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| Author | : M. M. Skriganov |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 132 |
| Release | : 1987 |
| Genre | : Mathematics |
| ISBN | : 9780821831045 |
| Author | : Maksim M. Skriganov |
| Publisher | : |
| Total Pages | : 121 |
| Release | : 1985 |
| Genre | : |
| ISBN | : |
| Author | : Oktay Veliev |
| Publisher | : Springer Nature |
| Total Pages | : 420 |
| Release | : |
| Genre | : |
| ISBN | : 3031490355 |
| Author | : Matthias Keller |
| Publisher | : Cambridge University Press |
| Total Pages | : 493 |
| Release | : 2020-08-20 |
| Genre | : Mathematics |
| ISBN | : 1108587380 |
This book addresses the interplay between several rapidly expanding areas of mathematics. Suitable for graduate students as well as researchers, it provides surveys of topics linking geometry, spectral theory and stochastics.
| Author | : Christian Constanda |
| Publisher | : Springer Nature |
| Total Pages | : 361 |
| Release | : 2022-10-13 |
| Genre | : Mathematics |
| ISBN | : 3031071719 |
This contributed volume contains a collection of articles on state-of-the-art developments on the construction of theoretical integral techniques and their application to specific problems in science and engineering. Chapters in this book are based on talks given at the Symposium on the Theory and Applications of Integral Methods in Science and Engineering, held virtually in July 2021, and are written by internationally recognized researchers. This collection will be of interest to researchers in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines and other professionals for whom integration is an essential tool.
| Author | : Gang Bao |
| Publisher | : SIAM |
| Total Pages | : 349 |
| Release | : 2001-01-01 |
| Genre | : Science |
| ISBN | : 9780898717594 |
This volume addresses recent developments in mathematical modeling in three areas of optical science: diffractive optics, photonic band gap structures, and waveguides. Particular emphasis is on the formulation of mathematical models and the design and analysis of new computational approaches. The book contains cutting-edge discourses on emerging technology in optics that provides significant challenges and opportunities for applied mathematicians, researchers, and engineers.
| Author | : Habib Ammari |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 509 |
| Release | : 2018-10-15 |
| Genre | : Photonics |
| ISBN | : 1470448009 |
The fields of photonics and phononics encompass the fundamental science of light and sound propagation and interactions in complex structures, as well as its technological applications. This book reviews new and fundamental mathematical tools, computational approaches, and inversion and optimal design methods to address challenging problems in photonics and phononics. An emphasis is placed on analyzing sub-wavelength resonators, super-focusing and super-resolution of electromagnetic and acoustic waves, photonic and phononic crystals, electromagnetic cloaking, and electromagnetic and elastic metamaterials and metasurfaces. Throughout this book, the authors demonstrate the power of layer potential techniques for solving challenging problems in photonics and phononics when they are combined with asymptotic analysis. This book might be of interest to researchers and graduate students working in the fields of applied and computational mathematics, partial differential equations, electromagnetic theory, elasticity, integral equations, and inverse and optimal design problems in photonics and phononics.
| Author | : Peter Kuchment |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 232 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 0821832867 |
Science and engineering have been great sources of problems and inspiration for generations of mathematicians. This is probably true now more than ever as numerous challenges in science and technology are met by mathematicians. One of these challenges is understanding propagation of waves of different nature in systems of complex structure. This book contains the proceedings of the research conference, ``Waves in Periodic and Random Media''. Papers are devoted to a number of related themes, including spectral theory of periodic differential operators, Anderson localization and spectral theory of random operators, photonic crystals, waveguide theory, mesoscopic systems, and designer random surfaces. Contributions are written by prominent experts and are of interest to researchers and graduate students in mathematical physics.
| Author | : Gregory Berkolaiko |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 291 |
| Release | : 2013 |
| Genre | : Mathematics |
| ISBN | : 0821892118 |
A ``quantum graph'' is a graph considered as a one-dimensional complex and equipped with a differential operator (``Hamiltonian''). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., ``meso-'' or ``nano-scale'') system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on quantum graphs has brought together tools and intuition coming from graph theory, combinatorics, mathematical physics, PDEs, and spectral theory. This book provides a comprehensive introduction to the topic, collecting the main notions and techniques. It also contains a survey of the current state of the quantum graph research and applications.
| Author | : Sergio Albeverio |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 506 |
| Release | : 2005 |
| Genre | : Science |
| ISBN | : 0821836242 |
"This monograph presents a detailed study of a class of solvable models in quantum mechanics that describe the motion of a particle in a potential having support at the positions of a discrete (finite or infinite) set of point sources. Both situations–where the strengths of the sources and their locations are precisely known and where these are only known with a given probability distribution–are covered. The authors present a systematic mathematical approach to these models and illustrate its connections with previous heuristic derivations and computations. Results obtained by different methods in disparate contexts are thus unified and a systematic control over approximations to the models, in which the point interactions are replaced by more regular ones, is provided. The first edition of this book generated considerable interest for those learning advanced mathematical topics in quantum mechanics, especially those connected to the Schrödinger equations. This second edition includes a new appendix by Pavel Exner, who has prepared a summary of the progress made in the field since 1988. His summary, centering around two-body point interaction problems, is followed by a bibliography focusing on essential developments made since 1988. appendix by Pavel Exner, who has prepared a summary of the progress made in the field since 1988. His summary, centering around two-body point interaction problems, is followed by a bibliography focusing on essential developments made since 1988."--Résumé de l'éditeur.
