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To solve them, they apply methods of Riemannian geometry, modern control theory, and the theory of localized wave packets, also known as Gaussian beams. The treatment includes the relevant background of each of these areas. Although the theory of inverse boundary spectral problems has been in development for at least 10 years, until now the literature has been scattered throughout various journals. This self-contained monograph summarizes the relevant concepts and the techniques useful for dealing with them. Enter your search terms. Advanced search Browse by: Inverse boundary spectral problems.

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In the view of many probabilists, author Anatolii Puhalskii's research results stand among the most significant achievements in the modern theory of large deviations. In fact, his work marked a turning point in the depth of our understanding of the connections between the large deviation principle….

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Melnikova , Alexei Filinkov. Although the theory of well-posed Cauchy problems is reasonably understood, ill-posed problems-involved in a numerous mathematical models in physics, engineering, and finance- can be approached in a variety of ways. Historically, there have been three major strategies for dealing with such problems…. This important new book sets forth a comprehensive description of various mathematical aspects of problems originating in numerical solution of hyperbolic systems of partial differential equations. The authors present the material in the context of the important mechanical applications of such….

By Bijan Kumar Bagchi. Following Witten's remarkable discovery of the quantum mechanical scheme in which all the salient features of supersymmetry are embedded, SCQM supersymmetric classical and quantum mechanics has become a separate area of research. In recent years, progress in this field has been dramatic and the…. Nonlinearity plays a major role in the understanding of most physical, chemical, biological, and engineering sciences.

Nonlinear problems fascinate scientists and engineers, but often elude exact treatment. However elusive they may be, the solutions do exist-if only one perseveres in seeking them…. Infinite dimensional representation theory blossomed in the latter half of the twentieth century, developing in part with quantum mechanics and becoming one of the mainstays of modern mathematics. Fundamentals of Infinite Dimensional Representation Theory provides an accessible account of the….

By Reinhard Racke , Song Jiang. Although the study of classical thermoelasticity has provided information on linear systems, only recently have results on the asymptotic behavior completed our basic understanding of the generic behavior of solutions. Through systematic work that began in the 80s, we now also understand the basic…. Carl , Seppo Heikkila.

Extremality results proved in this Monograph for an abstract operator equation provide the theoretical framework for developing new methods that allow the treatment of a variety of discontinuous initial and boundary value problems for both ordinary and partial differential equations, in explicit…. Chudinovich , Christian Constanda. Elastic plates form a class of very important mechanical structures that appear in a wide range of practical applications, from building bodies to microchip production.

As the sophistication of industrial designs has increased, so has the demand for greater accuracy in analysis. This in turn has…. Dynamic programming is a powerful method for solving optimization problems, but has a number of drawbacks that limit its use to solving problems of very low dimension. To overcome these limitations, author Rein Luus suggested using it in an iterative fashion. Although this method required vast…. With interest in the study of nonlinear systems at an all-time high, researchers are eager to explore the mysteries behind the nonlinear equations that govern various physical processes.

Singular Partial Differential Equations provides an analytical, constructive, and elementary approach to non-elementary problems. In the first monograph to consider such equations, the author investigates the solvability of partial differential equations and systems in a class of bounded functions…. By v Mityushev , S V Rogosin.

73 Series Titles

Constructive methods developed in the framework of analytic functions effectively extend the use of mathematical constructions, both within different branches of mathematics and to other disciplines. This monograph presents some constructive methods-based primarily on original techniques-for…. By Yakov Yakubov , Sasun Yakubov. The theory of differential-operator equations is one of two modern theories for the study of both ordinary and partial differential equations, with numerous applications in mechanics and theoretical physics.

Although a number of published works address differential-operator equations of the first…. Useful in physics, economics, psychology, and other fields, random matrices play an important role in the study of multivariate statistical methods. Until now, however, most of the material on random matrices could only be found scattered in various statistical journals.

The International Society for the Interaction of Mechanics and Mathematics has a long-standing and respected tradition of hosting symposia that provide a forum for disseminating new developments and methods. Trends in Applications of Mathematics to Mechanics represents the proceedings of the…. By Gordon E Swaters. Hamiltonian fluid dynamics and stability theory work hand-in-hand in a variety of engineering, physics, and physical science fields.

Until now, however, no single reference addressed and provided background in both of these closely linked subjects. Introduction to Hamiltonian Fluid Dynamics and…. The computational power currently available means that practitioners can find extremely accurate approximations to the solutions of more and more sophisticated mathematical models-providing they know the right analytical techniques. In relatively simple terms, this book describes a class of…. Despite decades of research and progress in the theory of generalized solutions to first-order nonlinear partial differential equations, a gap between the local and the global theories remains: The Cauchy characteristic method yields the local theory of classical solutions.

Statistical and Computational Inverse Problems Applied Mathematical Sciences v 160

Clifford analysis represents one of the most remarkable fields of modern mathematics. With the recent finding that almost all classical linear partial differential equations of mathematical physics can be set in the context of Clifford analysis-and that they can be obtained without applying any…. Edited by Heinrich Freistuhler. Systems of partial differential equations reflecting conservation laws hold significant relevance to a variety of theoretical and practical applications, including compressible fluid flow, electromagnetism, elasticity theory, and other areas of continuum mechanics.

This field of nonlinear analysis…. By Jiequan Li , Tong. Zhang , Shuli Yang. The Riemann problem is the most fundamental problem in the entire field of non-linear hyperbolic conservation laws. Since first posed and solved in , great progress has been achieved in the one-dimensional case.

Inverse Boundary Spectral Problems

However, the two-dimensional case is substantially different. Antonevich , Andrei V Lebedev , m. Together with the authors' Volume I. The two parts of…. By Dragisa Mitrovic , Darko Zubrinic. The discovery of chaotic motion in low-dimensional systems raised the question: What kind of thermodynamics describes a system if it is neither ergodic nor Hamiltonian or possesses a finite number of degrees of freedom? This Monographs is the first to discuss this question. The book consists of two parts. The first studies the geometry of indefinite metric spaces Krein and Pi kappa -spaces and describes….

Higher Order Derivatives 1st Edition By Satya Mukhopadhyay The concept of higher order derivatives is useful in many branches of mathematics and its applications. Sharma Filled with practical examples, Quasilinear Hyperbolic Systems, Compressible Flows, and Waves presents a self-contained discussion of quasilinear hyperbolic equations and systems with applications. Asymptotics and Borel Summability 1st Edition By Ovidiu Costin Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books.

Inverse Boundary Spectral Problems - CRC Press Book

Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications 1st Edition By Janusz Mierczynski , Wenxian Shen Providing a basic tool for studying nonlinear problems, Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications focuses on the principal spectral theory for general time-dependent and random parabolic equations and systems. Smooth Homogeneous Structures in Operator Theory 1st Edition By Daniel Beltita Geometric ideas and techniques play an important role in operator theory and the theory of operator algebras.

MacGregor Presenting new results along with research spanning five decades, Fractional Cauchy Transforms provides a full treatment of the topic, from its roots in classical complex analysis to its current state. Koksch This book introduces the class of dynamical systems called semiflows, which includes systems defined or modeled by certain types of differential evolution equations DEEs. Sachdev Understanding the causes and effects of explosions is important to experts in a broad range of disciplines, including the military, industrial and environmental research, aeronautic engineering, and applied mathematics.

Vermani Homological algebra was developed as an area of study almost 50 years ago, and many books on the subject exist. Jamison Fundamental to the study of any mathematical structure is an understanding of its symmetries. Hyperbolic Conservation Laws and the Compensated Compactness Method 1st Edition By Yunguang Lu The method of compensated compactness as a technique for studying hyperbolic conservation laws is of fundamental importance in many branches of applied mathematics. Vinogradova Although the analysis of scattering for closed bodies of simple geometric shape is well developed, structures with edges, cavities, or inclusions have seemed, until now, intractable to analytical methods.

1st Edition