Differential forms satisfying the A-harmonic equations have found wide applications in fields such as general relativity, theory of elasticity, quasiconformal analysis, differential geometry, and nonlinear differential equations in domains on manifolds.
Our motivation for writing this book is twofold: First, the theory of waves propagating in randomly layered media has been studied extensively during the last thirty years but the results are scattered in many di?
For many years, first as a student and later as a teacher, I have ob- served graduate students in ecology and other environmental sci- ences who had been required as undergraduates to take calculus courses.
Although some examples of phase portraits of quadratic systems can already be found in the work of Poincare, the first paper dealing exclusively with these systems was published by Buchel in 1904.
Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary.
Since the birth of the calculus of variations, researchers have discovered that variational methods, when they apply, can obtain better results than most other methods.
In this new text, designed for sophomores studying mathematics and computer science, the authors cover the basics of difference equations and some of their applications in computing and in population biology.
Perturbation theory, one of the most intriguing and essential topics in mathematics, and its applications to the natural and engineering sciences is the main focus of this workbook.
Since the publication of our first book [80], there has been a real resiu-gence of interest in the study of almost automorphic functions and their applications ([16, 17, 28, 29, 30, 31, 32, 40, 41, 42, 46, 51, 58, 74, 75, 77, 78, 79]).
This volume, "e;Theory and Applications of Special Functions,"e; is d- icated to Mizan Rahman in honoring him for the many important c- tributions to the theory of special functions that he has made over the years, and still continues to make.
At present, in order to resolve problems of ecology and to save mineral resources for future population generations, it is quite necessary to know how to maintain nature arrangement in an efficient way.
Inverse Problems is a monograph which contains a self-contained presentation of the theory of several major inverse problems and the closely related results from the theory of ill-posed problems.
The importance of mathematics in the study of problems arising from the real world, and the increasing success with which it has been used to model situations ranging from the purely deterministic to the stochastic, is well established.
The basic stochastic approximation algorithms introduced by Robbins and MonroandbyKieferandWolfowitzintheearly1950shavebeenthesubject of an enormous literature, both theoretical and applied.
The book provides a comprehensive, detailed and self-contained treatment of the fundamental mathematical properties of boundary-value problems related to the Navier-Stokes equations.
