Learn How to Program Stochastic Models Highly recommended, the best-selling first edition of Introduction to Scientific Programming and Simulation Using R was lauded as an excellent, easy-to-read introduction with extensive examples and exercises. This second edition continues to introduce scientific programming and stochastic modelling in a clear, practical, and thorough way. Readers learn programming by experimenting with the provided R code and data. The book’s four parts teach: Core knowledge of R and programming concepts How to think about mathematics from a numerical point of view, including the application of these concepts to root finding, numerical integration, and optimisation Essentials of probability, random variables, and expectation required to understand simulation Stochastic modelling and simulation, including random number generation and Monte Carlo integration In a new chapter on systems of ordinary differential equations (ODEs), the authors cover the Euler, midpoint, and fourth-order Runge-Kutta (RK4) schemes for solving systems of first-order ODEs. They compare the numerical efficiency of the different schemes experimentally and show how to improve the RK4 scheme by using an adaptive step size. Another new chapter focuses on both discrete- and continuous-time Markov chains. It describes transition and rate matrices, classification of states, limiting behaviour, Kolmogorov forward and backward equations, finite absorbing chains, and expected hitting times. It also presents methods for simulating discrete- and continuous-time chains as well as techniques for defining the state space, including lumping states and supplementary variables. Building readers’ statistical intuition, Introduction to Scientific Programming and Simulation Using R, Second Edition shows how to turn algorithms into code. It is designed for those who want to make tools, not just use them. The code and data are available for download from CRAN.
Acclaimed for its thorough presentation of mediation, moderation, and conditional process analysis, this book has been updated to reflect the latest developments in PROCESS for SPSS, SAS, and, new to this edition, R. Using the principles of ordinary least squares regression, Andrew F. Hayes illustrates each step in an analysis using diverse examples from published studies, and displays SPSS, SAS, and R code for each example. Procedures are outlined for estimating and interpreting direct, indirect, and conditional effects; probing and visualizing interactions; testing hypotheses about the moderation of mechanisms; and reporting different types of analyses. Readers gain an understanding of the link between statistics and causality, as well as what the data are telling them. The companion website (www.afhayes.com) provides data for all the examples, plus the free PROCESS download. New to This Edition *Rewritten Appendix A, which provides the only documentation of PROCESS, including a discussion of the syntax structure of PROCESS for R compared to SPSS and SAS. *Expanded discussion of effect scaling and the difference between unstandardized, completely standardized, and partially standardized effects. *Discussion of the meaning of and how to generate the correlation between mediator residuals in a multiple-mediator model, using a new PROCESS option. *Discussion of a method for comparing the strength of two specific indirect effects that are different in sign. *Introduction of a bootstrap-based Johnson–Neyman-like approach for probing moderation of mediation in a conditional process model. *Discussion of testing for interaction between a causal antecedent variable [ital]X[/ital] and a mediator [ital]M[/ital] in a mediation analysis, and how to test this assumption in a new PROCESS feature.
Is the death penalty a more effective deterrent than lengthy prison sentences? Does a judge's gender influence their decisions? Do independent judiciaries promote economic freedom? Answering such questions requires empirical evidence, and arguments based on empirical research have become an everyday part of legal practice, scholarship, and teaching. In litigation judges are confronted with empirical evidence in cases ranging from bankruptcy and taxation to criminal law and environmental infringement. In academia researchers are increasingly turning to sophisticated empirical methods to assess and challenge fundamental assumptions about the law. As empirical methods impact on traditional legal scholarship and practice, new forms of education are needed for today's lawyers. All lawyers asked to present or assess empirical arguments need to understand the fundamental principles of social science methodology that underpin sound empirical research. An Introduction to Empirical Legal Research introduces that methodology in a legal context, explaining how empirical analysis can inform legal arguments; how lawyers can set about framing empirical questions, conducting empirical research, analysing data, and presenting or evaluating the results. The fundamentals of understanding quantitative and qualitative data, statistical models, and the structure of empirical arguments are explained in a way accessible to lawyers with or without formal training in statistics. Written by two of the world's leading experts in empirical legal analysis, drawing on years of experience in training lawyers in empirical methods, An Introduction to Empirical Legal Research will be an invaluable primer for all students, academics, or practising lawyers coming to empirical research - whether they are embarking themselves on an empirical research project, or engaging with empirical arguments in their field of study, research, or practice.
Detailed coverage of probability theory, random variables and their functions, stochastic processes, linear system response to stochastic processes, Gaussian and Markov processes, and stochastic differential equations. 1973 edition.
This timely work is the first to comprehensively examine directors' responsibilities to creditors in times of financial strife, as well as addressing when these responsibilities arise, and what directors should have to do to ensure that they comply with their obligations. Keay explores the relevant issues from doctrinal, normative and comparative perspectives and addresses the question as to when directors are liable for wrongful trading, fraudulent trading or breach of their duties to creditors and whether directors should be held responsible for the before mentioned. Besides the relevant UK legislation and case law, legislation and case law from Australia, Canada, Ireland and the United States are examined and compared and reforms which take into account the aims and rationale of the relevant legislation as well as creditors' interests are proposed and assessed. Importantly, new approaches for courts which would make the nature of the responsibility and its timing more precise are suggested. Company directors have certain responsibilities to creditors of their companies. In particular, they should avoid fraudulent and wrongful trading and consider, as part of their duties, the interests of creditors when their companies might be, or are, in financial difficulty. The work is precipitated by the lack of coherence in the consideration of wrongful trading and the recent delivery of important cases on fraudulent trading. Also, this timely work is the first to comprehensively examine directors' responsibilities to creditors in times of financial strife, as well as addressing when these responsibilities arise, and what directors should have to do to ensure that they comply with their obligations. Keay explores the relevant issues from doctrinal, normative and comparative perspectives and seeks to address the question as to when directors are liable for wrongful trading, fraudulent trading or breach of their duties to creditors and whether directors should be held responsible for wrongful trading and failing to consider the interests of creditors. Besides the relevant UK legislation and case law, legislation and case law from Australia, Canada, Ireland and the United States are examined and compared, and reforms which take into account the aims and rationale of the relevant legislation as well as creditors' interests are proposed and assessed. Importantly, new approaches for courts which would make the nature of the responsibility and its timing more precise are suggested.
Statistics is confusing, even for smart, technically competent people. And many students and professionals find that existing books and web resources don’t give them an intuitive understanding of confusing statistical concepts. That is why this book is needed. Some of the unique qualities of this book are: • Easy to Understand: Uses unique “graphics that teach” such as concept flow diagrams, compare-and-contrast tables, and even cartoons to enhance “rememberability.” • Easy to Use: Alphabetically arranged, like a mini-encyclopedia, for easy lookup on the job, while studying, or during an open-book exam. • Wider Scope: Covers Statistics I and Statistics II and Six Sigma Black Belt, adding such topics as control charts and statistical process control, process capability analysis, and design of experiments. As a result, this book will be useful for business professionals and industrial engineers in addition to students and professionals in the social and physical sciences. In addition, each of the 60+ concepts is covered in one or more articles. The 75 articles in the book are usually 5–7 pages long, ensuring that things are presented in “bite-sized chunks.” The first page of each article typically lists five “Keys to Understanding” which tell the reader everything they need to know on one page. This book also contains an article on “Which Statistical Tool to Use to Solve Some Common Problems”, additional “Which to Use When” articles on Control Charts, Distributions, and Charts/Graphs/Plots, as well as articles explaining how different concepts work together (e.g., how Alpha, p, Critical Value, and Test Statistic interrelate). ANDREW A. JAWLIK received his B.S. in Mathematics and his M.S. in Mathematics and Computer Science from the University of Michigan. He held jobs with IBM in marketing, sales, finance, and information technology, as well as a position as Process Executive. In these jobs, he learned how to communicate difficult technical concepts in easy - to - understand terms. He completed Lean Six Sigma Black Belt coursework at the IASSC - accredited Pyzdek Institute. In order to understand the confusing statistics involved, he wrote explanations in his own words and graphics. Using this material, he passed the certification exam with a perfect score. Those statistical explanations then became the starting point for this book.
There is a nineteen-year recurrence in the apparent position of the sun and moon against the background of the stars, a pattern observed long ago by the Babylonians. In the course of those nineteen years the Earth experiences 235 lunar cycles. Suppose we calculate the ratio of Earth's period about the sun to the moon's period about Earth. That ratio has 235/19 as one of its early continued fraction convergents, which explains the apparent periodicity. Exploring Continued Fractions explains this and other recurrent phenomena—astronomical transits and conjunctions, lifecycles of cicadas, eclipses—by way of continued fraction expansions. The deeper purpose is to find patterns, solve puzzles, and discover some appealing number theory. The reader will explore several algorithms for computing continued fractions, including some new to the literature. He or she will also explore the surprisingly large portion of number theory connected to continued fractions: Pythagorean triples, Diophantine equations, the Stern-Brocot tree, and a number of combinatorial sequences. The book features a pleasantly discursive style with excursions into music (The Well-Tempered Clavier), history (the Ishango bone and Plimpton 322), classics (the shape of More's Utopia) and whimsy (dropping a black hole on Earth's surface). Andy Simoson has won both the Chauvenet Prize and Pólya Award for expository writing from the MAA and his Voltaire's Riddle was a Choice magazine Outstanding Academic Title. This book is an enjoyable ramble through some beautiful mathematics. For most of the journey the only necessary prerequisites are a minimal familiarity with mathematical reasoning and a sense of fun.
This comprehensive introduction to synthetic aperture radar (SAR) is a practical guide to the analysis, simulation, and design of SAR systems. The video eBook uses constructive examples and real-world collected datasets to demonstrate image registration and autofocus methods. Both two- and three-dimensional image formation algorithms are presented. Hardware, software, and environmental parameters are used to estimate performance limits for SAR operation and utilization. A set of Python and MATLAB software tools is included and provides you with an effective mechanism to analyze and predict SAR performance for various imaging scenarios and applications. Examples which use the software tools are provided at the end of each chapter to reinforce critical SAR imaging topics such as clutter-to-noise ratio, mapping rate, spatial resolution, Doppler bandwidth, pulse repetition frequency, and coherency. This is an excellent resource for engineering professionals working in areas of radar signal processing and imaging as well as students interested in studying SAR.
This book on modelling the electrical activity of the heart is an attempt to describe continuum based modelling of cardiac electrical activity from the cell level to the body surface (the forward problem), and back again (the inverse problem). Background anatomy and physiology is covered briefly to provide a suitable context for understanding the detailed modelling that is presented herein. The questions of what is mathematical modelling and why one would want to use mathematical modelling are addressed to give some perspective to the philosophy behind our approach. Our view of mathematical modelling is broad — it is not simply about obtaining a solution to a set of mathematical equations, but includes some material on aspects such as experimental and clinical validation.
This is the first comprehensive textbook on higher-order logic that is written specifically to introduce the subject matter to graduate students in philosophy. The book covers both the formal aspects of higher-order languages—their model theory and proof theory, the theory of λ-abstraction and its generalizations—and their philosophical applications, especially to the topics of modality and propositional granularity. The book has a strong focus on non-extensional higher-order logics, making it more appropriate for foundational metaphysics than other introductions to the subject from computer science, mathematics, and linguistics. A Philosophical Introduction to Higher-order Logics assumes only that readers have a basic knowledge of first-order logic. With an emphasis on exercises, it can be used as a textbook though is also ideal for self-study. Author Andrew Bacon organizes the book's 18 chapters around four main parts: I. Typed Language II. Higher-Order Languages III. General Higher-Order Languages IV. Higher-Order Model Theory In addition, two appendices cover the Curry-Howard isomorphism and its applications for modeling propositional structure. Each chapter includes exercises that move from easier to more difficult, strategically placed throughout the chapter, and concludes with an annotated suggested reading list providing graduate students with most valuable additional resources. Key Features: Is the first comprehensive introduction to higher-order logic as a grounding for addressing problems in metaphysics Introduces the basic formal tools that are needed to theorize in, and model, higher-order languages Offers an abundance of - Simple exercises throughout the book, serving as comprehension checks on basic concepts and definitions - More difficult exercises designed to facilitate long-term learning Contains annotated sections on further reading, pointing the reader to related literature, learning resources, and historical context
Known for its versatility, the free programming language R is widely used for statistical computing and graphics, but is also a fully functional programming language well suited to scientific programming.An Introduction to Scientific Programming and Simulation Using R teaches the skills needed to perform scientific programming while also introducin
Among the traditional purposes of such an introductory course is the training of a student in the conventions of pure mathematics: acquiring a feeling for what is considered a proof, and supplying literate written arguments to support mathematical propositions. To this extent, more than one proof is included for a theorem - where this is considered beneficial - so as to stimulate the students' reasoning for alternate approaches and ideas. The second half of this book, and consequently the second semester, covers differentiation and integration, as well as the connection between these concepts, as displayed in the general theorem of Stokes. Also included are some beautiful applications of this theory, such as Brouwer's fixed point theorem, and the Dirichlet principle for harmonic functions. Throughout, reference is made to earlier sections, so as to reinforce the main ideas by repetition. Unique in its applications to some topics not usually covered at this level.
The question arises whether logic was given to us by God or whether it is the result of human evolution. I believe that at least the modus ponens rule ( A and if A then B implies B) is inherent in humans, but probably many other modern systems (e.g., resource logic, non - monotonic logic etc.) are the result of humans adapating to the environment. It is therefore of interest to study and compare the way logic is used in ancient cultures as well as the way logic is going to be used in our 21st century. This welcome book studies and compares the way formation of logic in three cultures: Ancient Greek (4th century B.C.), Judaic (1st century B.C. – 1st century A.D.) and Indo-Buddhist (2nd century A.D.) The book notes that logic became especially popular during the period of late antiquity in countries covered by the international trade of the Silk Road. This study makes a valuable contribution to the history of logic and to the very understanding of the origions and nature of logical thinking. -Prof. Dov Gabbay, King's College London, UK Andrew Schumann in his book demonsrates that logic step-by-step arose in different places and cultural circles. He argues that if we apply a structural-genealogical method, as well as turn to various sources, particularly, religious, philosophical, linguistic, etc., then we can obtain a more general and more adequate picture of emengence and development of logic. This book is a new and very valuable contribution to the history of logic as a manifestation of the human mind. - Prof. Jan Wolenski, Jagiellonian University, Poland The author of the Archaeology of Logic defends the claim, calling it "logic is aftter all", which sees logical competence as a practical skill that people began to learn in antiquity, as soom as they realized that avoiding cognitive biases in their reasoning would make their daily activities more successful. The in-depth reading of the book with its diving into the comparative quotations in the long dead or hardly known to most of us languages like Sumerian-Akkadian, Aramatic, Hebrew and etc, will be rewarded by the response that the logical competence is diverse and it can be trained, despite the inevitabilitiy of the reasoning fallacies; and that critical discussions and agaonal character of the social lide are the necessary tools for that. - Prof. Elena Lisanyuk
The area of analysis and control of mechanical systems using differential geometry is flourishing. This book collects many results over the last decade and provides a comprehensive introduction to the area.
This book presents fundamental theoretical results for designing object-oriented programming languages for controlling swarms. It studies the logics of swarm behaviours. According to behaviourism, all behaviours can be controlled or even managed by stimuli in the environment: attractants (motivational reinforcement) and repellents (motivational punishment). At the same time, there are two main stages in reactions to stimuli: sensing (perceiving signals) and motoring (appropriate direct reactions to signals). This book examines the strict limits of behaviourism from the point of view of symbolic logic and algebraic mathematics: how far can animal behaviours be controlled by the topology of stimuli? On the one hand, we can try to design reversible logic gates in which the number of inputs is the same as the number of outputs. In this case, the behaviouristic stimuli are inputs in swarm computing and appropriate reactions at the motoring stage are its outputs. On the other hand, the problem is that even at the sensing stage each unicellular organism can be regarded as a logic gate in which the number of outputs (means of perceiving signals) greatly exceeds the number of inputs (signals).
This volume is intended to mark the 75th birthday of A R Mitchell, of the University of Dundee. It consists of a collection of articles written by numerical analysts having links with Ron Mitchell, as colleagues, collaborators, former students, or as visitors to Dundee. Ron Mitchell is known for his books and articles contributing to the numerical analysis of partial differential equations; he has also made major contributions to the development of numerical analysis in the UK and abroad, and his many human qualitites are such that he is held in high regard and looked on with great affection by the numerical analysis community. The list of contributors is evidence of the esteem in which he is held, and of the way in which his influence has spread through his former students and fellow workers. In addition to contributions relevant to his own specialist subjects, there are also papers on a wide range of subjects in numerical analysis.
This book develops the central aspect of fixed point theory – the topological fixed point index – to maximal generality, emphasizing correspondences and other aspects of the theory that are of special interest to economics. Numerous topological consequences are presented, along with important implications for dynamical systems. The book assumes the reader has no mathematical knowledge beyond that which is familiar to all theoretical economists. In addition to making the material available to a broad audience, avoiding algebraic topology results in more geometric and intuitive proofs. Graduate students and researchers in economics, and related fields in mathematics and computer science, will benefit from this book, both as a useful reference and as a well-written rigorous exposition of foundational mathematics. Numerous problems sketch key results from a wide variety of topics in theoretical economics, making the book an outstanding text for advanced graduate courses in economics and related disciplines.
The third edition of this introductory textbook for both science students and non-science majors has been brought completely up-to-date. It reflects recent scientific progress in the field, as well as advances in the political arena around climate change. As in previous editions, it is tightly focussed on anthropogenic climate change. The first part of the book concentrates on the science of modern climate change, including evidence that the Earth is warming and a basic description of climate physics. Concepts such as radiative forcing, climate feedbacks, and the carbon cycle are discussed and explained using basic physics and algebra. The second half of the book goes beyond the science to address the economics and policy options to address climate change. The book's goal is for a student to leave the class ready to engage in the public policy debate on the climate crisis.
A textual commentary on Jeremiah 32 whose textlinguistically-oriented methodology helps to uncover far more haplography in the Septuagint Vorlage than hitherto suspected..
Interesting and useful as all this will be for anyone interested in knowing more about Bayes, this is just part of the riches contained in this book . . . Beyond doubt this book is a work of the highest quality in terms of the scholarship it displays, and should be regarded as a must for every mathematical library." --MAA ONLINE
This self-contained treatment begins with three chapters on the basics of point-set topology, after which it proceeds to homology groups and continuous mapping, barycentric subdivision, and simplicial complexes. 1961 edition.
Game Theory and Experimental Games: The Study of Strategic Interaction focuses on the development of game theory, taking into consideration empirical research, theoretical formulations, and research procedures involved. The book proceeds with a discussion on the theory of one-person games. The individual decision that a player makes in these kinds of games is noted as influential as to the outcome of these games. This discussion is followed by a presentation of pure coordination games and minimal situation. The ability of players to anticipate the choices of others to achieve a mutually beneficial outcome is emphasized. A favorable social situation is also influential in these kinds of games. The text moves forward by presenting studies on various kinds of competitive games. The research studies presented are coupled with empirical evidence and discussion designed to support the claims that are pointed out. The book also discusses several kinds of approaches in the study of games. Voting as a way to resolve multi-person games is also emphasized, including voting procedures, the preferences of voters, and voting strategies. The book is a valuable source of data for readers and scholars who are interested in the exploration of game theories.
Covering the complete design cycle of nanopositioning systems, this is the first comprehensive text on the topic. The book first introduces concepts associated with nanopositioning stages and outlines their application in such tasks as scanning probe microscopy, nanofabrication, data storage, cell surgery and precision optics. Piezoelectric transducers, employed ubiquitously in nanopositioning applications are then discussed in detail including practical considerations and constraints on transducer response. The reader is then given an overview of the types of nanopositioner before the text turns to the in-depth coverage of mechanical design including flexures, materials, manufacturing techniques, and electronics. This process is illustrated by the example of a high-speed serial-kinematic nanopositioner. Position sensors are then catalogued and described and the text then focuses on control. Several forms of control are treated: shunt control, feedback control, force feedback control and feedforward control (including an appreciation of iterative learning control). Performance issues are given importance as are problems limiting that performance such as hysteresis and noise which arise in the treatment of control and are then given chapter-length attention in their own right. The reader also learns about cost functions and other issues involved in command shaping, charge drives and electrical considerations. All concepts are demonstrated experimentally including by direct application to atomic force microscope imaging. Design, Modeling and Control of Nanopositioning Systems will be of interest to researchers in mechatronics generally and in control applied to atomic force microscopy and other nanopositioning applications. Microscope developers and mechanical designers of nanopositioning devices will find the text essential reading.
For the many different deterministic non-linear dynamic systems (physical, mechanical, technical, chemical, ecological, economic, and civil and structural engineering), the discovery of irregular vibrations in addition to periodic and almost periodic vibrations is one of the most significant achievements of modern science. An in-depth study of the theory and application of non-linear science will certainly change one's perception of numerous non-linear phenomena and laws considerably, together with its great effects on many areas of application. As the important subject matter of non-linear science, bifurcation theory, singularity theory and chaos theory have developed rapidly in the past two or three decades. They are now advancing vigorously in their applications to mathematics, physics, mechanics and many technical areas worldwide, and they will be the main subjects of our concern. This book is concerned with applications of the methods of dynamic systems and subharmonic bifurcation theory in the study of non-linear dynamics in engineering. It has grown out of the class notes for graduate courses on bifurcation theory, chaos and application theory of non-linear dynamic systems, supplemented with our latest results of scientific research and materials from literature in this field. The bifurcation and chaotic vibration of deterministic non-linear dynamic systems are studied from the viewpoint of non-linear vibration.
A comprehensive overview of the theory of stochastic processes and its connections to asset pricing, accompanied by some concrete applications. This book presents a self-contained, comprehensive, and yet concise and condensed overview of the theory and methods of probability, integration, stochastic processes, optimal control, and their connections to the principles of asset pricing. The book is broader in scope than other introductory-level graduate texts on the subject, requires fewer prerequisites, and covers the relevant material at greater depth, mainly without rigorous technical proofs. The book brings to an introductory level certain concepts and topics that are usually found in advanced research monographs on stochastic processes and asset pricing, and it attempts to establish greater clarity on the connections between these two fields. The book begins with measure-theoretic probability and integration, and then develops the classical tools of stochastic calculus, including stochastic calculus with jumps and Lévy processes. For asset pricing, the book begins with a brief overview of risk preferences and general equilibrium in incomplete finite endowment economies, followed by the classical asset pricing setup in continuous time. The goal is to present a coherent single overview. For example, the text introduces discrete-time martingales as a consequence of market equilibrium considerations and connects them to the stochastic discount factors before offering a general definition. It covers concrete option pricing models (including stochastic volatility, exchange options, and the exercise of American options), Merton's investment–consumption problem, and several other applications. The book includes more than 450 exercises (with detailed hints). Appendixes cover analysis and topology and computer code related to the practical applications discussed in the text.
This book is a rigorous assessment of the ways in which the natural and cultural environments we inhabit are valued, offering a distinctive perspective on environmental ethics and policy making that is sensitive to real life conflicts and dilemmas.
The growth of biostatistics has been phenomenal in recent years and has been marked by considerable technical innovation in both methodology and computational practicality. One area that has experienced significant growth is Bayesian methods. The growing use of Bayesian methodology has taken place partly due to an increasing number of practitioners valuing the Bayesian paradigm as matching that of scientific discovery. In addition, computational advances have allowed for more complex models to be fitted routinely to realistic data sets. Through examples, exercises and a combination of introductory and more advanced chapters, this book provides an invaluable understanding of the complex world of biomedical statistics illustrated via a diverse range of applications taken from epidemiology, exploratory clinical studies, health promotion studies, image analysis and clinical trials. Key Features: Provides an authoritative account of Bayesian methodology, from its most basic elements to its practical implementation, with an emphasis on healthcare techniques. Contains introductory explanations of Bayesian principles common to all areas of application. Presents clear and concise examples in biostatistics applications such as clinical trials, longitudinal studies, bioassay, survival, image analysis and bioinformatics. Illustrated throughout with examples using software including WinBUGS, OpenBUGS, SAS and various dedicated R programs. Highlights the differences between the Bayesian and classical approaches. Supported by an accompanying website hosting free software and case study guides. Bayesian Biostatistics introduces the reader smoothly into the Bayesian statistical methods with chapters that gradually increase in level of complexity. Master students in biostatistics, applied statisticians and all researchers with a good background in classical statistics who have interest in Bayesian methods will find this book useful.
Written by two distinguished experts in the field of digital communications, this classic text remains a vital resource three decades after its initial publication. Its treatment is geared toward advanced students of communications theory and to designers of channels, links, terminals, modems, or networks used to transmit and receive digital messages. The three-part approach begins with the fundamentals of digital communication and block coding, including an analysis of block code ensemble performance. The second part introduces convolutional coding, exploring ensemble performance and sequential decoding. The final section addresses source coding and rate distortion theory, examining fundamental concepts for memoryless sources as well as precepts related to memory, Gaussian sources, and universal coding. Appendixes of useful information appear throughout the text, and each chapter concludes with a set of problems, the solutions to which are available online.
Presents thermodynamics as self-contained and elegant set of ideas and methods. Introduces the necessary mathematical methods assuming no prior knowledge. Explains concepts like entropy and free energy with many examples.
This volume is dedicated to the fundamentals of convex functional analysis. It presents those aspects of functional analysis that are extensively used in various applications to mechanics and control theory. The purpose of the text is essentially two-fold. On the one hand, a bare minimum of the theory required to understand the principles of functional, convex and set-valued analysis is presented. Numerous examples and diagrams provide as intuitive an explanation of the principles as possible. On the other hand, the volume is largely self-contained. Those with a background in graduate mathematics will find a concise summary of all main definitions and theorems.
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