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Evaluating Feynman Integrals
The problem of evaluating Feynman integrals over loop momenta has existed from the early days of perturbative quantum field theory. Although a great variety of methods for evaluating Feynman integrals has been developed over a span of more than fifty years, this book is a first attempt to summarize them. Evaluating Feynman Integrals characterizes the most powerful methods, in particular those used for recent, quite sophisticated calculations, and then illustrates them with numerous examples, starting from very simple ones and progressing to nontrivial examples.
Introduction to the Theory of Differential Inclusions
A differential inclusion is a relation of the form $dot x in F(x)$, where $F$ is a set-valued map associating any point $x in R^n$ with a set $F(x) subset R^n$. As such, the notion of a differential inclusion generalizes the notion of an ordinary differential equation of the form $dot x = f(x)$. Therefore, all problems usually studied in the theory of ordinary differential equations (existence and continuation of solutions, dependence on initial conditions and parameters, etc.) can be studied for differential inclusions as well. Since a differential inclusion usually has many solutions starting at a given point, new types of problems arise, such as investigation of topological properties of ...
Introduction to the Biophysics of Activated Water
This is the first book to reveal the mechanism of 'long-term water memory' effects. The theory is based on precise mathematical calculations and a fundamental physical model of clathrate hydrates developed by Pauling in 1959. This book gives a detailed review of modern theories dealing with structure and properties of water. It also provides theory regarding the effect of activated water on biological systems under the life suppressive conditions such as ionizing and non-ionizing radiation. In addition, it provides detail information regarding the mechanism of DNA self-reparation process under the influence of activated water. Also included is a chapter on the innovative patented technology based on mechanism of 'long-term water memory' to prove the feasilibity with experimental data and protocols.
Heavy Quark Effective Theory
This up-to-date review also serves as an introduction to Heavy Quark Effective Theory (HQET) - a new approach to heavy quark physics problems in Quantum Chromodynamics (QCD). The book also contains a detailed discussion of the methods of calculation used in HQET, along with numerous illustrations.
Stabilization Problems with Constraints
Presents and demonstrates stabilizer design techniques that can be used to solve stabilization problems with constraints. These methods have their origins in convex programming and stability theory. However, to provide a practical capability in stabilizer design, the methods are tailored to the special features and needs of this field. Hence, the main emphasis of this book is on the methods of stabilization, rather than optimization and stability theory. The text is divided into three parts. Part I contains some background material. Part II is devoted to behavior of control systems, taking examples from mechanics to illustrate the theory. Finally, Part III deals with nonlocal stabilization problems, including a study of the global stabilization problem.
A Course of Higher Mathematics
A Course of Higher Mathematics, Volume II: Advanced Calculus covers the theory of functions of real variable in advanced calculus. This volume is divided into seven chapters and begins with a full discussion of the solution of ordinary differential equations with many applications to the treatment of physical problems. This topic is followed by an account of the properties of multiple integrals and of line integrals, with a valuable section on the theory of measurable sets and of multiple integrals. The subsequent chapters deal with the mathematics necessary to the examination of problems in classical field theories in vector algebra and vector analysis and the elements of differential geometry in three-dimensional space. The final chapters explore the Fourier series and the solution of the partial differential equations of classical mathematical physics. This book will prove useful to advanced mathematics students, engineers, and physicists.
Applied Biophysics Of Activated Water: The Physical Properties, Biological Effects And Medical Applications Of Mret Activated Water
This book provides a detailed review of the modern theories dealing with the structure and properties of water. It also presents an analysis of the research on the effect of activated water on biological systems such as animals, microorganisms, and plants. The results of experiments on the influence of activated water on “pure” microbiological cultures and their natural associations are described, the studies being carried out under both aerobic and anaerobic conditions.The results demonstrate a significant influence of activated water on higher plants (vegetable crops), sterile plants, and callus tissues. It is shown that the activation of water under definite conditions gives rise to t...
