[share_ebook] Mathematical Theory of Dispersion Managed Optical Solitons (repost)

This book introduces the reader to the area of inverse problems. The study of inverse problems is of vital interest to many areas of science and technology such as geophysical exploration, system identification, nondestructive testing and ultrasonic tomography.

The book covers three main topics: the classical theory of linear elasticity, the mathematical theory of composite elastic structures, as an application of the theory of elliptic equations on composite manifolds developed by the first author, and the finite element method for solving elastic structural problems.

This inter-disciplinary work covering the continuum mechanics of novel materials, condensed matter physics and partial differential equations discusses the mathematical theory of elasticity of quasicrystals (a new condensed matter) and its applications by setting up new partial differential equations of higher order and their solutions under complicated boundary value and initial value conditions. The new theories developed here dramatically simplify the solving of complicated elasticity equation systems. Large numbers of complicated equations involving elasticity are reduced to a single or a few partial differential equations of higher order. Systematical and direct methods of mathematical physics and complex variable functions are developed to solve the equations under appropriate boundary value and initial value conditions, and many exact analytical solutions are constructed.

ASTRONOMICAL ECLIPSE PHENOMENA In looking over the long history of human science from time immemorial to our own times, it is impossible to overestimate the role played in it by the phenomena of eclipses of the celestial bodies-both within our solar system as well as in the stellar universe at large. Not later than in the 4th century B. C. , the observed features of the shadow cast on the Moon by the Earth during eclipses led Aristotle (384-322 B. C. ) to formulate the first scientific proof worthy of that name of the spherical shape of the Earth; and only somewhat later, the eclipses of the Sun provided Aristarchos (in the early part of the 3rd century B. C. ) or Hipparchos (2nd half ofthe same century) with the geometric means to ascertain the distance which separates the Earth from the Sun. In the 17th century A. D. (in 1676, to be exact) the timings of the eclipses of the satellites of Jupiter by their central planet enabled Olaf Romer to discover that the velocity with which light propagates through space is finite.