Download or read book Phase integral approximations applied to problems concerning a particle in an exponential potential and systematization of the evaluation of integrals by the method of steepest descents written by Erik Walles and published by . This book was released on 1980 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Phase integral Approximations Applied to Problems Concerning a Particle in an Exponential Potential and Systematization of the Evaluation of Integrals by the Method of Steepest Decents written by Erik Walles and published by . This book was released on 1980 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Phase Integral Approximations Applied to Problems Concerning a Particle in an Exponential Potential and Sysematization of the Evaluation of Integrals by the Method of Steepest Descents written by Uppsala universitet. Matematisk-naturvetenskapliga fakulteten and published by . This book was released on 1980 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Phase integral Methods written by John Heading and published by . This book was released on 1962 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Contact Mechanics written by Valentin L. Popov and published by Springer. This book was released on 2019-04-26 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book contains a structured collection of the complete solutions of all essential axisymmetric contact problems. Based on a systematic distinction regarding the type of contact, the regime of friction and the contact geometry, a multitude of technically relevant contact problems from mechanical engineering, the automotive industry and medical engineering are discussed. In addition to contact problems between isotropic elastic and viscoelastic media, contact problems between transversal-isotropic elastic materials and functionally graded materials are addressed, too. The optimization of the latter is a focus of current research especially in the fields of actuator technology and biomechanics. The book takes into account adhesive effects which allow access to contact-mechanical questions about micro- and nano-electromechanical systems. Solutions of the contact problems include both the relationships between the macroscopic force, displacement and contact length, as well as the stress and displacement fields at the surface and, if appropriate, within the half-space medium. Solutions are always obtained with the simplest available method - usually with the method of dimensionality reduction (MDR) or approaches which use the solution of the non-adhesive normal contact problem to solve the respective contact problem.
Download or read book Rigorous Time Slicing Approach to Feynman Path Integrals written by Daisuke Fujiwara and published by Springer. This book was released on 2018-08-15 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book proves that Feynman's original definition of the path integral actually converges to the fundamental solution of the Schrödinger equation at least in the short term if the potential is differentiable sufficiently many times and its derivatives of order equal to or higher than two are bounded. The semi-classical asymptotic formula up to the second term of the fundamental solution is also proved by a method different from that of Birkhoff. A bound of the remainder term is also proved.The Feynman path integral is a method of quantization using the Lagrangian function, whereas Schrödinger's quantization uses the Hamiltonian function. These two methods are believed to be equivalent. But equivalence is not fully proved mathematically, because, compared with Schrödinger's method, there is still much to be done concerning rigorous mathematical treatment of Feynman's method. Feynman himself defined a path integral as the limit of a sequence of integrals over finite-dimensional spaces which is obtained by dividing the time interval into small pieces. This method is called the time slicing approximation method or the time slicing method.This book consists of two parts. Part I is the main part. The time slicing method is performed step by step in detail in Part I. The time interval is divided into small pieces. Corresponding to each division a finite-dimensional integral is constructed following Feynman's famous paper. This finite-dimensional integral is not absolutely convergent. Owing to the assumption of the potential, it is an oscillatory integral. The oscillatory integral techniques developed in the theory of partial differential equations are applied to it. It turns out that the finite-dimensional integral gives a finite definite value. The stationary phase method is applied to it. Basic properties of oscillatory integrals and the stationary phase method are explained in the book in detail.Those finite-dimensional integrals form a sequence of approximation of the Feynman path integral when the division goes finer and finer. A careful discussion is required to prove the convergence of the approximate sequence as the length of each of the small subintervals tends to 0. For that purpose the book uses the stationary phase method of oscillatory integrals over a space of large dimension, of which the detailed proof is given in Part II of the book. By virtue of this method, the approximate sequence converges to the limit. This proves that the Feynman path integral converges. It turns out that the convergence occurs in a very strong topology. The fact that the limit is the fundamental solution of the Schrödinger equation is proved also by the stationary phase method. The semi-classical asymptotic formula naturally follows from the above discussion.A prerequisite for readers of this book is standard knowledge of functional analysis. Mathematical techniques required here are explained and proved from scratch in Part II, which occupies a large part of the book, because they are considerably different from techniques usually used in treating the Schrödinger equation.
Download or read book Functional Analysis Entering Hilbert Space Second Edition written by Vagn Lundsgaard Hansen and published by World Scientific Publishing Company. This book was released on 2015-12-01 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents basic elements of the theory of Hilbert spaces and operators on Hilbert spaces, culminating in a proof of the spectral theorem for compact, self-adjoint operators on separable Hilbert spaces. It exhibits a construction of the space of pth power Lebesgue integrable functions by a completion procedure with respect to a suitable norm in a space of continuous functions, including proofs of the basic inequalities of Hölder and Minkowski. The Lp-spaces thereby emerges in direct analogy with a construction of the real numbers from the rational numbers. This allows grasping the main ideas more rapidly. Other important Banach spaces arising from function spaces and sequence spaces are also treated.In this second edition, I have expanded the material on normed vector spaces and their operators presented in Chapter 1 to include proofs of the Open Mapping Theorem, the Closed Graph Theorem and the Hahn-Banach Theorem. The material on operators between normed vector spaces is further expanded in a new Chapter 6, which presents the basic elements of the theory of Fredholm operators on general Banach spaces, not only on Hilbert spaces. This requires that we develop the theory of dual operators between Banach spaces to replace the use of adjoint operators between Hilbert spaces.With the addition of the new material on normed vector spaces and their operators, the book can serve as a general introduction to functional analysis viewed as a theory of infinite dimensional linear spaces and linear operators acting on them.
Download or read book Handbook of X Ray Data written by Günter H. Zschornack and published by Springer Science & Business Media. This book was released on 2007-01-24 with total page 969 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the only handbook available on X-ray data. In a concise and informative manner, the most important data connected with the emission of characteristic X-ray lines are tabulated for all elements up to Z = 95 (Americium). The tabulated data are characterized and, in most cases, evaluated. Furthermore, all important processes and phenomena connected with the production, emission and detection of characteristic X-rays are discussed.
Download or read book Chemical Reactor Analysis and Design written by Gilbert F. Froment and published by . This book was released on 1990-01-16 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the Second Edition of the standard text on chemical reaction engineering, beginning with basic definitions and fundamental principles and continuing all the way to practical applications, emphasizing real-world aspects of industrial practice. The two main sections cover applied or engineering kinetics, reactor analysis and design. Includes updated coverage of computer modeling methods and many new worked examples. Most of the examples use real kinetic data from processes of industrial importance.
Download or read book Bulletin of the Atomic Scientists written by and published by . This book was released on 1970-12 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Bulletin of the Atomic Scientists is the premier public resource on scientific and technological developments that impact global security. Founded by Manhattan Project Scientists, the Bulletin's iconic "Doomsday Clock" stimulates solutions for a safer world.
Download or read book Contact Problems written by L. A. Galin and published by Springer Science & Business Media. This book was released on 2008-12-31 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: L.A. Galin’s book on contact problems is a remarkable work. Actually there are two books: the first, published in 1953 deals with contact problems in the classical theory of elasticity; this is the one that was translated into English in 1961. The second book, published in 1980, included the first, and then had new sections on contact problems for viscoelastic materials, and rough contact problems; this section has not previously been translated into English. In this new translation, the original text and the mathematical analysis have been completely revised, new material has been added, and the material appearing in the 1980 Russian translation has been completely rewritten. In addition there are three essays by students of Galin, bringing the analysis up to date.
Download or read book Nuclear Geophysics and Its Applications written by International Atomic Energy Agency and published by . This book was released on 1999 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This report aims at providing background information and a comprehensive account of the nature of nuclear geophysics, its fundamentals, its objectives, its tools for investigation and its wide range of applications benefiting society and industry. It reviews the achievements and performance of nuclear geophysical measurements, particularly in applications to mining, industry and agriculture. It also analyses many of these important applications for their economic impact and updates the available information on nuclear geophysics by giving an account of the most relevant achievements and concepts introduced during recent years.
Download or read book Introduction to Quantum Metrology written by Waldemar Nawrocki and published by Springer. This book was released on 2015-03-24 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the theory of quantum effects used in metrology and results of the author’s own research in the field of quantum electronics. The book provides also quantum measurement standards used in many branches of metrology for electrical quantities, mass, length, time and frequency. This book represents the first comprehensive survey of quantum metrology problems. As a scientific survey, it propagates a new approach to metrology with more emphasis on its connection with physics. This is of importance for the constantly developing technologies and nanotechnologies in particular. Providing a presentation of practical applications of the effects used in quantum metrology for the construction of quantum standards and sensitive electronic components, the book is useful for a wide audience of physicists and metrologists in the broad sense of both terms. In 2014 a new system of units, the so called Quantum SI, is introduced. This book helps to understand and approve the new system to both technology and academic community.
Download or read book Worlds of Flow written by Olivier Darrigol and published by Oxford University Press. This book was released on 2005-09 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the first fully-fledged history of hydrodynamics, including lively accounts of the concrete problems of hydraulics, navigation, blood circulation, meteorology, and aeronautics that motivated the main conceptual innovations. Richly illustrated, technically competent, and philosophically sensitive, it should attract a broad audience and become a standard reference for any one interested in fluid mechanics.
Download or read book Optimum Signal Processing written by Sophocles J. Orfanidis and published by . This book was released on 2007 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book NASA Glenn Coefficients for Calculating Thermodynamic Properties of Individual Species written by Bonnie J. McBride and published by . This book was released on 2002 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Physics of Tsunamis written by Boris Levin and published by Springer Science & Business Media. This book was released on 2008-10-27 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Till the very end of the twentieth century tsunami waves (or ‘waves in a harbour’, translated from Japanese) were considered an extremely rare and exotic natural p- nomenon, originating in the ocean and unexpectedly falling upon the seaside as gigantic waves. The 26th of December 2004, when tsunami waves wiped out, in a single day, more than 250,000 human lives, mourned in many countries, turned out to be a tragic date for all mankind. The authors of this book, who have studied tsunami waves for many years, - tended it to be a systematic exposition of modern ideas concerning • The mechanisms of tsunami wave generation • The peculiarities of tsunami wave propagation in the open ocean and of how waves run-up beaches • Methods for tsunami wave registration and the operation of a tsunami warning system • The mechanisms of other catastrophic processes in the ocean related to the se- mic activity of our planet The authors considered their main goal to be the creation of book prese- ing modern knowledge of tsunami waves and of other catastrophes in the ocean to scienti?c researchers and specialists in geophysics, oceanography, seismology, hydroacoustics, geology, geomorphology, civil and seaside engineering, postgr- uate students and students of relevant professions.
