Vladimir Semenov - Böcker

"Generalized Solutions of Operator Equations and Extreme Elements" presents recently obtained results in the study of the generalized solutions of operator equations and extreme elements in linear topological spaces.

Abstract models for many problems in science and engineering take the form of an operator equation. The resolution of these problems often requires determining the existence and uniqueness of solutions to these equations. "Generalized Solutions of Operator Equations and Extreme Elements" presents recently obtained results in the study of the generalized solutions of operator equations and extreme elements in linear topological spaces. The presented results offer new methods of identifying these solutions and studying their properties. These new methods involve the application of a priori estimations and a general topological approach to construct generalized solutions of linear and nonlinear operator equations. The monograph is intended for mathematicians, graduate students and researchers studying functional analysis, operator theory, and the theory of optimal control.

This book presents advanced methods for the electronic modeling of dynamical systems governed by ordinary differential equations. It offers a comprehensive toolkit and practical solutions for specialists in nonlinear dynamics who seek experimental validation of their mathematical models.

At the heart of this book is the generalized theoretical approach that is applied to investigate the geoelectrical structure of the Earth’s mantle. It also analyzes the results of regional and global induction sounding of the Earth’s mantle and compares them with the results obtained by other geophysical methods. The generalized theoretical approach employs the Induction Law as a basis for identifying extended relations between magnetic field components, including their plane divergence, impedances and spatial derivatives. The estimations of impedance values and spatial derivatives are performed using the theory of stochastic processes. The book also considers the external sources of magnetic fields used for sounding the Earths mantle from the modern theory perspective, as well as the problem of coincidence of magneto-variation and magnetotelluric methods. Further, it discusses secular variations in the Earth’s resistance caused by non-induction sources, factors that are correlatedwith the number of earthquakes in the region and shifted in time with global indexes. It is a valuable resource for scientists applying deep induction soundings or interested in the structures of and processes in the Earth’s interior.