There is an extensive literature in the form of papers (but no books) on lattice dynamical systems. The book focuses on dissipative lattice dynamical systems and their attractors of various forms such as autonomous, nonautonomous and random. The existence of such attractors is established by showing that the corresponding dynamical system has an appropriate kind of absorbing set and is asymptotically compact in some way.There is now a very large literature on lattice dynamical systems, especially on attractors of all kinds in such systems. We cannot hope to do justice to all of them here. Instead, we have focused on key areas of representative types of lattice systems and various types of attractors. Our selection is biased by our own interests, in particular to those dealing with biological applications. One of the important results is the approximation of Heaviside switching functions in LDS by sigmoidal functions.Nevertheless, we believe that this book will provide the reader with a solid introduction to the field, its main results and the methods that are used to obtain them.

Why can no two people ever see the same rainbow? What happens when you pull a pop song apart into pure sine waves and play it back on a piano? Why does the wake behind a duck always form an angle of exactly 39 degrees? And what did mathematicians have to do with the great pig stampede of 2012? The answer to each of these questions can be found in the triangle.

In Love Triangle, stand-up comedian, ex-maths teacher and Sunday Times number one bestselling author Matt Parker is on a mission to prove why we should all show a lot more love for triangles, along with the useful trigonometry and geometry they enable. To make his point, he uses triangles to create his own digital avatar, survive a harrowing motorcycle ride, cut a sandwich into three equal parts, and measure tall buildings while wearing silly shoes. But soon these hare-brained experiments begin to reveal a genuinely important truth: triangles are the hidden pattern beneath the surface of the contemporary world, used in everything from GPS to CGI via Spotify streaming, the play button and your best mate’s triangle tattoo.

Join Matt Parker as he demonstrates why there’s more to triangles than Pythagoras and SOHCAHTOA. Triangles are everything and everything is triangles.

Hyperidentities are important formulae of second-order logic, and research in hyperidentities paves way for the study of second-order logic and second-order model theory.This book illustrates many important current trends and perspectives for the field of hyperidentities and their applications, of interest to researchers in modern algebra and discrete mathematics. It covers a number of directions, including the characterizations of the Boolean algebra of n-ary Boolean functions and the distributive lattice of n-ary monotone Boolean functions; the classification of hyperidentities of the variety of lattices, the variety of distributive (modular) lattices, the variety of Boolean algebras, and the variety of De Morgan algebras; the characterization of algebras with aforementioned hyperidentities; the functional representations of finitely-generated free algebras of various varieties of lattices and bilattices via generalized Boolean functions (De Morgan functions, quasi-De Morgan functions, super-Boolean functions, super-De Morgan functions, etc); the structural results for De Morgan algebras, Boole-De Morgan algebras, super-Boolean algebras, bilattices, among others.While problems of Boolean functions theory are well known, the present book offers alternative, more general problems, involving the concepts of De Morgan functions, quasi-De Morgan functions, super-Boolean functions, and super-De Morgan functions, etc. In contrast to other generalized Boolean functions discovered and investigated so far, these functions have clearly normal forms. This quality is of crucial importance for their applications in pure and applied mathematics, especially in discrete mathematics, quantum computation, quantum information theory, quantum logic, and the theory of quantum computers.

The revision of this well-respected text presents a balanced approach of the classical and Bayesian methods and now includes a chapter on simulation (including Markov chain Monte Carlo and the Bootstrap), coverage of residual analysis in linear models, and many examples using real data. Probability & Statistics, Fourth Edition, was written for a one- or two-semester probability and statistics course. This course is offered primarily at four-year institutions and taken mostly by sophomore and junior level students majoring in mathematics or statistics. Calculus is a prerequisite, and a familiarity with the concepts and elementary properties of vectors and matrices is a plus.

Engineering Mathematics is the unparalleled undergraduate textbook for students of electrical, electronic, communications and systems engineering. Tried and tested over many years, this widely used textbook is now in its 5th edition, having been fully updated and revised. This new edition includes an even greater emphasis on the application of mathematics within a range of engineering contexts. It features detailed explanation of why a technique is important to engineers. In addition, it provides essential guidance in how to use mathematics to solve engineering problems. This approach ensures a deep and practical understanding of the role of mathematics in modern engineering.

Calculus: Single and Multivariable, 7th Edition continues the effort to promote courses in which understanding and computation reinforce each other. The 7th Edition reflects the many voices of users at research universities, four-year colleges, community colleges, and secondary schools. This new edition has been streamlined to create a flexible approach to both theory and modeling. The program includes a variety of problems and examples from the physical, health, and biological sciences, engineering and economics; emphasizing the connection between calculus and other fields.

This book is the third of a three-volume set of books on the theory of algebras, a study that provides a consistent framework for understanding algebraic systems, including groups, rings, modules, semigroups and lattices. Volume I, first published in the 1980s, built the foundations of the theory and is considered to be a classic in this field. The long-awaited volumes II and III are now available. Taken together, the three volumes provide a comprehensive picture of the state of art in general algebra today, and serve as a valuable resource for anyone working in the general theory of algebraic systems or in related fields. The two new volumes are arranged around six themes first introduced in Volume I. Volume II covers the Classification of Varieties, Equational Logic, and Rudiments of Model Theory, and Volume III covers Finite Algebras and their Clones, Abstract Clone Theory, and the Commutator. These topics are presented in six chapters with independent expositions, but are linked by themes and motifs that run through all three volumes.

This accessible guide is intended for those persons who need to polish up their rusty maths, or who need to get a grip on the basics of the subject for the first time. Each concept is explained, with appropriate examples, and is applied in an exercise. The solutions to all exercises are set out in detail. The book uses informal conversational language and will change the perception that mathematics is only for special people. The author has taught the subject at different levels for many years.

Economic theory and philosophy have discussed concepts of fairness, but the criteria of fairness are in each case absolute: a situation is either fair or it is not. This book draws on these literatures to propose two criteria of relative fairness, and a hierarchical rule for the priority of application of these criteria, with a view to comparison of practicable alternatives in public policy. A veil-of-ignorance device of representation of rational fairness is used to argue that these criteria are normatively relevant. Applications to intergenerational fairness, fairness among regions in the context of migration, externalities and Pigovian taxes, to fair prices and wages, and to relative fairness in the status of racial and caste groups are sketched. The book is designed with real world public policy practice. Scholars with an interest in the economic evaluation of public policy will find this compelling book essential reading.

Microfluidics: Modeling, Mechanics and Mathematics, Second Edition provides a practical, lab-based approach to nano- and microfluidics, including a wealth of practical techniques, protocols and experiments ready to be put into practice in both research and industrial settings. This practical approach is ideally suited to researchers and R&D staff in industry. Additionally, the interdisciplinary approach to the science of nano- and microfluidics enables readers from a range of different academic disciplines to broaden their understanding. Alongside traditional fluid/transport topics, the book contains a wealth of coverage of materials and manufacturing techniques, chemical modification/surface functionalization, biochemical analysis, and the biosensors involved. This fully updated new edition also includes new sections on viscous flows and centrifugal microfluidics, expanding the types of platforms covered to include centrifugal, capillary and electro kinetic platforms.

The UK's most trusted A level Mathematics resources With over 900,000 copies sold (plus 1.3 million copies sold of the previous edition), Pearson's own resources for Pearson Edexcel are the market-leading and most trusted for AS and A level Mathematics. This book covers all the content needed for the compulsory Edexcel AS level Core Pure Mathematics exam. It can also be used alongside Book 2 to cover all the content needed for the compulsory Edexcel A level Core Pure Mathematics exams Enhanced focus on problem-solving and modelling, as well as supporting the large data set and calculators Packed with worked examples with guidance, lots of exam-style questions, practice papers, and plenty of mixed and review exercises Full worked solutions to every question available free and online for quick and easy access. Plus free additional online content with GeoGebra interactives and Casio calculator tutorials Practice books also available offering the most comprehensive and flexible AS/A level Maths practice with over 2000 extra questions Includes access to an online digital edition (valid for 3 years once activated) Pearson Edexcel AS and A level Further Mathematics Core Pure Mathematics Book 1/AS Textbook + e-book matches the Pearson Edexcel exam structure and is fully integrated with Pearson Edexcel's interactive scheme of work. All of the books in this series focus on problem-solving and modelling, as well as supporting the large data set and calculators. They are packed with worked examples with guidance, lots of exam-style questions, practice papers, and plenty of mixed and review exercises. There are full worked solutions to every question available free and online for quick and easy access. You will also have access to lots of free additional online content with GeoGebra interactives and Casio calculator tutorials. There are separate Pure and Applied textbooks for AS and A level Maths, and a textbook per option for AS and A level Further Maths. Practice books are also available offering the most comprehensive and flexible AS/A level Maths practice with over 2000 extra questions. Pearson's revision resources are the smart choice for those revising for Pearson Edexcel AS and A level Mathematics - there is a Revision Workbook for exam practice and a Revision Guide for classroom and independent study. Practice Papers Plus+ books contain additional full length practice papers, so you can practice answering questions by writing straight into the book and perfect your responses with targeted hints, guidance and support for every question, including fully worked solutions.

Every day our numerical skills are tested in different ways, from shopping to budgeting and bill paying. But not everyone is comfortable with numbers. "The Complete Book of Fun Maths" is designed to build up confidence with maths through a series of progressively more challenging tests and puzzles. There is a hints section in case you get stuck and a complete set of answers at the back of the book so you can check how you are doing.

"The Complete Book of Fun Maths" starts with a gentle workout in an introductory 'limbering-up session', and then builds into a comprehensive programme via a range of puzzles and tests on 'lateral thinking', 'fun with numbers', 'logic puzzles', 'geometric puzzles' and 'numerical IQ tests', among others. Soon you will be handling all kinds of maths puzzles with complete confidence!

Use this and other books in "The IQ Workout Series" as a fun and informative way of testing, assessing and expanding your brainpower. These books are suitable for anyone from 18 to 80 who wants to put themselves to the test. Ken Russell and Philip Carter have written over 100 books on all aspects of testing, puzzles and crosswords.

Advancements in Bayesian Methods and Implementation, Volume 47 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters on a variety of timely topics, including Fisher Information, Cramer-Rao and Bayesian Paradigm, Compound beta binomial distribution functions, MCMC for GLMMS, Signal Processing and Bayesian, Mathematical theory of Bayesian statistics where all models are wrong, Machine Learning and Bayesian, Non-parametric Bayes, Bayesian testing, and Data Analysis with humans, Variational inference or Functional horseshoe, Generalized Bayes.

Optimized linear algebra (LA) libraries that are able to exploit the underlying hardware are always of interest in the high-performance computing community. The implementation of LA software has evolved along with computer architecture, while the specification remains unaltered almost from the beginning. It is important to differentiate between the specification of LA libraries and their implementation. Because LA libraries pursue high performance, the implementation for a given architecture needs to be optimized for it specifically. However, the type of operations included in the libraries, the input/output parameters, and the data types to be handled are common to all of them. This is why, while the specification remains constant, the implementation evolves with the creation of new architectures. Developing Linear Algebra Codes on Modern Processors: Emerging Research and Opportunities presents the main characteristics of LA libraries, showing the differences between the standards for sparse and dense versions. It further explores relevant linear algebra problems and shows, in a clear and understandable way, how to solve them using different computer architectures. Covering topics such as programming models, batched computing, and distributed memory platforms, this premier reference source is an excellent resource for programmers, computer scientists, engineers, students and faculty of higher education, librarians, researchers, and academicians.

Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities as well as their interactions with different ideational spectra. In all classical algebraic structures, the law of compositions on a given set are well-defined, but this is a restrictive case because there are situations in science where a law of composition defined on a set may be only partially defined and partially undefined, which we call NeutroDefined, or totally undefined, which we call AntiDefined. Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebra introduces NeutroAlgebra, an emerging field of research. This book provides a comprehensive collection of original work related to NeutroAlgebra and covers topics such as image retrieval, mathematical morphology, and NeutroAlgebraic structure. It is an essential resource for philosophers, mathematicians, researchers, educators and students of higher education, and academicians.

This book consists of the expanded notes from an upper level linear algebra course given some years ago by the author. Each section, or lecture, covers about a week's worth of material and includes a full set of exercises of interest. It should feel like a very readable series of lectures. The notes cover all the basics of linear algebra but from a mature point of view. The author starts by briefly discussing fields and uses those axioms to define and explain vector spaces. Then he carefully explores the relationship between linear transformations and matrices. Determinants are introduced as volume functions and as a way to determine whether vectors are linearly independent. Also included is a full chapter on bilinear forms and a brief chapter on infinite dimensional spaces.The book is very well written, with numerous examples and exercises. It includes proofs and techniques that the author has developed over the years to make the material easier to understand and to compute.

Biostatistics for the Biological and Health Sciences brings statistical theories and methods to life with real applications, emphasis on real data, and a friendly writing style. It suits a variety of students in their first statistics course and uses minimal algebra. Abundant examples and emphasis on real data help you develop skills in critical thinking, technology and communication. This collaboration from 2 biological sciences experts and the author of the #1 statistics book is an excellent introduction that is also highly readable, understandable and relevant. The 3rd Edition incorporates the latest methods used by professional statisticians. It offers a wealth of new data sets, examples, and exercises (such as those involving clinical trials, COVID-19, biometrics, and anthropometrics) and includes features that address all recommendations included in the Guidelines for Assessment and Instruction in Statistics Education (GAISE) as recommended by the American Statistical Association.