Professor Hiroshi Ezawa / K. Watanabe -- 1. Quantum mechanics. Direct observation of the microscopic world by using phase shifts of electron waves / A. Tonomura -- Electron correlations in atoms: hyperspherical approach to multiply excited states of atoms / T. Morishita and C.D. Lin -- Bifurcation of periodic instantons and quantum-classical transition in a biaxial anisotropy nano-ferromagnet / Y.-H. Nie [und weitere] -- 2. Path integrals and stochastic processes. The Feynman path integral: an historical slice / J.R. Klauder -- Time-sliced approximation to path integral and Lie-Trotter-Kato product formula / T. Ichinose -- Innovation approach to some problems in quantum dynamics / T. Hida and Si Si -- Feynman paths, sticky walls, white noise / L. Streit -- White noise path integrals: applications in polymer entanglement / C.C. Bernido and M.V. Carpio-Bernido -- Double strata of time for construction of path-space measure for stochastic differential equations / T. Nakamura -- Olbers' paradox, wireless telephones, and Poisson random sets. Is the universe finite? / S. Heath and L. Shepp -- 3. Quantum field theory. Nonrelativistic QED at large momentum of photons / F. Hiroshima -- Enhanced binding in models of nonrelativistic quantum field theory / A. Arai -- Recent developments in mathematical methods for models in non-relativistic quantum electrodynamics / M. Hirokawa -- Localization in quantum field theory / S. Nagamachi and E. Brüning -- Remarks on the commutator of quark mass matrices / M. Kobayashi -- Probing extra dimensions with neutrino oscillations / C.S. Lam -- BPS wall in N = 2 SUSY nonlinear sigma model with Eguchi-Hanson manifold / M. Arai [und weitere] -- Current algebra approach to string theory / M. Hatsuda and W. Siegel -- 4. Statistical mechanics. Statistical mechanics of thermodynamic processes / J. Fröhlich [und weitere] -- How to formulate non-equilibrium local states in QFT? - General characterization and extension to curved spacetime - / J. Ojima -- Some applications of renormalization group analysis / H. Watanabe -- Seven-vertex solutions of the colored Yang-Baxter equation / S.-K. Wang and K. Wu -- Brownian motion as a model for B-cell movement / F.W. Wiegel -- The Lorentz force and the Casimir force at finite temperature and Casimir entropy / M. Revzen, K. Nakamura and A. Mann -- 5. Mathematical problems. Information dynamics and its application to recognition process / M. Ohya -- Amenability for weighted Hopf C*-algebras / Y. Nakagami -- The Bessel equation and dissipation / E. Alfinito and G. Vitiello -- 6. History. Simon Stevin and the cultural revolution in the 16th century / Y. Yamamoto
This invaluable book presents reviews of some recent topics in thetheory of SchrAdinger operators. It includes a short introduction tothe subject, a survey of the theory of the SchrAdinger equation whenthe potential depends on the time periodically, an introduction to theso-called FBI transformation (also known as coherent state expansion)with application to the semi-classical limit of the S-matrix, anoverview of inverse spectral and scattering problems, and a study ofthe ground state of the PauliOCoFierz model with the use of thefunctional integral. The material is accessible to graduate studentsand non-expert researchers.
This invaluable book presents reviews of some recent topics in the theory of Schrdinger operators. It includes a short introduction to the subject, a survey of the theory of the Schrdinger equation when the potential depends on the time periodically, an introduction to the so-called FBI transformation (also known as coherent state expansion) with application to the semi-classical limit of the S-matrix, an overview of inverse spectral and scattering problems, and a study of the ground state of the Pauli-Fierz model with the use of the functional integral. The material is accessible to graduate students and non-expert researchers.
Professor Hiroshi Ezawa / K. Watanabe -- 1. Quantum mechanics. Direct observation of the microscopic world by using phase shifts of electron waves / A. Tonomura -- Electron correlations in atoms: hyperspherical approach to multiply excited states of atoms / T. Morishita and C.D. Lin -- Bifurcation of periodic instantons and quantum-classical transition in a biaxial anisotropy nano-ferromagnet / Y.-H. Nie [und weitere] -- 2. Path integrals and stochastic processes. The Feynman path integral: an historical slice / J.R. Klauder -- Time-sliced approximation to path integral and Lie-Trotter-Kato product formula / T. Ichinose -- Innovation approach to some problems in quantum dynamics / T. Hida and Si Si -- Feynman paths, sticky walls, white noise / L. Streit -- White noise path integrals: applications in polymer entanglement / C.C. Bernido and M.V. Carpio-Bernido -- Double strata of time for construction of path-space measure for stochastic differential equations / T. Nakamura -- Olbers' paradox, wireless telephones, and Poisson random sets. Is the universe finite? / S. Heath and L. Shepp -- 3. Quantum field theory. Nonrelativistic QED at large momentum of photons / F. Hiroshima -- Enhanced binding in models of nonrelativistic quantum field theory / A. Arai -- Recent developments in mathematical methods for models in non-relativistic quantum electrodynamics / M. Hirokawa -- Localization in quantum field theory / S. Nagamachi and E. Brüning -- Remarks on the commutator of quark mass matrices / M. Kobayashi -- Probing extra dimensions with neutrino oscillations / C.S. Lam -- BPS wall in N = 2 SUSY nonlinear sigma model with Eguchi-Hanson manifold / M. Arai [und weitere] -- Current algebra approach to string theory / M. Hatsuda and W. Siegel -- 4. Statistical mechanics. Statistical mechanics of thermodynamic processes / J. Fröhlich [und weitere] -- How to formulate non-equilibrium local states in QFT? - General characterization and extension to curved spacetime - / J. Ojima -- Some applications of renormalization group analysis / H. Watanabe -- Seven-vertex solutions of the colored Yang-Baxter equation / S.-K. Wang and K. Wu -- Brownian motion as a model for B-cell movement / F.W. Wiegel -- The Lorentz force and the Casimir force at finite temperature and Casimir entropy / M. Revzen, K. Nakamura and A. Mann -- 5. Mathematical problems. Information dynamics and its application to recognition process / M. Ohya -- Amenability for weighted Hopf C*-algebras / Y. Nakagami -- The Bessel equation and dissipation / E. Alfinito and G. Vitiello -- 6. History. Simon Stevin and the cultural revolution in the 16th century / Y. Yamamoto
Professor Kiyosi Ito is well known as the creator of the modern theory of stochastic analysis. Although Ito first proposed his theory, now known as Ito's stochastic analysis or Ito's stochastic calculus, about fifty years ago, its value in both pure and applied mathematics is becoming greater and greater. For almost all modern theories at the forefront of probability and related fields, Ito's analysis is indispensable as an essential instrument, and it will remain so in the future. For example, a basic formula, called the Ito formula, is well known and widely used in fields as diverse as physics and economics. This volume contains 27 papers written by world-renowned probability theorists. Their subjects vary widely and they present new results and ideas in the fields where stochastic analysis plays an important role. Also included are several expository articles by well-known experts surveying recent developments. Not only mathematicians but also physicists, biologists, economists and researchers in other fields who are interested in the effectiveness of stochastic theory will find valuable suggestions for their research. In addition, students who are beginning their study and research in stochastic analysis and related fields will find instructive and useful guidance here. This volume is dedicated to Professor Ito on the occasion of his eightieth birthday as a token of deep appreciation for his great achievements and contributions. An introduction to and commentary on the scientific works of Professor Ito are also included.
This book describes baryon models constructed from quarks, mesons and chiral symmetry. The role of chiral symmetry and of quark model structure with SU(6) spin-flavor symmetry are discussed in detail, starting from a pedagogic introduction. Emphasis is placed on symmetry aspects of the theories. As an application, the chiral bag model is studied for nucleon structure, where important methods of theoretical physics, mostly related to the semiclassical approach for a system of strong interactions, are demonstrated. The text is more practical than formal; tools and ideas are explained in detail while solving actual problems. By checking each step of the computations, readers can learn not only the calculational techniques but also the essential ideas behind them.
For a company to survive in the manufacturing industry, it must not only accumulate light-weight 3D data, but also share this information within the company and with related companies as well as train key personnel. 3D Manufacturing Innovation introduces the best practices developed by Toyota, Sony, Nikon, Casio and other pioneers in the global engineering scene, providing the reader with invaluable tips for manufacturing innovation.
How can one determine the physical properties of the medium or the geometrical properties of the domain by observing electromagnetic waves? To answer this fundamental problem in mathematics and physics, this book leads the reader to the frontier of inverse scattering theory for electromagnetism.The first three chapters, written comprehensively, can be used as a textbook for undergraduate students. Beginning with elementary vector calculus, this book provides fundamental results for wave equations and Helmholtz equations, and summarizes the potential theory. It also explains the cohomology theory in an easy and straightforward way, which is an essential part of electromagnetism related to geometry. It then describes the scattering theory for the Maxwell equation by the time-dependent method and also by the stationary method in a concise, but almost self-contained manner. Based on these preliminary results, the book proceeds to the inverse problem for the Maxwell equation.The chapters for the potential theory and elementary cohomology theory are good introduction to graduate students. The results in the last chapter on the inverse scattering for the medium and the determination of Betti numbers are new, and will give a current scope for the inverse spectral problem on non-compact manifolds. It will be useful for young researchers who are interested in this field and trying to find new problems.
This book treats procedures for the determination of aluminium through lithium. Strontium, a section included in calcium in the third edition, will be a separate chapter in the 4th edition. An effort has been made to keep to the aim of the previous editions of presenting a limited number of useful methods. Revision of magnesium through zirconium will require another several years.
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