Stochastic Geometry and Its Applications

Develops the theory of jet single-time Lagrange geometry and presents modern-day applications Jet Single-Time Lagrange Geometry and Its Applications guides readers through the advantages of jet single-time Lagrange geometry for geometrical modeling. With comprehensive chapters that outline topics ranging in complexity from basic to advanced, the book explores current and emerging applications across a broad range of fields, including mathematics, theoretical and atmospheric physics, economics, and theoretical biology. The authors begin by presenting basic theoretical concepts that serve as the foundation for understanding how and why the discussed theory works. Subusequent chapters compare the geometrical and physical aspects of jet relativistic time-dependent Lagrange geometry to the classical time-dependent Lagrange geometry. A collection of jet geometrical objects are also examined such as d-tensors, relativistic time-dependent semisprays, harmonic curves, and nonlinear connections. Numerous applications, including the gravitational theory developed by both the Berwald-Mo?r metric and the Chernov metric, are also presented. Throughout the book, the authors offer numerous examples that illustrate how the theory is put into practice, and they also present numerous applications in which the solutions of first-order ordinary differential equation systems are regarded as harmonic curves on 1-jet spaces. In addition, numerous opportunities are provided for readers to gain skill in applying jet single-time Lagrange geometry to solve a wide range of problems. Extensively classroom-tested to ensure an accessible presentation, Jet Single-Time Lagrange Geometry and Its Applications is an excellent book for courses on differential geometry, relativity theory, and mathematical models at the graduate level. The book also serves as an excellent reference for researchers, professionals, and academics in physics, biology, mathematics, and economics who would like to learn more about model-providing geometric structures.

This book is concerned with the theory of stochastic processes and the theoretical aspects of statistics for stochastic processes. It combines classic topics such as construction of stochastic processes, associated filtrations, processes with independent increments, Gaussian processes, martingales, Markov properties, continuity and related properties of trajectories with contemporary subjects: integration with respect to Gaussian processes, Itȏ integration, stochastic analysis, stochastic differential equations, fractional Brownian motion and parameter estimation in diffusion models.

Discover a unique and modern treatment of topology employing a cross-disciplinary approach Implemented recently to understand diverse topics, such as cell biology, superconductors, and robot motion, topology has been transformed from a theoretical field that highlights mathematical theory to a subject that plays a growing role in nearly all fields of scientific investigation. Moving from the concrete to the abstract, Topology and Its Applications displays both the beauty and utility of topology, first presenting the essentials of topology followed by its emerging role within the new frontiers in research. Filling a gap between the teaching of topology and its modern uses in real-world phenomena, Topology and Its Applications is organized around the mathematical theory of topology, a framework of rigorous theorems, and clear, elegant proofs. This book is the first of its kind to present applications in computer graphics, economics, dynamical systems, condensed matter physics, biology, robotics, chemistry, cosmology, material science, computational topology, and population modeling, as well as other areas of science and engineering. Many of these applications are presented in optional sections, allowing an instructor to customize the presentation. The author presents a diversity of topological areas, including point-set topology, geometric topology, differential topology, and algebraic/combinatorial topology. Topics within these areas include: Open sets Compactness Homotopy Surface classification Index theory on surfaces Manifolds and complexes Topological groups The fundamental group and homology Special «core intuition» segments throughout the book briefly explain the basic intuition essential to understanding several topics. A generous number of figures and examples, many of which come from applications such as liquid crystals, space probe data, and computer graphics, are all available from the publisher's Web site.

The seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own right and as a concept that is central to many areas of mathematics, science and scientific research. Since its initial publication in 1990 Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. The book introduces and develops the general theory and applications of fractals in a way that is accessible to students and researchers from a wide range of disciplines. Fractal Geometry: Mathematical Foundations and Applications is an excellent course book for undergraduate and graduate students studying fractal geometry, with suggestions for material appropriate for a first course indicated. The book also provides an invaluable foundation and reference for researchers who encounter fractals not only in mathematics but also in other areas across physics, engineering and the applied sciences. Provides a comprehensive and accessible introduction to the mathematical theory and applications of fractals Carefully explains each topic using illustrative examples and diagrams Includes the necessary mathematical background material, along with notes and references to enable the reader to pursue individual topics Features a wide range of exercises, enabling readers to consolidate their understanding Supported by a website with solutions to exercises and additional material http://www.wileyeurope.com/fractal Leads onto the more advanced sequel Techniques in Fractal Geometry (also by Kenneth Falconer and available from Wiley)

Stochastic Simulation and Applications in Finance with MATLAB Programs explains the fundamentals of Monte Carlo simulation techniques, their use in the numerical resolution of stochastic differential equations and their current applications in finance. Building on an integrated approach, it provides a pedagogical treatment of the need-to-know materials in risk management and financial engineering. The book takes readers through the basic concepts, covering the most recent research and problems in the area, including: the quadratic re-sampling technique, the Least Squared Method, the dynamic programming and Stratified State Aggregation technique to price American options, the extreme value simulation technique to price exotic options and the retrieval of volatility method to estimate Greeks. The authors also present modern term structure of interest rate models and pricing swaptions with the BGM market model, and give a full explanation of corporate securities valuation and credit risk based on the structural approach of Merton. Case studies on financial guarantees illustrate how to implement the simulation techniques in pricing and hedging. NOTE TO READER: The CD has been converted to URL. Go to the following website www.wiley.com/go/huyhnstochastic which provides MATLAB programs for the practical examples and case studies, which will give the reader confidence in using and adapting specific ways to solve problems involving stochastic processes in finance.

This book develops the stochastic geometry framework for image analysis purpose. Two main frameworks are described: marked point process and random closed sets models. We derive the main issues for defining an appropriate model. The algorithms for sampling and optimizing the models as well as for estimating parameters are reviewed. Numerous applications, covering remote sensing images, biological and medical imaging, are detailed. This book provides all the necessary tools for developing an image analysis application based on modern stochastic modeling.

SOLID STATE CHEMISTRY AND ITS APPLICATIONS A comprehensive treatment of solid state chemistry complete with supplementary material and full colour illustrations from a leading expert in the field. Solid State Chemistry and its Applications, Second Edition delivers an advanced version of West’s classic text in solid state chemistry, expanding on the undergraduate Student Edition to present a comprehensive treatment of solid state chemistry suitable for advanced students and researchers. The book provides the reader with an up-to-date account of essential topics in solid state chemistry and recent developments in this rapidly developing field of inorganic chemistry. Significant updates and new content in this second edition include: A more extensive overview of important families of inorganic solids including spinels, perovskites, pyrochlores, garnets, Ruddlesden-Popper phases and many more New methods to synthesise inorganic solids, including sol-gel methods, combustion synthesis, atomic layer deposition, spray pyrolysis and microwave techniques Advances in electron microscopy, X-ray and electron spectroscopies New developments in electrical properties of materials, including high Tc superconductivity, lithium batteries, solid oxide fuel cells and smart windows Recent developments in optical properties, including fibre optics, solar cells and transparent conducting oxides Advances in magnetic properties including magnetoresistance and multiferroic materials Homogeneous and heterogeneous ceramics, characterization using impedance spectroscopy Thermoelectric materials, MXenes, low dimensional structures, memristors and many other functional materials Expanded coverage of glass, including metallic and fluoride glasses, cement and concrete, geopolymers, refractories and structural ceramics Overview of binary oxides of all the elements, their structures, properties and applications Featuring full color illustrations throughout, readers will also benefit from online supplementary materials including access to CrystalMaker® software and over 100 interactive crystal structure models. Perfect for advanced students seeking a detailed treatment of solid state chemistry, this new edition of Solid State Chemistry and its Applications will also earn a place as a desk reference in the libraries of experienced researchers in chemistry, crystallography, physics, and materials science.

Solid State Chemistry and its Applications, 2nd Edition: Student Edition is an extensive update and sequel to the bestselling textbook Basic Solid State Chemistry, the classic text for undergraduate teaching in solid state chemistry worldwide. Solid state chemistry lies at the heart of many significant scientific advances from recent decades, including the discovery of high-temperature superconductors, new forms of carbon and countless other developments in the synthesis, characterisation and applications of inorganic materials. Looking forward, solid state chemistry will be crucial for the development of new functional materials in areas such as energy, catalysis and electronic materials. This revised edition of Basic Solid State Chemistry has been completely rewritten and expanded to present an up-to-date account of the essential topics and recent developments in this exciting field of inorganic chemistry. Each section commences with a gentle introduction, covering basic principles, progressing seamlessly to a more advanced level in order to present a comprehensive overview of the subject. This new Student Edition includes the following updates and new features: Expanded coverage of bonding in solids, including a new section on covalent bonding and more extensive treatment of metallic bonding. Synthetic methods are covered extensively and new topics include microwave synthesis, combinatorial synthesis, mechano-synthesis, atomic layer deposition and spray pyrolysis. Revised coverage of electrical, magnetic and optical properties, with additional material on semiconductors, giant and colossal magnetoresistance, multiferroics, LEDs, fibre optics and solar cells, lasers, graphene and quasicrystals. Extended chapters on crystal defects and characterisation techniques. Published in full colour to aid comprehension. Extensive coverage of crystal structures for important families of inorganic solids is complemented by access to CrystalMaker® visualization software, allowing readers to view and rotate over 100 crystal structures in three dimensions. Solutions to exercises and supplementary lecture material are available online. Solid State Chemistry and its Applications, 2nd Edition: Student Edition is a must-have textbook for any undergraduate or new research worker studying solid state chemistry.

A comprehensive, coherent, and in depth presentation of the state of the art in fuzzy clustering. Fuzzy clustering is now a mature and vibrant area of research with highly innovative advanced applications. Encapsulating this through presenting a careful selection of research contributions, this book addresses timely and relevant concepts and methods, whilst identifying major challenges and recent developments in the area. Split into five clear sections, Fundamentals, Visualization, Algorithms and Computational Aspects, Real-Time and Dynamic Clustering, and Applications and Case Studies, the book covers a wealth of novel, original and fully updated material, and in particular offers: a focus on the algorithmic and computational augmentations of fuzzy clustering and its effectiveness in handling high dimensional problems, distributed problem solving and uncertainty management. presentations of the important and relevant phases of cluster design, including the role of information granules, fuzzy sets in the realization of human-centricity facet of data analysis, as well as system modelling demonstrations of how the results facilitate further detailed development of models, and enhance interpretation aspects a carefully organized illustrative series of applications and case studies in which fuzzy clustering plays a pivotal role This book will be of key interest to engineers associated with fuzzy control, bioinformatics, data mining, image processing, and pattern recognition, while computer engineers, students and researchers, in most engineering disciplines, will find this an invaluable resource and research tool.