These notes present a rigorous mathematical formulation of quantum mechanics based on the algebraic framework of observables and states. The underlying mathematics is that of topological algebras, locally convex spaces and distribution theory.
This book presents basic geometric and algebraic properties of the Heisenberg group and its relation to the skew field of quaternions, symplectic structures and representations, and describes some of its applications. It offers a clear exposition of mathematical topics referring to applications in signal theory, physics and information theory. It has relevance for undergraduate and graduate students, a variety of researchers, and specialists in data processing.
This book presents a functional calculus for n-tuples of not necessarily commuting linear operators. In particular, a functional calculus for quaternionic linear operators is developed. These calculi are based on a new theory of hyperholomorphicity for functions with values in a Clifford algebra: the so-called slice monogenic functions which are carefully described in the book. In the case of functions with values in the algebra of quaternions these functions are named slice regular functions. Except for the appendix and the introduction all results are new and appear for the first time organized in a monograph. The material has been carefully prepared to be as self-contained as possible. The intended audience consists of researchers, graduate and postgraduate students interested in operator theory, spectral theory, hypercomplex analysis, and mathematical physics.
This book is a collection of reviews and essays about the recent developments in the area of Symmetries and applications of Group Theory. Contributions have been written mostly at the graduate level but some are accessible to advanced undergraduates. The book is of interest to a wide audience and covers a broad range of topics with a strong degree of thematical unity. The book is part of a Series of books on Symmetries in Science and may be compared to the published Proceedings of the Colloquia on Group Theoretical Methods in Physics. Here, however, prevails a distinguished character for presenting extended reviews on present applications to Science, not restricted to Theoretical Physics.
Human-Like Biomechanics is a comprehensive introduction into modern geometrical methods to be used as a unified research approach in two apparently separate and rapidly growing fields: mathematical biomechanics and humanoid robotics. The book contains six Chapters and an Appendix. The first Chapter is an Introduction, giving a brief review of mathematical techniques to be used in the text. The second Chapter develops geometrical basis of human-like biomechanics, while the third Chapter develops its mechanical basis, mainly from generalized Lagrangian and Hamiltonian perspective. The fourth Chapter develops topology of human-like biomechanics, while the fifth Chapter reviews related nonlinear control techniques. The sixth Chapter develops covariant biophysics of electro-muscular stimulation. The Appendix consists of two parts: classical muscular mechanics and modern path integral methods, which are both used frequently in the main text. The whole book is based on the authors’ own research papers in human-like biomechanics.
This book contains three lectures each of 10 sessions; the first on Potential Theory on graphs and manifolds, the second on annealing and another algorithms for image reconstruction, the third on Malliavin Calculus.
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 monograph focuses on the construction of regression models with linear and non-linear constrain inequalities from the theoretical point of view. Unlike previous publications, this volume analyses the properties of regression with inequality constrains, investigating the flexibility of inequality constrains and their ability to adapt in the presence of additional a priori information The implementation of inequality constrains improves the accuracy of models, and decreases the likelihood of errors. Based on the obtained theoretical results, a computational technique for estimation and prognostication problems is suggested. This approach lends itself to numerous applications in various practical problems, several of which are discussed in detail The book is useful resource for graduate students, PhD students, as well as for researchers who specialize in applied statistics and optimization. This book may also be useful to specialists in other branches of applied mathematics, technology, econometrics and finance