A Textbook of B.Sc. Mathematics [Linear Algebra]" strictly covers the new curriculum for Course 5 (2nd year, 2nd semester) of universities in Andhra Pradesh. It covers Vector Spaces, Basis and Dimension, Linear Transformation, Fundamentals of Matrices, Characteristic Values and Characteristic Vectors, Cayley-Hamilton Theorem and Orthogonality.
Statistical inference carries great significance in model building from both the theoretical and the applications points of view. Its applications to engineering and economic systems, financial economics, and the biological and medical sciences have made statistical inference for stochastic processes a well-recognized and important branch of statistics and probability. The class of semimartingales includes a large class of stochastic processes, including diffusion type processes, point processes, and diffusion type processes with jumps, widely used for stochastic modeling. Until now, however, researchers have had no single reference that collected the research conducted on the asymptotic theory for semimartingales. Semimartingales and their Statistical Inference, fills this need by presenting a comprehensive discussion of the asymptotic theory of semimartingales at a level needed for researchers working in the area of statistical inference for stochastic processes. The author brings together into one volume the state-of-the-art in the inferential aspect for such processes. The topics discussed include: Asymptotic likelihood theory Quasi-likelihood Likelihood and efficiency Inference for counting processes Inference for semimartingale regression models The author addresses a number of stochastic modeling applications from engineering, economic systems, financial economics, and medical sciences. He also includes some of the new and challenging statistical and probabilistic problems facing today's active researchers working in the area of inference for stochastic processes.
Scalar diffraction from a circular aperture is a ubiquitous problem that arises in a variety of disciplines, such as optics (lenses), acoustics (speakers), electromagnetics (dish antennas), and ultrasonics (piston transducers). The problem endures despite centuries of research because each new generation of researchers rediscovers it and adds some novel insight or new result to the existing literature. Scalar Diffraction from a Circular Aperture promises a few new results and several novel insights, particularly with regard to spatial averaging. Although the text emphasizes ultrasonic diffraction, the results and insights developed are general and may be applied to the many practical problems involving scalar diffraction from a circular aperture. Included are novel insights on mirror-image diffraction, autoconvolution diffraction, and coherent and incoherent averaging. Examples from ultrasonic imaging, a coherent imaging modality, are used to develop a fairly general theory that connects over a century of research on scalar diffraction from a circular aperture. The material is based on a synthesis of mathematics, physical optics, linear systems theory, and scalar diffraction theory. Thus, engineers, scientists, mathematicians, and students working in optics, acoustics, antenna design, biomedical engineering, non-destructive testing, and astronomy will find Scalar Diffraction from a Circular Aperture interesting, provocative, and useful.
Many new DCT-like transforms have been proposed since the first edition of this book. For example, the integer DCT that yields integer transform coefficients, the directional DCT to take advantage of several directions of the image and the steerable DCT. The advent of higher dimensional frames such as UHDTV and 4K-TV demand for small and large transform blocks to encode small or large similar areas respectively in an efficient way. Therefore, a new updated book on DCT, adapted to the modern days, considering the new advances in this area and targeted for students, researchers and the industry is a necessity.
Besides giving an introduction to Commutative Algebra - the theory of c- mutative rings - this book is devoted to the study of projective modules and the minimal number of generators of modules and ideals. The notion of a module over a ring R is a generalization of that of a vector space over a field k. The axioms are identical. But whereas every vector space possesses a basis, a module need not always have one. Modules possessing a basis are called free. So a finitely generated free R-module is of the form Rn for some n E IN, equipped with the usual operations. A module is called p- jective, iff it is a direct summand of a free one. Especially a finitely generated R-module P is projective iff there is an R-module Q with P @ Q S Rn for some n. Remarkably enough there do exist nonfree projective modules. Even there are nonfree P such that P @ Rm S Rn for some m and n. Modules P having the latter property are called stably free. On the other hand there are many rings, all of whose projective modules are free, e. g. local rings and principal ideal domains. (A commutative ring is called local iff it has exactly one maximal ideal. ) For two decades it was a challenging problem whether every projective module over the polynomial ring k[X1,. . .
This is the revised and enlarged 2nd edition of the authors’ original text, which was intended to be a modest complement to Grenander's fundamental memoir on stochastic processes and related inference theory. The present volume gives a substantial account of regression analysis, both for stochastic processes and measures, and includes recent material on Ridge regression with some unexpected applications, for example in econometrics. The first three chapters can be used for a quarter or semester graduate course on inference on stochastic processes. The remaining chapters provide more advanced material on stochastic analysis suitable for graduate seminars and discussions, leading to dissertation or research work. In general, the book will be of interest to researchers in probability theory, mathematical statistics and electrical and information theory.
This book sheds new light on stochastic calculus, the branch of mathematics that is most widely applied in financial engineering and mathematical finance. The first book to introduce pathwise formulae for the stochastic integral, it provides a simple but rigorous treatment of the subject, including a range of advanced topics. The book discusses in-depth topics such as quadratic variation, Ito formula, and Emery topology. The authors briefly addresses continuous semi-martingales to obtain growth estimates and study solution of a stochastic differential equation (SDE) by using the technique of random time change. Later, by using Metivier–Pellaumail inequality, the solutions to SDEs driven by general semi-martingales are discussed. The connection of the theory with mathematical finance is briefly discussed and the book has extensive treatment on the representation of martingales as stochastic integrals and a second fundamental theorem of asset pricing. Intended for undergraduate- and beginning graduate-level students in the engineering and mathematics disciplines, the book is also an excellent reference resource for applied mathematicians and statisticians looking for a review of the topic.
The material accumulated and presented in this volume can be ex plained easily. At the start of my graduate studies in the early 1950s, I Grenander's (1950) thesis, and was much attracted to the came across entire subject considered there. I then began preparing for the neces sary mathematics to appreciate and possibly make some contributions to the area. Thus after a decade of learning and some publications on the way, I wanted to write a modest monograph complementing Grenander's fundamental memoir. So I took a sabbatical leave from my teaching position at the Carnegie-Mellon University, encouraged by an Air Force Grant for the purpose, and followed by a couple of years more learning opportunity at the Institute for Advanced Study to complete the project. As I progressed, the plan grew larger needing a substantial background material which was made into an independent initial volume in (1979). In its preface I said: "My intension was to present the following material as the first part of a book treating the In ference Theory of stochastic processes, but the latter account has now receded to a distant future," namely for two more decades! Meanwhile, a much enlarged second edition of that early work has appeared (1995), and now I am able to present the main part of the original plan.
This book presents a unified course in BE-algebras with a comprehensive introduction, general theoretical basis and several examples. It introduces the general theoretical basis of BE-algebras, adopting a credible style to offer students a conceptual understanding of the subject. BE-algebras are important tools for certain investigations in algebraic logic, because they can be considered as fragments of any propositional logic containing a logical connective implication and the constant "1", which is considered as the logical value “true”. Primarily aimed at graduate and postgraduate students of mathematics, it also helps researchers and mathematicians to build a strong foundation in applied abstract algebra. Presenting insights into some of the abstract thinking that constitutes modern abstract algebra, it provides a transition from elementary topics to advanced topics in BE-algebras. With abundant examples and exercises arranged after each section, it offers readers a comprehensive, easy-to-follow introduction to this field.
This volume is composed of two parts: Mathematical and Numerical Analysis for Strongly Nonlinear Plasma Models and Exact Controllability and Observability for Quasilinear Hyperbolic Systems and Applications. It presents recent progress and results obtained in the domains related to both subjects without attaching much importance to the details of proofs but rather to difficulties encountered, to open problems and possible ways to be exploited. It will be very useful for promoting further study on some important problems in the future.
The cost of capital concept has myriad applications in business decision-making. The standard methodology for deriving cost of capital estimates is based on the seminal Modigliani-Miller analyses. This book generalizes this framework to include non-debt tax shields (e.g., depreciation), interactions between the borrowing rate and tax shields, and default considerations. It develops several new results and shows how better cost of capital and marginal tax rate estimates can be generated. The book's unified cost of capital theory is discussed with comprehensive numerical examples and graphical illustrations.This book will be of interest to corporate managers, academics, investment bankers, governmental agencies, and private companies that generate cost of capital estimates for public consumption.
Handbook of Statistics: Advances in Survival Analysis covers all important topics in the area of Survival Analysis. Each topic has been covered by one or more chapters written by internationally renowned experts. Each chapter provides a comprehensive and up-to-date review of the topic. Several new illustrative examples have been used to demonstrate the methodologies developed. The book also includes an exhaustive list of important references in the area of Survival Analysis. Includes up-to-date reviews on many important topics Chapters written by many internationally renowned experts Some Chapters provide completely new methodologies and analyses Includes some new data and methods of analyzing them
The book presents, for the first time, a detailed analysis of harmonizable processes and fields (in the weak sense) that contain the corresponding stationary theory as a subclass. It also gives the structural and some key applications in detail. These include Levy's Brownian motion, a probabilistic proof of the longstanding Riemann's hypothesis, random fields indexed by LCA and hypergroups, extensions to bistochastic operators, Cramér-Karhunen classes, as well as bistochastic operators with some statistical applications.The material is accessible to graduate students in probability and statistics as well as to engineers in theoretical applications. There are numerous extensions and applications pointed out in the book that will inspire readers to delve deeper.
Targeted at graduate students, researchers and practitioners in the field of science and engineering, this book gives a self-contained introduction to a measure-theoretic framework in laying out the definitions and basic concepts of random variables and stochastic diffusion processes. It then continues to weave into a framework of several practical tools and applications involving stochastic dynamical systems. These include tools for the numerical integration of such dynamical systems, nonlinear stochastic filtering and generalized Bayesian update theories for solving inverse problems and a new stochastic search technique for treating a broad class of non-convex optimization problems. MATLAB® codes for all the applications are uploaded on the companion website.
Error Coding for Arithmetic Processors provides an understanding of arithmetically invariant codes as a primary technique of fault-tolerant computing by discussing the progress in arithmetic coding theory. The book provides an introduction to arithmetic error code, single-error detection, and long-distance codes. It also discusses algebraic structures, linear congruences, and residues. Organized into eight chapters, this volume begins with an overview of the mathematical background in number theory, algebra, and error control techniques. It then explains the basic mathematical models on a register and its number representation system. The reader is also introduced to arithmetic processors, as well as to error control techniques. The text also explores the functional units of a digital computer, including control unit, arithmetic processor, memory unit, program unit, and input/output unit. Students in advanced undergraduate or graduate level courses, researchers, and readers who are interested in applicable knowledge on arithmetic codes will find this book extremely useful.
The agents approach is not just another abstract computing paradigm, but has matured during recent years into a booming research area and software engineering technology which holds great promise for the design and application of complex distributed systems. This book presents 12 revised full chapters grouped around 3 main topics in intelligent agent systems; agent architectures, formal theories of rationality and cooperation and collaboration. Among the topics addressed are software agents, BDI architectures, social commitment, believable agents and artificial life. The book is based on the Workshop on Theoretical and Practical Foundations of Intelligent Agents held at the Fourth Pacific Rim International Conference on Artificial Intelligence in Cairns, Australia, in August 1996.
Real and Stochastic Analysis: Recent Advances presents a carefully edited collection of research articles written by research mathematicians and highlighting advances in RSA. A balanced blend of both theory and applications, this book covers six aspects of stochastic analysis in depth and detail. The first chapters cover the state of the art in tracers analysis, stochastic modeling as it applies to AIDS epidemiology, and the current state of higher order SDEs. Subsequent chapters present a simple approach to Gaussian dichotomy, an overview of harmonizable processes, and stochastic Fubini and Green theorems. Common to all the chapters, the employment of functional analytic methods creates a unified approach. Each chapter includes detailed proofs. Throughout the book, a substantial amount of new material is presented, much of it for the first time. This forward-looking work presents current accounts of important areas of research, evaluates recent advances, and identifies research frontiers and new challenges.
This book presents a systematic, comprehensive treatment of analog and discrete signal analysis and synthesis and an introduction to analog communication theory. This evolved from my 40 years of teaching at Oklahoma State University (OSU). It is based on three courses, Signal Analysis (a second semester junior level course), Active Filters (a first semester senior level course), and Digital signal processing (a second semester senior level course). I have taught these courses a number of times using this material along with existing texts. The references for the books and journals (over 160 references) are listed in the bibliography section. At the undergraduate level, most signal analysis courses do not require probability theory. Only, a very small portion of this topic is included here. I emphasized the basics in the book with simple mathematics and the soph- tication is minimal. Theorem-proof type of material is not emphasized. The book uses the following model: 1. Learn basics 2. Check the work using bench marks 3. Use software to see if the results are accurate The book provides detailed examples (over 400) with applications. A thr- number system is used consisting of chapter number – section number – example or problem number, thus allowing the student to quickly identify the related material in the appropriate section of the book. The book includes well over 400 homework problems. Problem numbers are identified using the above three-number system.
Foundations of Reinforcement Learning with Applications in Finance aims to demystify Reinforcement Learning, and to make it a practically useful tool for those studying and working in applied areas — especially finance. Reinforcement Learning is emerging as a powerful technique for solving a variety of complex problems across industries that involve Sequential Optimal Decisioning under Uncertainty. Its penetration in high-profile problems like self-driving cars, robotics, and strategy games points to a future where Reinforcement Learning algorithms will have decisioning abilities far superior to humans. But when it comes getting educated in this area, there seems to be a reluctance to jump right in, because Reinforcement Learning appears to have acquired a reputation for being mysterious and technically challenging. This book strives to impart a lucid and insightful understanding of the topic by emphasizing the foundational mathematics and implementing models and algorithms in well-designed Python code, along with robust coverage of several financial trading problems that can be solved with Reinforcement Learning. This book has been created after years of iterative experimentation on the pedagogy of these topics while being taught to university students as well as industry practitioners. Features Focus on the foundational theory underpinning Reinforcement Learning and software design of the corresponding models and algorithms Suitable as a primary text for courses in Reinforcement Learning, but also as supplementary reading for applied/financial mathematics, programming, and other related courses Suitable for a professional audience of quantitative analysts or data scientists Blends theory/mathematics, programming/algorithms and real-world financial nuances while always striving to maintain simplicity and to build intuitive understanding To access the code base for this book, please go to: https://github.com/TikhonJelvis/RL-book.
This is a revised and expanded edition of a successful graduate and reference text. The book is designed for a standard graduate course on probability theory, including some important applications. The new edition offers a detailed treatment of the core area of probability, and both structural and limit results are presented in detail. Compared to the first edition, the material and presentation are better highlighted; each chapter is improved and updated.
Stochastic Processes: General Theory starts with the fundamental existence theorem of Kolmogorov, together with several of its extensions to stochastic processes. It treats the function theoretical aspects of processes and includes an extended account of martingales and their generalizations. Various compositions of (quasi- or semi-)martingales and their integrals are given. Here the Bochner boundedness principle plays a unifying role: a unique feature of the book. Applications to higher order stochastic differential equations and their special features are presented in detail. Stochastic processes in a manifold and multiparameter stochastic analysis are also discussed. Each of the seven chapters includes complements, exercises and extensive references: many avenues of research are suggested. The book is a completely revised and enlarged version of the author's Stochastic Processes and Integration (Noordhoff, 1979). The new title reflects the content and generality of the extensive amount of new material. Audience: Suitable as a text/reference for second year graduate classes and seminars. A knowledge of real analysis, including Lebesgue integration, is a prerequisite.
Beginning with the formulation of specific design problems, this book goes on explains theories of failure. It considers factors involved in optimization of design, followed by a detailed description of static, transient and dynamic analysis.
The interplay between functional and stochastic analysis has wide implications for problems in partial differential equations, noncommutative or "free" probability, and Riemannian geometry. Written by active researchers, each of the six independent chapters in this volume is devoted to a particular application of functional analytic methods in stochastic analysis, ranging from work in hypoelliptic operators to quantum field theory. Every chapter contains substantial new results as well as a clear, unified account of the existing theory; relevant references and numerous open problems are also included.Key topics:* Stochastic differential equations (SDEs), hypoelliptic operators, and SDEs based on Lévy processes* Stochastic calculus on Riemannian manifolds and curved Wiener spaces* Noncommutative and quantum probability* The Feynman integral, evolution processes, the Feynman-Kac formula, and applications to quantum field theory* Convolution operators and the amenability of the underlying locally compact groups, with connections among classical random walks, spectral theory, and Beurling and Segal subalgebrasSelf-contained, well-motivated, and replete with suggestions for further investigation, this book will be especially valuable as a seminar text for dissertation-level graduate students. Research mathematicians and physicists will also find it a useful and stimulating reference.Contributors: D.R. Bell; B.K. Driver; S. Gudder; B. Jefferies; H. Kunita; and M.M. Rao.
A revised and up-to-date guide to advanced vibration analysis written by a noted expert The revised and updated second edition of Vibration of Continuous Systems offers a guide to all aspects of vibration of continuous systems including: derivation of equations of motion, exact and approximate solutions and computational aspects. The author—a noted expert in the field—reviews all possible types of continuous structural members and systems including strings, shafts, beams, membranes, plates, shells, three-dimensional bodies, and composite structural members. Designed to be a useful aid in the understanding of the vibration of continuous systems, the book contains exact analytical solutions, approximate analytical solutions, and numerical solutions. All the methods are presented in clear and simple terms and the second edition offers a more detailed explanation of the fundamentals and basic concepts. Vibration of Continuous Systems revised second edition: Contains new chapters on Vibration of three-dimensional solid bodies; Vibration of composite structures; and Numerical solution using the finite element method Reviews the fundamental concepts in clear and concise language Includes newly formatted content that is streamlined for effectiveness Offers many new illustrative examples and problems Presents answers to selected problems Written for professors, students of mechanics of vibration courses, and researchers, the revised second edition of Vibration of Continuous Systems offers an authoritative guide filled with illustrative examples of the theory, computational details, and applications of vibration of continuous systems.
In response to unanswered difficulties in the generalized case of conditional expectation and to treat the topic in a well-deservedly thorough manner, M.M. Rao gave us the highly successful first edition of Conditional Measures and Applications. Until this groundbreaking work, conditional probability was relegated to scattered journal articles and
Although I feel honored to write a foreword for this important book, it is a task that I approach with some trepidation. The topics covered in the book summarize the current state of the art in technical demography. However, my knowledge and expertise with respect to technical demography are limited to the most fundamental and intermediate-level methods; hence, critical commentary on the contents of this volume is beyond my scope in this fore word. Since I have some understanding of the logic and substantive aspects of the methods rather than the complicated mathematics used in describing them, my comments will necessarily be restricted to the book's general or ganization and content. To date, most texts published on technical demography have been limited to traditional demographic methods: sources and limitations of data, life table construction and applications, standardization techniques, various methods for preparing population estimates and forecasts, etc. However, population specialists have in recent years been developing and successfully applying a variety of sophisticated techniques not covered in the more standard intro ductory texts. In addition, many traditional methods that are unique to the demographic discipline have been improved and extended.
This book is a very useful reference that contains worked-out solutions for all the exercise problems in the book Chemical Engineering Thermodynamics by the same author. Step-by-step solutions to all exercise problems are provided and solutions are explained with detailed and extensive illustrations. It will come in handy for all teachers and users of Chemical Engineering Thermodynamics.
This invaluable book comprises assorted recent papers of Professor C N R Rao, a well-known chemist. It presents current trends in materials chemistry and physics, offering in-depth information to young researchers and pleasant reading to experts. Advances in Chemistry brings out the single-minded dedication of Professor Rao to the promotion of science.
The book is devoted to the structural analysis of vector and random (or both) valued countably additive measures, and used for integral representations of random fields. The spaces can be Banach or Frechet types. Several stationary aspects and related processes are analyzed whilst numerous new results are included and many research avenues are opened up.
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