The state-of-the-art theoretical studies of ground state properties, electronic states and atomic vibrations for bulk semiconductors and their surfaces by the application of the pseudopotential method are discussed. Studies of bulk and surface phonon modes have been extended by the application of the phenomenological bond charge model. The coverage of the material, especially of the rapidly growing and technologically important topics of surface reconstruction and chemisorption, is up-to-date and beyond what is currently available in book form. Although theoretical in nature, the book provides a good deal of discussion of available experimental results. Each chapter provides an adequate list of references, relevant for both theoretical and experimental studies. The presentation is coherent and self-contained, and is aimed at the postgraduate and postdoctoral levels.
This volume is a collection of research-and-survey articles by eminent and active workers around the world on the various areas of current research in the theory of analytic functions.Many of these articles emerged essentially from the proceedings of, and various deliberations at, three recent conferences in Japan and Korea: An International Seminar on Current Topics in Univalent Functions and Their Applications which was held in August 1990, in conjunction with the International Congress of Mathematicians at Kyoto, at Kinki University in Osaka; An International Seminar on Univalent Functions, Fractional Calculus, and Their Applications which was held in October 1990 at Fukuoka University; and also the Japan-Korea Symposium on Univalent Functions which was held in January 1991 at Gyeongsang National University in Chinju.
This unique monograph brings together important material in the field of noncommutative rings and modules. It provides an up-to-date account of the topic of cyclic modules and the structure of rings which will be of particular interest to those working in abstract algebra and to graduate students who are exploring potential research topics.
This work aims to present, in a systematic manner, results including the existence and uniqueness of solutions for the Cauchy Type and Cauchy problems involving nonlinear ordinary fractional differential equations.
Zeta and q-Zeta Functions and Associated Series and Integrals is a thoroughly revised, enlarged and updated version of Series Associated with the Zeta and Related Functions. Many of the chapters and sections of the book have been significantly modified or rewritten, and a new chapter on the theory and applications of the basic (or q-) extensions of various special functions is included. This book will be invaluable because it covers not only detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions, but stimulating historical accounts of a large number of problems and well-classified tables of series and integrals. Detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions
This self-contained book is an exposition of the fundamental ideas of model theory. It presents the necessary background from logic, set theory and other topics of mathematics. Only some degree of mathematical maturity and willingness to assimilate ideas from diverse areas are required. The book can be used for both teaching and self-study, ideally over two semesters. It is primarily aimed at graduate students in mathematical logic who want to specialise in model theory. However, the first two chapters constitute the first introduction to the subject and can be covered in one-semester course to senior undergraduate students in mathematical logic. The book is also suitable for researchers who wish to use model theory in their work.
This book brings together the scattered literature associated with the seemingly unrelated regression equations (SURE) model used by econometricians and others. It focuses on the theoretical statistical results associated with the SURE model.
This is a short, modern, and motivated introduction to mathematical logic for upper undergraduate and beginning graduate students in mathematics and computer science. Any mathematician who is interested in getting acquainted with logic and would like to learn Gödel’s incompleteness theorems should find this book particularly useful. The treatment is thoroughly mathematical and prepares students to branch out in several areas of mathematics related to foundations and computability, such as logic, axiomatic set theory, model theory, recursion theory, and computability. In this new edition, many small and large changes have been made throughout the text. The main purpose of this new edition is to provide a healthy first introduction to model theory, which is a very important branch of logic. Topics in the new chapter include ultraproduct of models, elimination of quantifiers, types, applications of types to model theory, and applications to algebra, number theory and geometry. Some proofs, such as the proof of the very important completeness theorem, have been completely rewritten in a more clear and concise manner. The new edition also introduces new topics, such as the notion of elementary class of structures, elementary diagrams, partial elementary maps, homogeneous structures, definability, and many more.
Quantum Mechanics has wide applications in experimental physics and theoretical physics, and this book aims at presenting the fundamentals of quantum mechanics in a clear and concise manner. Primarily intended as a textbook for the postgraduate students of physics, it provides a discussion of the physical concepts to introduce the readers to quantum mechanics. The text begins with the formulation of Schrödinger wave mechanics. Then it moves on to give insights into Heisenberg matrix formulation, Dirac notations, Pauli theory of spin and semi-classical theory of radiation. It concludes with the relativistic theory of a single particle and elements of second quantisation including the interaction of radiation with matter. Key Features Comprehensive and lucid discussion on the fundamentals of quantum mechanics. Chapter-end exercises enable to test the conceptual understanding and analytical skills of the students.
The roots of Borel sets go back to the work of Baire [8]. He was trying to come to grips with the abstract notion of a function introduced by Dirich let and Riemann. According to them, a function was to be an arbitrary correspondence between objects without giving any method or procedure by which the correspondence could be established. Since all the specific functions that one studied were determined by simple analytic expressions, Baire delineated those functions that can be constructed starting from con tinuous functions and iterating the operation 0/ pointwise limit on a se quence 0/ functions. These functions are now known as Baire functions. Lebesgue [65] and Borel [19] continued this work. In [19], Borel sets were defined for the first time. In his paper, Lebesgue made a systematic study of Baire functions and introduced many tools and techniques that are used even today. Among other results, he showed that Borel functions coincide with Baire functions. The study of Borel sets got an impetus from an error in Lebesgue's paper, which was spotted by Souslin. Lebesgue was trying to prove the following: Suppose / : )R2 -- R is a Baire function such that for every x, the equation /(x,y) = 0 has a. unique solution. Then y as a function 0/ x defined by the above equation is Baire.
This book presents an introduction to the key topics in Real Analysis and makes the subject easily understood by the learners. The book is primarily useful for students of mathematics and engineering studying the subject of Real Analysis. It includes many examples and exercises at the end of chapters. This book is very authentic for students, instructors, as well as those doing research in areas demanding a basic knowledge of Real Analysis. It describes several useful topics in Real Analysis such as sets and functions, completeness, ordered field, neighborhoods, limit points of a set, open sets, closed sets, countable and uncountable sets, sequences of real numbers, limit, continuity and differentiability of real functions, uniform continuity, point-wise and uniform convergence of sequences and series of real functions, Riemann integration, improper integrals and metric spaces.
Analysis and Design of Certain Quantitative Multiresponse Experiments highlights (i) the need for multivariate analysis of variance (MANOVA); (ii) the need for multivariate design for multiresponse experiments; and (iii) the actual procedures and interpretation that have been used for this purpose by the authors. The development in this monograph is such that the theory and methods of uniresponse analysis and design stay very close to classical ANOVA. The book first discusses the multivariate aspect of linear models for location type of parameters, but under a univariate design, i.e. one in which each experimental unit is measured or studied with respect to all the responses. Separate chapters cover point estimation of location parameters; testing of linear hypotheses; properties of test procedures; and confidence bounds on a set of parametric functions. Subsequent chapters discuss a graphical internal comparison method for analyzing certain kinds of multiresponse experimental data; two classes of multiresponse designs, i.e. designated hierarchical and p-block designs; and the construction of various kinds of multiresponse designs.
An up-to-date, rigorous, and lucid treatment of the theory, methods, and applications of regression analysis, and thus ideally suited for those interested in the theory as well as those whose interests lie primarily with applications. It is further enhanced through real-life examples drawn from many disciplines, showing the difficulties typically encountered in the practice of regression analysis. Consequently, this book provides a sound foundation in the theory of this important subject.
Any method of fitting equations to data may be called regression. Such equations are valuable for at least two purposes: making predictions and judging the strength of relationships. Because they provide a way of em pirically identifying how a variable is affected by other variables, regression methods have become essential in a wide range of fields, including the soeial seiences, engineering, medical research and business. Of the various methods of performing regression, least squares is the most widely used. In fact, linear least squares regression is by far the most widely used of any statistical technique. Although nonlinear least squares is covered in an appendix, this book is mainly ab out linear least squares applied to fit a single equation (as opposed to a system of equations). The writing of this book started in 1982. Since then, various drafts have been used at the University of Toronto for teaching a semester-Iong course to juniors, seniors and graduate students in a number of fields, including statistics, pharmacology, pharmacology, engineering, economics, forestry and the behav ioral seiences. Parts of the book have also been used in a quarter-Iong course given to Master's and Ph.D. students in public administration, urban plan ning and engineering at the University of Illinois at Chicago (UIC). This experience and the comments and critieisms from students helped forge the final version.
Get up-to-speed on the latest methods of multivariate statistics Multivariate statistical methods provide a powerful tool for analyzing data when observations are taken over a period of time on the same subject. With the advent of fast and efficient computers and the availability of computer packages such as S-plus and SAS, multivariate methods once too complex to tackle are now within reach of most researchers and data analysts. With an emphasis on computing techniques in combination with a full understanding of the mathematics behind the methods, Methods of Multivariate Statistics offers an up-to-date account of multivariate methods. Focusing on the maximum likelihood method for estimation, testing of hypotheses, and "profile analysis," this book offers comprehensive discussions of commonly encountered multivariate data and also covers some practical and important problems lacking in other texts. These include: * Missing at-random observations * "Growth Curve Models" and multivariate one-sided tests applicable in pharmaceutical and medical trials * Bootstrap methods * Principal component method for predicting a multivariate response vector * Outlier detection and handling inference when covariance is singular With clear chapter introductions and numerous problem sets, Methods of Multivariate Statistics meets every statistician's need for a comprehensive investigation of the latest methods in multivariate statistics.
This book provides detailed analysis methods and design guidelines for fire resistance, a vital consideration for offshore processing and production platforms. Recent advancements in the selection of various geometric structural forms for deep-water oil exploration and production require a detailed understanding of the design of offshore structures under special loads. Focusing on a relatively new aspect of offshore engineering, the book offers essential teaching material, illustrating and explaining the concepts discussed through many tutorials. It creates a basis for designing new courses for students of ocean engineering and naval architecture, civil engineering, and applied mechanics at both undergraduate and graduate levels. As such, its content can be used for self-study or as a text in structured courses and professional development programs.
The general theory of relativity and its applications to cosmology requires very deep understanding of mathematics and physics. Keeping this in mind, this self-contained textbook is written which addresses to general relativity and cosmology. In this book, the attempts have been made to explain mathematicians’ notions in the language of a physicist. Primarily intended for the postgraduate students of mathematics and physics, it gives equal importance to mathematical and physical aspects, and thus sharpens understanding of the theory. The text covers many modern concepts and current developments in gravity and cosmology including Brans-Dicke theory, higher-derivative gravity, Kaluza-Klein theory with extension to higher-dimensions. Besides PG students this book would also be useful for research scholars. KEY FEATURES Highlights special features of general relativity and cosmology. Discusses structure formation in the universe, inflationary models and dark energy models with special focus on basic concepts. Provides problems at the end of each chapter to stimulate thinking. Reveals interconnections between required mathematical concepts. Explains “how to apply mathematical concepts to physical problems”. Discusses lagrangian formulation of the field theory and action principle as it provides a powerful tool to derive field equations and energy-momentum tensor components.
Marketing of Alcoholic Beverages ( Wine, Beer, Spirits and Liqueurs)" : A Comprehensive Guide to Marketing Alcoholic Beverages.' This illuminating book provides a deep dive into the intricacies of promoting wines, beers, spirits, and liquors in a dynamic and competitive market. From branding to digital campaigns, discover the innovative tactics that shape the success stories of renowned beverage brands. Whether you're a seasoned marketer seeking fresh insights or a curious enthusiast exploring the business behind the bottle, this book offers a spirited exploration of the marketing landscape, blending industry expertise with captivating narratives.
During the last three decades, interest in the field of interaction of microwaves with ferrimagnetics has steadily increased. Investigations in tlris field have led to the development of a number of devices used for a variety of applications. The initial emphasis of the investigators was on the microwave behavior of ferrimagnetics placed in cavities and metallic waveguides and associated devices. This work has been presented in various books, monographs, and reviews written during the sixties. In recent years, interest in microwave propagation in ferrimagnetics has shifted from loaded waveguides to relatively new areas, e. g. , magnetostatic and magnetoelastic waves in layered structures, microwave propagation in ferrimagnetic strip lines and microstrips, etc. Such investigations are important from the viewpoint of devices such as delay lines, filters, convolvers, guided wave amplifiers, striplines, and microstrip phase shif ters, circulators, edge guided mode isolators, etc. As such, we feit the need for a text (meant for graduate students starting work in these areas as weil as practicing electrical engineers and applied physicists) which presents a coherent account of the various aspects of propagation of microwaves (electromagnetic as weil as magnetoelastic) in biased ferrimagnetics and discusses the relatively recent developments in the theory and operation of the aforementioned devices, and this book is the result. A biased ferrimagnetic is, in the mathematical sense, a complicated medium, electromagnetically as weil as elastically.
This fully updated second edition of The Physics of Phonons remains the most comprehensive theoretical discussion devoted to the study of phonons, a major area of condensed matter physics. It contains exciting new sections on phonon-related properties of solid surfaces, atomically thin materials (such as graphene and monolayer transition metal chalcogenides), in addition to nano- structures and nanocomposites, thermoelectric nanomaterials, and topological nanomaterials, with an entirely new chapter dedicated to topological nanophononics and chiralphononics. Although primarily theoretical in approach, the author refers to experimental results wherever possible, ensuring an ideal book for both experimental and theoretical researchers. The author begins with an introduction to crystal symmetry and continues with a discussion of lattice dynamics in the harmonic approximation, including the traditional phenomenological approach and the more recent ab initio approach, detailed for the first time in this book. A discussion of anharmonicity is followed by the theory of lattice thermal conductivity, presented at a level far beyond that available in any other book. The chapter on phonon interactions is likewise more comprehensive than any similar discussion elsewhere. The sections on phonons in superlattices, impure and mixed crystals, quasicrystals, phonon spectroscopy, Kapitza resistance, and quantum evaporation also contain material appearing in book form for the first time. The book is complemented by numerous diagrams that aid understanding and is comprehensively referenced for further study. With its unprecedented wide coverage of the field, The Physics of Phonons is an indispensable guide for advanced undergraduates, postgraduates, and researchers working in condensed matter physics and materials science. Features Fully updated throughout, with exciting new coverage on graphene, nanostructures and nanocomposites, thermoelectric nanomaterials, and topological nanomaterials. Authored by an authority on phonons. Interdisciplinary, with broad applications through condensed matter physics, nanoscience, and materials science. --
This textbook for courses on function data analysis and shape data analysis describes how to define, compare, and mathematically represent shapes, with a focus on statistical modeling and inference. It is aimed at graduate students in analysis in statistics, engineering, applied mathematics, neuroscience, biology, bioinformatics, and other related areas. The interdisciplinary nature of the broad range of ideas covered—from introductory theory to algorithmic implementations and some statistical case studies—is meant to familiarize graduate students with an array of tools that are relevant in developing computational solutions for shape and related analyses. These tools, gleaned from geometry, algebra, statistics, and computational science, are traditionally scattered across different courses, departments, and disciplines; Functional and Shape Data Analysis offers a unified, comprehensive solution by integrating the registration problem into shape analysis, better preparing graduate students for handling future scientific challenges. Recently, a data-driven and application-oriented focus on shape analysis has been trending. This text offers a self-contained treatment of this new generation of methods in shape analysis of curves. Its main focus is shape analysis of functions and curves—in one, two, and higher dimensions—both closed and open. It develops elegant Riemannian frameworks that provide both quantification of shape differences and registration of curves at the same time. Additionally, these methods are used for statistically summarizing given curve data, performing dimension reduction, and modeling observed variability. It is recommended that the reader have a background in calculus, linear algebra, numerical analysis, and computation.
The controversial Leslie Fiedler (1917-2003) was one of the first critics of popular culture as well as an early proponent of queer theory. This book traces the evolution of this larger-than-life figure through an extensive examination of his works. Beginning with his homoerotic reading of the relationship between Jim and Huck Finn in the Mark Twain novel, this book covers how his many contributions have been provocative, outrageous, novel, and enduring.
This Book Is Designed To Serve As A Text For Management, Economics, Accountancy (Chartered And Cost Accountancy), And Commerce Students. The Book Covers Concepts, Illustrations And Problems In Statistics And Operations Research. Part I Deals With Statistical Techniques For Decision Making. Part Ii Studies Various Operations Research Techniques For Managerial Decisions.The Book Contains Illustrations And Problems, Drawn Extensively From Various Functional Areas Of Management, Viz., Production, Finance, Marketing And Personnel, Which Are Designed To Understand Real Life Decision Making Situations. In Order To Make The Book Self-Contained, All Relevant Mathematical Concepts And Their Applications Have Been Included. To Enhance The Understanding Of The Subject Matter By The Students Belonging To Different Disciplines, The Approach Adopted In This Book, Both In Statistics And Operations Research, Is Conceptional Rather Than Mathematical. Hence Complicated Mathematical Proofs Have Been Avoided.This Book Would Be An Ideal Reference To Executives, Computer Professionals, Industrial Engineers, Economic Planners And Social Scientists. The Other Books By The Same Authors Are: Operations Research For Management And Business Statistics.
Researchers in the field of exploration geophysics have developed new methods for the acquisition, processing and interpretation of gravity and magnetic data, based on detailed investigations of bore wells around the globe. Fractal Models in Exploration Geophysics describes fractal-based models for characterizing these complex subsurface geological structures. The authors introduce the inverse problem using a fractal approach which they then develop with the implementation of a global optimization algorithm for seismic data: very fast simulated annealing (VFSA). This approach provides high-resolution inverse modeling results—particularly useful for reservoir characterization. Serves as a valuable resource for researchers studying the application of fractals in exploration, and for practitioners directly applying field data for geo-modeling Discusses the basic principles and practical applications of time-lapse seismic reservoir monitoring technology - application rapidly advancing topic Provides the fundamentals for those interested in reservoir geophysics and reservoir simulation study Demonstrates an example of reservoir simulation for enhanced oil recovery using CO2 injection
3D Face Modeling, Analysis and Recognition presents methodologies for analyzing shapes of facial surfaces, develops computational tools for analyzing 3D face data, and illustrates them using state-of-the-art applications. The methodologies chosen are based on efficient representations, metrics, comparisons, and classifications of features that are especially relevant in the context of 3D measurements of human faces. These frameworks have a long-term utility in face analysis, taking into account the anticipated improvements in data collection, data storage, processing speeds, and application scenarios expected as the discipline develops further. The book covers face acquisition through 3D scanners and 3D face pre-processing, before examining the three main approaches for 3D facial surface analysis and recognition: facial curves; facial surface features; and 3D morphable models. Whilst the focus of these chapters is fundamentals and methodologies, the algorithms provided are tested on facial biometric data, thereby continually showing how the methods can be applied. Key features: • Explores the underlying mathematics and will apply these mathematical techniques to 3D face analysis and recognition • Provides coverage of a wide range of applications including biometrics, forensic applications, facial expression analysis, and model fitting to 2D images • Contains numerous exercises and algorithms throughout the book
Poor people confront the state on an everyday basis all over the world. But how do they see the state, and how are these engagements conducted? This book considers the Indian case where people's accounts, in particular in the countryside, are shaped by a series of encounters that are staged at the local level, and which are also informed by ideas that are circulated by the government and the broader development community. Drawing extensively on fieldwork conducted in eastern India and their broad range of expertise, the authors review a series of key debates in development studies on participation, good governance, and the structuring of political society. They do so with particular reference to the Employment Assurance Scheme and primary education provision. Seeing the State engages with the work of James Scott, James Ferguson and Partha Chatterjee, and offers a new interpretation of the formation of citizenship in South Asia.
This book is an up-to-date reference on some of the major global health issues and the role of nutrition in their prevention and management. The book covers undernutrition, degenerative diseases, mental health disorders and COVID-19 and reviews feeding and eating disorders like anorexia, bulimia, binge-eating, and delineates the risk factors and management. The book addresses the gaps in tackling these health problems and proposes comprehensive models and frameworks to manage them. Key Features: Explores practical solutions and management of looming health issues in terms of diet and nutrition Reviews health threats like obesity, diabetes, hypertension and COVID-19 Includes a section on feeding and eating disorders and sustainable models to manage them Covers mental-health issues like depression and dementia Discusses conditions like undernutrition, hidden hunger, and cardiovascular diseases The book is meant for health professionals, nutritionists, and policymakers. It is also useful for post-graduates in public health and nutrition.
In recent years there has been an increasing interest in problems involving closed form evaluations of (and representations of the Riemann Zeta function at positive integer arguments as) various families of series associated with the Riemann Zeta function ((s), the Hurwitz Zeta function ((s,a), and their such extensions and generalizations as (for example) Lerch's transcendent (or the Hurwitz-Lerch Zeta function) iI>(z, s, a). Some of these developments have apparently stemmed from an over two-century-old theorem of Christian Goldbach (1690-1764), which was stated in a letter dated 1729 from Goldbach to Daniel Bernoulli (1700-1782), from recent rediscoveries of a fairly rapidly convergent series representation for ((3), which is actually contained in a 1772 paper by Leonhard Euler (1707-1783), and from another known series representation for ((3), which was used by Roger Apery (1916-1994) in 1978 in his celebrated proof of the irrationality of ((3). This book is motivated essentially by the fact that the theories and applications of the various methods and techniques used in dealing with many different families of series associated with the Riemann Zeta function and its aforementioned relatives are to be found so far only"in widely scattered journal articles. Thus our systematic (and unified) presentation of these results on the evaluation and representation of the Zeta and related functions is expected to fill a conspicuous gap in the existing books dealing exclusively with these Zeta functions.
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