Download or read book Invariant Imbedding and Wave Propagation in Stochastic Media written by Richard Bellman and published by . This book was released on 1958 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principle of invariant imbedding leads to the formulation of various functional equations describing plane wave propagation in stochastic media. The approach involves first the derivation of stochastic functional equations for reflection and transmission coefficients, followed by the taking of expected values of appropriate functions of the random state variables. This makes possible the determination of their characteristic functions and distribution functions, by means of still other functional equations, or by computational schemes of the Monte Carlo type. The particular example in which a plane wave is incident on a stratified slab which is characterized by stochastic wave numbers in each stratum is discussed. The distribution functions for the amplitude of the random reflected and transmitted waves are then determined as functions of the thickness of the slab. The effects of multiple scattering are taken into account.
Download or read book Stochastic Wave Propagation written by K. Sobczyk and published by Elsevier. This book was released on 2012-12-02 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a concise, unified exposition of the existing methods of analysis of linear stochastic waves with particular reference to the most recent results. Both scalar and vector waves are considered. Principal attention is concentrated on wave propagation in stochastic media and wave scattering at stochastic surfaces. However, discussion extends also to various mathematical aspects of stochastic wave equations and problems of modelling stochastic media.
Download or read book Invariant Imbedding written by R.E. Bellman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: Imbedding is a powerful and versatile tool for problem solving. Rather than treat a question in isolation, we view it as a member of a family of related problems. Each member then becomes a stepping stone in a path to a simultaneous solution of the entire set of problems. As might be expected, there are many ways of accomplishing this imbedding. Time and space variables have been widely employed in the past, while modern approaches combine these structural features with others less immediate. Why should one search for alternate imbeddings when elegant classical formalisms already exist? There are many reasons. To begin with, different imbeddings are useful for different purposes. Some are well suited to the derivation of existence and uniqueness theorems, some to the derivation of conservation relations, some to perturbation techniques and sensitivity analysis, some to computa tional studies. The digital computer is designed for initial value problems; the analog computer for boundary-value problems. It is essential then to be flexible and possess the ability to use one device or the other, or both. In economics, engineering, biology and physics, some pro cesses lend themselves more easily to one type of imbedding rather than another. Thus, for example, stochastic decision processes are well adapted to dynamic programming. In any case, to go hunting in the wilds of the scientific world armed with only one arrow in one's quiver is quite foolhardy.
Download or read book Wave Propagation written by N.D. Bellman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The SCQlldIII of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gu!ik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with . physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They· draw upon widely different sections of mathematics.
Download or read book Invariant Imbedding and Wave Propagation in Inhomgeneous Media written by Crawford J. MacCallum and published by . This book was released on 1961 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Invariant Imbedding and Wave Propagation in Inhomogeneous Media written by Crawford J. MacCallum and published by . This book was released on 1961 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Invariant Imbedding and Radiative Transfer in Slabs of Finite Thickness written by Richard Bellman and published by . This book was released on 1963 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book NBS Technical Note written by and published by . This book was released on 1965-04 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Processes in Mathematical Physics and Engineering written by Richard Ernest Bellman and published by American Mathematical Soc.. This book was released on 1964-12-31 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Systems written by Adomian and published by Academic Press. This book was released on 1983-07-29 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Systems
Download or read book Journal of Research written by United States. National Bureau of Standards and published by . This book was released on 1964 with total page 1354 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Application of Invariant Imbedding Techniques to Wave Propagation Through Turbulent Media written by and published by . This book was released on 1991 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Journal of Research National Bureau of Standards written by United States. National Bureau of Standards and published by . This book was released on 1964 with total page 1400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Invariant Imbedding Techniques Used to Solve Wave Propagation in a Horizontally Stratified Plasma Media written by Hugh Alfred Davies and published by . This book was released on 1969 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Bellman Continuum written by Robert S Roth and published by World Scientific. This book was released on 1987-02-01 with total page 895 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of some of the most significant mathematical works of Prof Richard E Bellman. Ten areas of Prof Bellman's mathematical research were selected by his co-workers for this volume. Each chapter starts with an introductory comment on the significance of Bellman's contribution. Some important mathematical theories are put forward and their applications in physics and biology such as the mathematical aspect of chemotherapy and the analysis of biological systems are included in this book.
Download or read book Introduction to Matrix Analysis written by Richard Bellman and published by SIAM. This book was released on 1997-12-01 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: Long considered to be a classic in its field, this was the first book in English to include three basic fields of the analysis of matrices -- symmetric matrices and quadratic forms, matrices and differential equations, and positive matrices and their use in probability theory and mathematical economics. Written in lucid, concise terms, this volume covers all the key aspects of matrix analysis and presents a variety of fundamental methods. Originally published in 1970, this book replaces the first edition previously published by SIAM in the Classics series. Here you will find a basic guide to operations with matrices and the theory of symmetric matrices, plus an understanding of general square matrices, origins of Markov matrices and non-negative matrices in general, minimum- maximum characterization of characteristic roots, Krnoecker products, functions of matrices, and much more. These ideas and methods will serve as powerful analytical tools. In addition, this volume includes exercises of all levels of difficulty and many references to original papers containing further results. The problem sections contain many useful and interesting results that are not easily found elsewhere. A discussion of the theoretical treatment of matrices in the computational solution of ordinary and partial differential equations, as well as important chapters on dynamic programming and stochastic matrices are also included.
Download or read book OAR written by and published by . This book was released on 1969 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:
