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الصفحة 2
Compact Riemann Surfaces : An Introduction to Contemporary Mathematics
Although Riemann surfaces are a time-honoured field, this book is novel in its broad perspective that systematically explores the connection with other fields of mathematics. It can serve as an introduction to contemporary mathematics as a whole as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. It is unique among textbooks on Riemann surfaces in including an introduction to Teichmüller theory.
Characterization of Polymer Surfaces and Thin Films
Comprehensive characterization of surfaces and interfaces is essential to relate surface and thin film properties to micro structure and molecular origin, which is, on the other hand, the key to technological control and improvement of materials. This volume cover a representative spectrum of surface sensitive techniques and their application to polymer surface and thin film characterization as well as recent examples of technologically relevant materials and process development.
Characterization of Corrosion Products on Steel Surfaces
It is well known that corrosion products, i.e. rust, on iron and steel surfaces cannot be assigned a typical crystallographic structure with long-range order. In fact, the structure of rust is considered to be very complicated, and some forms of rust are assigned to the amorphous state for this reason. Accurate information about the atomic-scale structure of rust is important to shed light on corrosion mechanisms of metallic materials. And, since life of steel structures is often dominated by environmental degradation or corrosion of the surface, the structure of the rust formed on iron and steel surfaces during prolonged exposure to air is of great interest. This book describes the fundamental aspects of materials characterization for the ferric oxyhydroxides formed on steel surfaces.
Cathodic Arcs : From Fractal Spots to Energetic Condensation
Cathodic Arcs: From Fractal Spots to Energetic Condensation is the first book in over a decade dedicated to the physics and technology of cathodic arcs. It includes a detailed account of arc history, a textbook-like introduction to cathode phenomena, and some basic physics of expanding plasmas; it deals with the infamous macroparticle issue and describes a host of practical plasma filter solutions. In contrast to previous books on cathodic arcs, the focus is on the relation of arc plasmas and their properties to surface modification and thin film deposition. The book contains sections on basic plasma physics and thin film materials science. It also deals with practical issues of coatings such as stress control and the often-underrated issue of the coating’s color. By stressing the fractal nature of cathode spots, the theme of fluctuations can be found throughout the book: fluctuations affect all plasma properties and thereby have consequences for plasma-based surface modifications and film growth.
Braid Groups
Braids and braid groups have been at the heart of mathematical development over the last two decades. Braids play an important role in diverse areas of mathematics and theoretical physics. The special beauty of the theory of braids stems from their attractive geometric nature and their close relations to other fundamental geometric objects, such as knots, links, mapping class groups of surfaces, and configuration spaces. In this presentation the authors thoroughly examine various aspects of the theory of braids, starting from basic definitions and then moving to more recent results. The advanced topics cover the Burau and the Lawrence--Krammer--Bigelow representations of the braid groups, the Alexander--Conway and Jones link polynomials, connections with the representation theory of the Iwahori--Hecke algebras, and the Garside structure and orderability of the braid groups.
Atomic Force Microscopy, Scanning Nearfield Optical Microscopy and Nanoscratching : Application to Rough and Natural Surfaces
Making a clear distinction is made between nano- and micro-mechanical testing for physical reasons, this monograph describes the basics and applications of the supermicroscopies AFM and SNOM, and of the nanomechanical testing on rough and technical natural surfaces in the submicron range down to a lateral resolution of a few nm. New or improved instrumentation, new physical laws and unforeseen new applications in all branches of natural sciences (around physics, chemistry, mineralogy, materials science, biology and medicine) and nanotechnology are covered as well as the sources for pitfalls and errors.
Analysis and Control of Ultrafast Photoinduced Reactions
The present monograph summarizes, in a comprehensive way, several years of joint experimental and theoretical frontier research on ultrafast laser-induced molecular dynamics and its control. Emphasis is set on the characterization of the nuclear dynamics within molecular systems in various environments (gas phase, surfaces, solids, solution, strong fields) triggered by optical excitations spanning from the infrared to the ultraviolet. Building on the converged analysis between experiment and theory, control of chemical reactions is established by means of optimally shaped laser pulses. This paves the road toward new applications and future challenges in this rapidly developing research field.
An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces
This book gives an introduction to modern geometry. Starting from an elementary level the author develops deep geometrical concepts, playing an important role nowadays in contemporary theoretical physics. He presents various techniques and viewpoints, thereby showing the relations between the alternative approaches.
An Introduction to Manifolds
Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way the reader acquires the knowledge and skills necessary for further study of geometry and topology.
An introduction to differential geometry with applications to elasticity
Interestingly, notions that pertain to di?erential geometry per se,suchas covariant derivatives of tensor ?elds, are also introduced in Chapters 3 and 4, where they appear most naturally in the derivation of the basic boundary value problems of three-dimensional elasticity and shell theory.
Advances in Multiresolution for Geometric Modelling
Multiresolution methods in geometric modelling are concerned with the generation, representation, and manipulation of geometric objects at several levels of detail. Applications include fast visualization and rendering as well as coding, compression, and digital transmission of 3D geometric objects.The book contains seven survey papers, providing a detailed overview of recent advances in the various fields within multiresolution modelling, and sixteen additional research papers. Each of the seven parts of the book starts with a survey paper, followed by the associated research papers in that area.
Advanced Numerical Methods to Optimize Cutting Operations of Five-Axis Milling Machines
Presents new optimization algorithms designed to improve the efficiency of tool paths for five-axis NC machining of sculptured surfaces. The book introduces the reader to fundamental issues involved in the tool path planning such as the kinematics of five-axis machines, types of 5 axis machines, part surface representation, machining strips, optimal tool orientation, gouging avoidance and forward step error. It also introduces new methods of optimization based on research conducted by the authors, including schemes performed in the spatial domain, angular domain as well as procedures to optimize the initial setup. The book can be used by undergraduate and graduate students and researchers in the field of NC machining and CAD/CAM as well as by the corporate research groups for advanced optimization of cutting operations.
Adhesive Bonding of Aircraft Composite Structures: Non-destructive Testing and Quality Assurance Concepts
This book is under a CC BY 4.0 license. It presents the results of the ComBoNDT European project, which aimed at the development of more secure, time- and cost-saving extended non-destructive inspection tools for carbon fiber reinforced plastics, adhered surfaces and bonded joints. The book reports the optimal use of composite materials to allow weight savings, reduction in fuel consumptions, savings during production and higher cost efficiency for ground operations.
A First Course in Modular Forms
This book introduces the theory of modular forms with an eye toward the Modularity Theorem: All rational elliptic curves arise from modular forms. The topics covered include • elliptic curves as complex tori and as algebraic curves, • modular curves as Riemann surfaces and as algebraic curves, • Hecke operators and Atkin–Lehner theory, • Hecke eigenforms and their arithmetic properties, • the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms, • elliptic and modular curves modulo p and the Eichler–Shimura Relation, • the Galois representations associated to elliptic curves and to Hecke eigenforms. As it presents these ideas, the book states the Modularity Theorem in various forms, relating them to each other and touching on their applications to number theory.
A Computational Differential Geometry Approach to Grid Generation
This monograph gives a detailed treatment of applications of geometric methods to advanced grid technology. It focuses on and describes a comprehensive approach based on the numerical solution of inverted Beltramian and diffusion equations with respect to monitor metrics for generating both structured and unstructured grids in domains and on surfaces.
