition, thepapers explore the spectral aspects of homogenization and ofproperties of ergodic dynamical systems. All the papers containoriginal results published for the first time. ... Read more

Product Description
This is the first monograph devoted to the Sturm oscillatory theory for infinite systems of differential equations and its relations with the spectral theory. It aims to study a theory of self-adjoint problems for such systems, based on an elegant method of binary relations. Another topic investigated in the book is the behavior of discrete eigenvalues which appear in spectral gaps of the Hill operator and almost periodic Schrödinger operators due to local perturbations of the potential (e.g., modeling impurities in crystals).The book is based on results that have not been presented in other monographs. The only prerequisites needed to read it are basics of ordinary differential equations and operator theory. It should be accessible to graduate students, though its main topics are of interest to research mathematicians working in functional analysis, differential equations and mathematical physics, as well as to physicists interested in spectral theory of differential operators. ... Read more

Book Description

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. These processes are described by PDEs with rapidly oscillating coefficients or boundary value problems in domains with complex microstructure. From the technical point of view, given the complexity of these processes, the best techniques to solve a wide variety of problems involve constructing appropriate macroscopic (homogenized) models.