Elements of the Random Walk: An introduction for Advanced Students and Researchers
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Author: Joseph Rudnick
Brand: Brand: Cambridge University Press

Random walks have proven to be a useful model in understanding processes across a wide spectrum of scientific disciplines. This book is an introduction to some of the most powerful and general techniques used in the application of these ideas. Its selfcontained text will appeal to graduate students across science, engineering and mathematics who need to understand the applications of random walk techniques, as well as to established researchers.
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From Pythagoras to Einstein
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Author: K. O. Friedrichs
Brand: Brand: Mathematical Assn of Amer

The main thread running through this somewhat unorthodox approach to the special theory of relativity is the Pythagorean theorem. It appears in its most elementary geometric form in the very beginning of this monograph. Then it reappears in algebraic garb, is further modified and finally reinterpreted to play the role of one of the main characters in the special theory of relativity. The first four chapters are easily accessible to high school sophmores or juniors. the remaining part of the book may be a little difficult for students who never studied physics, although the author actually employs only the notion of impact and presupposes no background in physics. With the aid of the vector geometry introduced earlier, he leads the reader from the impact conversation laws to the famous formula e=mc2.
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Kalman Filtering: With RealTime Applications
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Author: C.K. Chui

"Kalman Filtering with RealTime Applications" presents a thorough discussion of the mathematical theory and computational schemes of Kalman filtering. The filtering algorithms are derived via different approaches, including a direct method consisting of a series of elementary steps, and an indirect method based on innovation projection. Other topics include Kalman filtering for systems with correlated noise or colored noise, limiting Kalman filtering for timeinvariant systems, extended Kalman filtering for nonlinear systems, interval Kalman filtering for uncertain systems, and wavelet Kalman filtering for multiresolution analysis of random signals. The last two topics are new additions to this third edition. Most filtering algorithms are illustrated by using simplified radar tracking examples. The style of the book is informal, and the mathematics is elementary but rigorous. The text is selfcontained, suitable for selfstudy, and accessible to all readers with a minimum knowledge.
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Generalized Coherent States and Their Applications (Texts and Monographs in Physics)
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Author: A. Perelomov
Brand: Brand: SpringerVerlag

This monograph treats an extensively developed field in modern mathematical physics  the theory of generalized coherent states and their applications to various physical problems. Coherent states, introduced originally by Schrodinger and von Neumann, were later employed by Glauber for a quantal description of laser light beams. The concept was generalized by the author for an arbitrary Lie group. In the last decade the formalism has been widely applied to various domains of theoretical physics and mathematics. The area of applications of generalized coherent states is very wide, and a comprehensive exposition of the results in the field would be helpful. This monograph is the first attempt toward this aim. My purpose was to compile and expound systematically the vast amount of material dealing with the coherent states and available through numerous journal articles. The book is based on a number of undergraduate and postgraduate courses I delivered at the Moscow PhysicoTechnical Institute. In its present form it is intended for professional mathematicians and theoretical physicists; it may also be useful for university students of mathematics and physics. In Part I the formalism is elaborated and explained for some of the simplest typical groups. Part II contains more sophisticated material; arbitrary Lie groups and symmetrical spaces are considered. A number of examples from various areas of theoretical and mathematical physics illustrate advantages of this approach, in Part III. It is a pleasure for me to thank Dr. Yu. Danilov for many useful remarks.
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Fundamentals of the Finite Element Method
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Author: Hartley, Jr. Grandin

The basic concepts of the finite element method are presented in a clear and logical manner. The first chapter offers a brief discussion of matrix analysis of structures and is designed to establish a working knowledge of the matrix operations common to finite element solution procedures. The finite element method is then introduced as a discretized application of the RayleighRitz method using the energy functional of the uniaxial elasticity problem. The method's applicability to other physical problems is set forth with an introduction to variational calculus and the derivation of the functionals corresponding to the differential equations of these problems. Finally, the Galerkin weighted residual method is developed as an alternative technique.


Geocubic Cosmology
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Author: Tom Gilmore
Brand: Brand: Mini Novel Pub

A fully developed geometric model is presented with 3dimensional illustrations of all the atomic elements, accounting for the chemical properties of valence, isotope, and crystal lattice structure. The 4 basic forces (strong atomic force, weak atomic force, electromagnetism and gravity) are unified for the first time, and the paradox of time's arrow is resolved, in this longawaited "theory of everything".
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Applied Integral Transforms (Crm Monograph Series)
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Author: M. Ya. Antimirov
Brand: Brand: Amer Mathematical Society

This book does what few books on integral transforms do: it constructs the kernels of the integral transforms by solving the generalized SturmLiouville problems associated with the partial differential equations at hand. In the first part of the book, the authors construct the kernels and then use them to solve elementary problems of mathematical physics. This section, which proceeds mainly by examples and includes exercises, requires little mathematical background and provides an introduction to the subject of integral transforms. In the second part of the book, the method of integral transforms is used to solve modern applied problems in convective stability, temperature fields in oil strata, and eddy current testing. The choice of topics reflects the authors' research experience and involvement in industrial applications. The first part of the book is accessible to undergraduates, while the second part is aimed more at graduate students and researchers. Because of the applications it discusses, the book will interest engineers (especially petroleum engineers) and physicists.
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Viscous Vortical Flows (Lecture Notes in Physics)
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Author: Lu Ting

This monograph provides indepth analyses of vortex dominated flows via matched and multiscale asymptotics, and demonstrates how insight gained through these analyses can be exploited in the construction of robust, efficient, and accurate numerical techniques. The book explores the dynamics of slender vortex filaments in detail, including fundamental derivations, compressible core structure, weakly nonlinear limit regimes, and associated numerical methods. Similarly, the volume covers asymptotic analysis and computational techniques for weakly compressible flows involving vortexgenerated sound and thermoacoustics. The book is addressed to both graduate students and researchers.


Geometry and Theoretical Physics
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Author: J. Debrus

The interaction between geometry and theoretical physics has often been very fruitful. A highlight in this century was Einstein's creation of the theory of general relativity. Equally impressive was the recognition, starting from the work of Yang and Mills and culminating in the WeinbergSalam theory of the electroweak interaction and quantum chromodynamics, that the fundamental interactions of elementary particles are governed by gauge fields, which in ma thematical terms are connections in principal fibre bundles. Theoretical physi cists became increasingly aware of the fact that the use of modern mathematical methods may be necessary in the treatment of problems of physical interest. Since some of these topics are covered at most summarily in the usual curricu lum, there is a need for extracurricular efforts to provide an opportunity for learning these techniques and their physical applications. In this context we arranged a meeting at the Physikzentrum Bad Ronnef 1216 February 1990 on the subject "Geometry and Theoretical Physics", in the series of physics schools organized by the German Physical Society. The participants were graduate students from German universities and research institutes. Since the meeting occurred only a short time after freedom of travel between East and West Germany became a reality, this was for many from the East the first opportunity to attend a scientific meeting in the West, and for many from the West the first chance to become personally acquainted with colleagues from the East.


Inverse Schrodinger Scattering in Three Dimensions (Texts and Monographs in Physics)
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Author: Roger G. Newton

Most of the laws of physics are expressed in the form of differential equations; that is our legacy from Isaac Newton. The customary separation of the laws of nature from contingent boundary or initial conditions, which has become part of our physical intuition, is both based on and expressed in the properties of solutions of differential equations. Within these equations we make a further distinction: that between what in mechanics are called the equations of motion on the one hand and the specific forces and shapes on the other. The latter enter as given functions into the former. In most observations and experiments the "equations of motion," i. e. , the structure of the differential equations, are taken for granted and it is the form and the details of the forces that are under investigation. The method by which we learn what the shapes of objects and the forces between them are when they are too small, too large, too remote, or too inaccessi ble for direct experimentation, is to observe their detectable effects. The question then is how to infer these properties from observational data. For the theoreti cal physicist, the calculation of observable consequences from given differential equations with known or assumed forces and shapes or boundary conditions is the standard task of solving a "direct problem. " Comparison of the results with experiments confronts the theoretical predictions with nature.

