الصفحة 24
الصفحة 24
Idempotent matrices over complex group algebras
The study of idempotent elements in the group algebras originates from geometric and analytic considerations. … This book provides an introduction to the study of these problems.It collects and presents in a systematic way basic techniques and important results that have been obtained during the past few decades.The book is suitable for independent study. Moreover, all chapters and appendices finish with a sufficient number of exercises that also increase the quality of the book.
Ideals, Varieties, and Algorithms : An Introduction to Computational Algebraic Geometry and Commutative Algebra
Algebraic Geometry is the study of systems of polynomial equations in one or more variables.The solutions of a system of polynomial equations form a geometric object called a variety; the corresponding algebraic object is an ideal. There is a close relationship between ideals and varieties which reveals the intimate link between algebra and geometry. Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory.
Ideals and Reality : Projective Modules and Number of Generators of Ideals
The book gives a comprehensive introduction to basic commutative algebra, together with the related methods from homological algebra, which will enable students who know only the fundamentals of algebra to enjoy the power of using these tools. At the same time, it also serves as a valuable reference for the research specialist and as potential course material, because the authors present, for the first time in book form, an approach here that is an intermix of classical algebraic K-theory and complete intersection techniques, making connections with the famous results of Forster-Swan and Eisenbud-Evans. A study of projective modules and their connections with topological vector bundles in a form due to Vaserstein is included. Important subsidiary results appear in the copious exercises.
I numeri nel cuore = Numbers in the heart
An extremely varied gallery of ironic reflections on the academic world, of mild anecdotes, of calm provocations, of travel notes, of portraits of famous mathematicians, suspended between joke and seriousness, between dream and reality. Two exquisite fantasies by Arthur Porges and Arthur Koestler open the collection, followed by short stories written by professional mathematicians, who have literature as a hobby, inspired by characters and facts, emotions and fantasies related to the world of mathematics.
Hypoelliptic estimates and spectral theory for Fokker-Planck operators and witten Laplacians
There has recently been a renewal of interest in Fokker-Planck operators, motivated by problems in statistical physics, in kinetic equations and differential geometry. Compared to more standard problems in the spectral theory of partial differential operators, those operators are not self-adjoint and only hypoelliptic. The aim of the analysis is to give, as generally as possible, an accurate qualitative and quantitative description of the exponential return to the thermodynamical equilibrium. While exploring and improving recent results in this direction this volume proposes a review of known techniques on: the hypoellipticity of polynomial of vector fields and its global counterpart; the global Weyl-Hörmander pseudo-differential calculus, the spectral theory of non-self-adjoint operators, the semi-classical analysis of Schrödinger-type operators.
Hyperparameter tuning for machine and deep learning with R : A practical guide
Equips readers with the ability to achieve better results with significantly less time, costs, effort and resources using the methods described here. The case studies presented in this book can be run on a regular desktop or notebook computer. The content focuses on the hyperparameter tuning of ML and DL algorithms, and is divided into two main parts: theory (Part I) and application (Part II). Essential topics covered include: a survey of important model parameters; four parameter tuning studies and one extensive global parameter tuning study; statistical analysis of the performance of ML and DL methods based on severity; and a new, consensus-ranking-based way to aggregate and analyze results from multiple algorithms.
Hyperbolic Systems of Balance Laws : Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 14-21, 2003
The present Cime volume includes four lectures by Bressan, Serre, Zumbrun and Williams and an appendix with a Tutorial on Center Manifold Theorem by Bressan. Bressan’s notes start with an extensive review of the theory of hyperbolic conservation laws. Then he introduces the vanishing viscosity approach and explains clearly the building blocks of the theory in particular the crucial role of the decomposition by travelling waves. Serre focuses on existence and stability for discrete shock profiles, he reviews the existence both in the rational and in the irrational cases and gives a concise introduction to the use of spectral methods for stability analysis. Finally the lectures by Williams and Zumbrun deal with the stability of multidimensional fronts.
Hyperbolic Problems and Regularity Questions
This book discusses new challenges in the quickly developing field of hyperbolic problems. Particular emphasis lies on the interaction between nonlinear partial differential equations, functional analysis and applied analysis as well as mechanics.The book originates from a recent conference focusing on hyperbolic problems and regularity questions. It is intended for researchers in functional analysis, PDE, fluid dynamics and differential geometry.
Hyperbolic Problems : Theory, Numerics, Applications ; Proceedings of the Eleventh International Conference on Hyperbolic Problems held in Ecole Normale Supérieure, Lyon, July 17-21, 2006
This volume contains papers that were presented at HYP2006, the eleventh international Conference on Hyperbolic Problems: Theory, Numerics and Applications held at the Ecole Normale Supérieure de Lyon, France, July 17-21, 2006. This biennial series of conferences has become one of the most important international events in Applied Mathematics. As computers became more and more powerful, the interplay between theory, modelling, and numerical algorithms gained considerable impact, and the scope of HYP conferences expanded accordingly. The field is currently in interaction with a variety of scientific domains, including fluid dynamics, physics, electromagnetism, chemistry, biology, road and network traffic, and engineering. Many of these papers present new effective numerical methods and their application in various contexts.
Hyperbolic Geometry
The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries. The basic approach taken is to define hyperbolic lines and develop a natural group of transformations preserving hyperbolic lines, and then study hyperbolic geometry as those quantities invariant under this group of transformations. Topics covered include the upper half-plane model of the hyperbolic plane, Möbius transformations, the general Möbius group, and their subgroups preserving the upper half-plane, hyperbolic arc-length and distance as quantities invariant under these subgroups, the Poincaré disc model, convex subsets of the hyperbolic plane, hyperbolic area, the Gauss-Bonnet formula and its applications.
Hydropower Economics
HYDROPOWER ECONOMICS examines sustainable alternate energy sources beginning with modeling hydropower and extending the model to include thermal power and wind power. The book will use various econometric measures, equilibrium metrics, OR methods, and DEA/productivity analyses to analyze and model the optimal use of these alternate energy sources. Because these problems are dynamic in nature, dynamic methods are used to model the problems. The book derives results on the allocation of the amounts of alternate sources of energy (water, thermal, and wind) required to produce electricity at acceptable levels over time. Graphic illustrations of the analytical and mathematical modeling used to reach research conclusions are used throughout the book.
Hydrodynamics of Explosion : Experiments and Models
Hydronamics of Explosion presents the research results for the problems of underwater explosions and contains a detailed analysis of the structure and the parameters of the wave fields generated by explosions of cord and spiral charges, a description of the formation mechanisms for a wide range of cumulative flows at underwater explosions near the free surface, and the relevant mathematical models. Shock-wave transformation in bubbly liquids, shock-wave amplification due to collision and focusing, and the formation of bubble detonation waves in reactive bubbly liquids are studied in detail. Particular emphasis is placed on the investigation of wave processes in cavitating liquids, which incorporates the concepts of the strength of real liquids containing natural microinhomogeneities, the relaxation of tensile stress, and the cavitation fracture of a liquid as the inversion of its two-phase state under impulsive (explosive) loading. The problems are classed among essentially nonlinear processes that occur under shock loading of liquids and may be of interest to researchers in physical acoustics, mechanics of multiphase media, shock-wave processes in condensed media, explosive hydroacoustics, and cumulation.
Hybrid Methods of Molecular Modeling
Hybrid Methods of Molecular Modeling is a self-contained advanced review volume. It provides a step by step derivation of the consistent theoretical picture of hybrid modeling methods and a thorough analysis of the concepts and current practical methods of hybrid modeling based on this theory. The book presents its material sequentially, paying attention both to the physical soundness of the approximations used and to the mathematical rigor necessary for the practical development of the robust modeling code.
Hybrid metaheuristics : An emerging approach to optimization
The book is intended both to provide an overview of hybrid metaheuristics to novices of the field, and to provide researchers from the field with a collection of some of the most interesting recent developments.
Hybrid Artificial Intelligent Systems ; 15th International Conference, HAIS 2020, Gijón, Spain, November 11-13, 2020, Proceedings
This book constitutes the refereed proceedings of the 15th International Conference on Hybrid Artificial Intelligent Systems, HAIS 2020, held in Gijón, Spain, in November 2020. The 65 regular papers presented in this book were carefully reviewed and selected from 106 submissions. The papers are grouped into these topics: advanced data processing and visualization techniques; bio-inspired models and optimization; learning algorithms; data mining, knowledge discovery and big data; and hybrid artificial intelligence applications.
Hyberbolic Conservation Laws in Continuum Physics
This masterly exposition of the mathematical theory of hyperbolic system for conservation laws brings out the intimate connection with continuum thermodynamics, by emphasising issues in which the analysis may reveal something about the physics and, in return, the underlying physical structure may direct and drive the analysis.Theis edition contains chapter recounting the exciting recent developments on the vanishing viscosity method. Numerous new sections have been incorporated in preexisting chapters, to introduce newly derived results or present older material
Humans-with-media and the reorganization of mathematical thinking : Information and communication technologies, modeling, visualization and experimentation
Offers a new conceptual framework for reflecting on the role of information and communication technology in mathematics education. Borba and Villarreal provide examples from research conducted at the level of basic and university-level education, developed by their research group based in Brazil, and discuss their findings in the light of the relevant literature. Arguing that different media reorganize mathematical thinking in different ways, they discuss how computers, writing and oral discourse transform education at an epistemological as well as a political level. Modeling and experimentation are seen as pedagogical approaches which are in harmony with changes brought about by the presence of information and communication technology in educational settings. Examples of research about on-line mathematics education courses, and Internet used in regular mathematics courses, are presented and discussed at a theoretical level. In this book, mathematical knowledge is seen as developed by collectives of humans-with-media.
Human-Like Biomechanics : A Unified Mathematical Approach to Human 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.
Human reliability and error in transportation systems
Each year billions of dollars are being spent to develop, manufacture, and operate transportation systems such as aircraft, ships, trains, and motor vehicles throughout the world. During their operation thousands of lives are lost annually due to various types accidents. Needless to say, approximately 70 to 90 percent of transportation crashes are the result of human error to a certain degree. Moreover, it may be added that human errors contribute significantly to most transportation crashes across all modes of transportation. Human Reliability and Error in Transportation Systems is the first book to cover the subject of human reliability across all types of transportation systems. The material will be accessible to readers with no previous knowledge in the field, and is supported with a full explanation of the necessary mathematical concepts together with numerous examples and test problems.
Human Longevity, Individual Life Duration, and the Growth of the Oldest-Old Population
Old-age survival has considerably improved in the second half of the twentieth century. In this book, these fundamental questions are explored by experts from such diverse fields as biology, medicine, epidemiology, demography, sociology, and mathematics: they report on recent cutting-edge studies about essential issues of human longevity such as evolution of lifespan of species, genetics of human longevity, reasons for the recent improvement in survival of the elderly, medical and behavioral causes of deaths among very old people, and social factors of long survival in old age.
