الصفحة 1
الصفحة 1
Number Theory ; Vol. I : Tools and Diophantine Equations
The central theme of this graduate-level number theory textbook is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three aspects.
Number Theory : An Introduction to Mathematics ; Part B
This book attempts to provide such an understanding of the nature and extent of mathematics. It is a modern introduction to the theory of numbers, emphasizing its connections with other branches of mathematics. This part B is more advanced than the first and should give the reader some idea of the scope of mathematics today. The connecting theme is the theory of numbers. By exploring its many connections with other branches, we may obtain a broad picture.
Nuclear Condensed Matter Physics with Synchrotron : Basic Principles, Methodology and Applications
This book provides a comprehensive introduction to the growing field of nuclear condensed matter physics with synchrotron radiation, a technique which finds numerous applications in fields such as magnetism, physics of surfaces and interfaces, lattice dynamics and more. Due to the enormous brilliance of modern synchrotron radiation sources, the method is particularly suited for the investigation of low-dimensional structures such as thin films and nanoparticles. The use of isotopic probe layers, for example, allows one to determine magnetic and vibrational properties with very high spatial resolution; focusing techniques and x-ray interference effects lead to a very high sensitivity for smallest amounts of material. The book is written on an introductory level with many examples employed to illustrate the special experimental possibilities.
Non-spectral Asymptotic Analysis of One-Parameter Operator Semigroups
In this book, non-spectral methods are presented and discussed that have been developed over the last two decades for the investigation of asymptotic behavior of one-parameter operator semigroups in Banach spaces. This concerns in particular Markov semigroups in L1-spaces, motivated by applications to probability theory and dynamical systems. Recently many results on the asymptotic behaviour of Markov semigroups were extended to positive semigroups in Banach lattices with order-continuous norm, and to positive semigroups in non-commutative L1-spaces. Related results, historical notes, exercises, and open problems accompany each chapter.
Nonlinear Waves : Classical and Quantum Aspects
Leading scientists discuss the most recent physical and experimental results in the physics of Bose-Einstein condensate theory, the theory of nonlinear lattices (including quantum and nonlinear lattices), and nonlinear optics and photonics. Classical and quantum aspects of the dynamics of nonlinear waves are considered. The contributions focus on the Gross-Pitaevskii equation and on the quantum nonlinear Schrödinger equation. Recent experimental results on atomic condensates and hydrogen bonded systems are reviewed. Particular attention is given to nonlinear matter waves in periodic potential.
Multiscale Biomechanics and Tribology of Inorganic and Organic Systems : In memory of Professor Sergey Psakhie
This book gathers authoritative contributions concerning multiscale problems in biomechanics, geomechanics, materials science and tribology. It is written in memory of Sergey Grigorievich Psakhie to feature various aspects of his multifaceted research interests, ranging from theoretical physics, computer modeling of materials and material characterization at the atomic scale, to applications in space industry, medicine and geotectonics, and including organizational, psychological and philosophical aspects of scientific research and teaching as well
Multiplicative Invariant Theory
Multiplicative invariant theory, as a research area in its own right within the wider spectrum of invariant theory, is of relatively recent vintage. The present text offers a coherent account of the basic results achieved thus far.. Multiplicative invariant theory is intimately tied to integral representations of finite groups. Therefore, the field has a predominantly discrete, algebraic flavor. Geometry, specifically the theory of algebraic groups, enters through Weyl groups and their root lattices as well as via character lattices of algebraic tori.
Modern Hematology : Biology and Clinical Management
The first chapters of this book contain a self-contained introduction to path integrals in Euclidean quantum mechanics and statistical mechanics. The resulting high-dimensional integrals can be estimated with the help of Monte Carlo simulations based on Markov processes. The most commonly used algorithms are presented in detail so as to prepare the reader for the use of high-performance computers as an “experimental” tool for this burgeoning field of theoretical physics. Several chapters are then devoted to an introduction to simple lattice field theories and a variety of spin systems with discrete and continuous spins, where the ubiquitous Ising model serves as an ideal guide for introducing the fascinating area of phase transitions. As an alternative to the lattice formulation of quantum field theories, variants of the flexible renormalization group methods are discussed in detail. Since, according to our present-day knowledge, all fundamental interactions in nature are described by gauge theories, the remaining chapters of the book deal with gauge theories without and with matter.
Models of the Atomic Nucleus
Models of the Atomic Nucleus is a largely non-technical introduction to nuclear theory – an attempt to explain the nucleus in a way that makes nuclear physics as comprehensible as chemistry or cell biology. Unlike many other scientific fields, the "popularization" of nuclear physics has not previously been successful because many fundamental issues remain controversial and a unified theory of nuclear structure has not yet been established. The theme developed in this book is that the many models of nuclear theory each provide a partial perspective on the nucleus and that the many models can in fact be integrated into a coherent whole and expressed in terms of a lattice of nucleons.
Microscopy of Semiconducting Materials 2007 ; Proceedings of the 15th Conference, 2-5 April 2007, Cambridge, UK
The conference focused upon the most recent advances in the study of the structural and electronic properties of semiconducting materials by the application of transmission and scanning electron microscopy, scanning probe microscopy and X-ray-based methods. Conference sessions concentrated on key topics including state-of-the-art studies in high resolution imaging and analytical electron microscopy, advanced scanning probe microscopy, scanning electron microscopy and focused ion beam applications, novel epitaxial layer phenomena, the properties of quantum nanostructures, III-nitride developments, GeSi/Si for advanced devices, metal-semiconductor contacts and silicides and the important effects of critical device processing treatments.
Mathematical Morphology : 40 Years On ; Proceedings of the 7th International Symposium on Mathematical Morphology, April 18-20, 2005
Mathematical Morphology is a speciality in Image Processing and Analysis, which considers images as geometrical objects, to be analyzed through their interactions with other geometrical objects. It relies on several branches of mathematics, such as discrete geometry, topology, lattice theory, partial differential equations, integral geometry and geometrical probability. It has produced fast and efficient algorithms for computer analysis of images, and has found applications in bio-medical imaging, materials science, geoscience, remote sensing, quality control, document processing and data analysis. This book contains the 43 papers presented at the 7th International Symposium on Mathematical Morphology, held in Paris on April 18-20, 2005. It gives a lively state of the art of current research topics in this field. It also marks a milestone, the 40 years of uninterrupted development of this ever-expanding domain.
Isomorphisms Between H¹ Spaces
Presents a thorough and self-contained presentation of H¹ and its known isomorphic invariants, such as the uniform approximation property, the dimension conjecture, and dichotomies for the complemented subspaces. The necessary background is developed from scratch. This includes a detailed discussion of the Haar system, together with the operators that can be built from it (averaging projections, rearrangement operators, paraproducts, Calderon-Zygmund singular integrals). Complete proofs are given for the classical martingale inequalities of C. Fefferman, Burkholder, and Khinchine-Kahane, and for large deviation inequalities. Complex interpolation, analytic families of operators, and the Calderon product of Banach lattices are treated in the context of H^p spaces. Througout the book, special attention is given to the combinatorial methods developed in the field, particularly J. Bourgain's proof of the dimension conjecture, L. Carleson's biorthogonal system in H¹, T. Figiel's integral representation, W.B. Johnson's factorization of operators, B. Maurey's isomorphism, and P. Jones' proof of the uniform approximation property. An entire chapter is devoted to the study of combinatorics of colored dyadic intervals."
Ion Implantation and Synthesis of Materials
This book presents the physics and materials science of ion implantation and ion beam modification of materials. It covers ion-solid interactions used to predict ion ranges, ion straggling and lattice disorder. Also treated are shallow-junction formation and slicing silicon with hydrogen ion beams. Topics important for materials modification, such as ion-beam mixing, stresses, and sputtering, are also described.
Integral Foam Molding of Light Metals : Technology, Foam Physics and Foam Simulation
This book shows in three parts the technology, the fundamentals and the simulation models for the Integral Foam Molding of Light Metals Part I: “Technology” shows for the first time that foaming of metals is possible by applying molding techniques very similar to polymer integral foam molding. Part II: “Physics” is devoted to the physics of foaming with special emphasis on the very short time scale which is characteristic for integral foam molding. Part III: “Numerical Simulation” presents a new lattice Boltzmann approach for the treatment of free surfaces is developed and applied on foam evolution problems. For the first time, the numerical simulation of foam evolution starting from nucleation until decay is accessible.
High Performance Tensegrity-Inspired Metamaterials and Structures
New metamaterials, smart materials and structures, and adaptive systems with adjustable behaviour or which use high performance or 'extremal' materials can be applied to bigger structural systems, such as cellular tensegrity lattices with extremal mechanical properties. Numerical analyses justify tensegrities and discrete and continuum models offer two main approaches to the analysis of tensegrity-based mechanical metamaterials and lattices. Two examples of 2D and 3D tensegrity modules and lattices, and potential applications in civil engineering are presented.
Hexagonal image processing : A practical approach
Hexagonal Image Processing provides an introduction to the processing of hexagonally sampled images, includes a survey of the work done in the field, and presents a novel framework for hexagonal image processing (HIP) based on hierarchical aggregates. Digital image processing is currently dominated by the use of square sampling lattices, however, hexagonal sampling lattices can also be used to define digital images. The strengths offered by hexagonal lattices over square lattices are considerable: • higher packing density, • uniform connectivity of points (pixels) in the lattice, • better angular resolution by virtue of having more nearest neighbours, and • superlative representation of curves. The utility of the HIP framework is demonstrated by implementing several basic image processing techniques (for the spatial and frequency domain) and some applications. The HIP framework serves as a tool for comparing processing of images defined on a square vs hexagonal grid, to determine their relative merits and demerits. The theory and algorithms covered are supplemented by attention to practical details such as accommodating hardware that support only images sampled on a square lattice. Including a Foreword written by Professor Narendra Ahuja, an eminent researcher in the field of Image Processing and Computer Vision, the book’s fresh approach to the subject offers insight and workable know-how to both researchers and postgraduates.
Graph structures for knowledge representation and reasoning ; 6th International Workshop, GKR 2020, virtual event, September 5, 2020, revised selected papers
This book constitutes the thoroughly refereed post-conference proceedings of the 6th International Workshop on Graph Structures for Knowledge Representation and Reasoning, GKR 2020, held virtually in September 2020, associated with ECAI 2020, the 24th European Conference on Artificial Intelligence.
Geometry and Dynamics of Groups and Spaces : In Memory of Alexander Reznikov
Alexander Reznikov (1960-2003) was a brilliant and highly original mathematician. This book presents 18 articles by prominent mathematicians and is dedicated to his memory. The book further provides an extensive survey on Kleinian groups in higher dimensions and some articles centering on Reznikov as a person.
Fundamentals of the Physics of Solids ; Vol. I : Structure and Dynamics
This book aims to deliver a comprehensive and self-contained account of the vast field of solid-state physics. It goes far beyond most classic texts in the presentation of the properties of solids and experimentally observed phenomena, along with the basic concepts and theoretical methods used to understand them and the essential features of various experimental techniques.
From microphysics to macrophysics : Methods and applications of statistical physics ; Vol.2
Volume 2 applies statistical methods to systems governed by quantum effects, in particular to solid state physics, explaining properties due to the crystal structure or to the lattice excitations or to the electrons. Liquid helium is discussed and radiative equilibrium and transport are studied. The last chapters are devoted to non-equilibrium processes and to kinetic equations, with many applications included.
