This book collects chapters which discuss interdisciplinary solutions to complex problems by using different approaches in order to save money, time and resources. The book presents the results on the recent advancements in artificial intelligence, computational intelligence, decision-making problems, emerging problems and practical achievements in the broad knowledge management field. q-ROFS is one of the hot topics for all the researchers, industrialists as well as academicians. This book is of interest to professionals and researchers working in the field of decision making and computational intelligence, as well as postgraduate and undergraduate students studying applications of fuzzy sets. The book helps solve different kinds of the decision-making problems such as medical diagnosis, pattern recognition, construction problems and technology selection under the uncertain fuzzy environment. Containing 19 chapters, the book begins by giving a topology of the q-ROFSs and their applications. It then progresses in a logical fashion, dedicating a chapter to each approach, including the generalized information measures for q-ROFSs, implementation of q-ROFSs to medical diagnosis, inventory model, multi-attribute decision-making and approaches to real-life industrial problems such as green campus transportation, social responsibility evaluation pattern and extensions of the q-ROFSs.

This series is designed to meet the needs of students and lecturers of the National Certificate Vocational. Features for the student include: Easy-to-understand language; Real-life examples; A key word feature for important subject terms; A dictionary feature for difficult words; A reflect-on-how-you-learn feature to explore personal learning styles; Workplace-oriented activities; and Chapter summaries that are useful for exam revision.

Real Scientists Don't Wear Ties links science to general and popular culture and everyday life in an easy-to-understand style. When a gifted writer of science selects his best pieces published in the world's most reputable periodicals such as Nature, Discover, and MIT Technology Review, we get an eminently readable collection of his varied work in book form. That it covers all-time relevant topics like quantum physics, gravitational waves, genetic engineering, space exploration, and artificial intelligence is an added delight. Prof. Perkowitz also discusses how science can be found in medical practice, cooking, soccer, and art, and also science and science fiction in the media. On the lighter side, he reports on his efforts to teach a computer to understand poetry, explains why scientists resist dressing up, and shows that unlike many people, scientists actually enjoy math.

Felix Hausdorff gehort zu den herausragenden Mathematikern der ersten Halfte des 20. Jahrhunderts. Er hinterliess einen ungewohnlich reichhaltigen Korpus wissenschaftlicher Manuskripe. Sein Gesamtwerk soll nun in 9 Banden, jeweils mit detaillierten Kommentaren, herausgegeben werden. Der vorliegende Band II enthalt Hausdorffs wohl wichtigstes Werk, die "Grundzuge der Mengenlehre" Dieses Buch gehort zu den Klassikern der mathematischen Literatur und hat auf die Entwicklung der Mathematik im 20. Jahrhundert einen bedeutenden Einfluss ausgeubt. Daher erschien es geboten, ausfuhrliche Kommentare beizufugen. In diesen Kommentaren werden vor allem die bedeutenden originellen Beitrage, die Hausdorff in den "Grundzugen" zur Topologie, allgemeinen und deskriptiven Mengenlehre geleistet hat, eingehend behandelt. Insbesondere wird versucht, Hausdorffs Leistungen in die historische Entwicklung einzuordnen und ihre jeweilige Wirkungsgeschichte zu skizzieren."

This book offers an introduction to artificial adaptive systems and a general model of the relationships between the data and algorithms used to analyze them. It subsequently describes artificial neural networks as a subclass of artificial adaptive systems, and reports on the backpropagation algorithm, while also identifying an important connection between supervised and unsupervised artificial neural networks. The book's primary focus is on the auto contractive map, an unsupervised artificial neural network employing a fixed point method versus traditional energy minimization. This is a powerful tool for understanding, associating and transforming data, as demonstrated in the numerous examples presented here. A supervised version of the auto contracting map is also introduced as an outstanding method for recognizing digits and defects. In closing, the book walks the readers through the theory and examples of how the auto contracting map can be used in conjunction with another artificial neural network, the "spin-net," as a dynamic form of auto-associative memory.

All students taking laboratory courses within the physical sciences and engineering will benefit from this book, whilst researchers will find it an invaluable reference. This concise, practical guide brings the reader up-to-speed on the proper handling and presentation of scientific data and its inaccuracies. It covers all the vital topics with practical guidelines, computer programs (in Python), and recipes for handling experimental errors and reporting experimental data. In addition to the essentials, it also provides further background material for advanced readers who want to understand how the methods work. Plenty of examples, exercises and solutions are provided to aid and test understanding, whilst useful data, tables and formulas are compiled in a handy section for easy reference.

Mathematics of Keno and Lotteries is an elementary treatment of the mathematics, primarily probability and simple combinatorics, involved in lotteries and keno. Keno has a long history as a high-advantage, high-payoff casino game, and state lottery games such as Powerball are mathematically similar. MKL also considers such lottery games as passive tickets, daily number drawings, and specialized games offered around the world. In addition, there is a section on financial mathematics that explains the connection between lump-sum lottery prizes (as with Powerball) and their multi-year annuity options. So-called "winning systems" for keno and lotteries are examined mathematically and their flaws identified.

Twists, Tilings, and Tessellation describes the underlying principles and mathematics of the broad and exciting field of abstract and mathematical origami, most notably the field of origami tessellations. It contains folding instructions, underlying principles, mathematical concepts, and many beautiful photos of the latest work in this fast-expanding field.

Bei Problemen in Technik, Natur- und Wirtschaftswissenschaften werden h ufig maximale Ergebnisse unter minimalem Aufwand gesucht. Deshalb gewinnt die mathematische Optimierung sowohl f r Ingenieure als auch Natur- und Wirtschaftswissenschaftler zunehmend an Bedeutung. Das vorliegende Lehrbuch gibt eine Einf hrung in die lineare, nichtlineare und vektorielle Optimierung, wobei auch Spezialf lle wie quadratische, parametrische und diskrete Optimierung betrachtet werden. Des Weiteren wird der Gegenstand der Spieltheorie und dynamischen Optimierung skizziert. Im Buch wird auf Beweise verzichtet und daf r die Problematik anhand von Beispielen illustriert. Ein zweiter Schwerpunkt des Buches liegt auf der Berechnung der behandelten Optimierungsaufgaben mittels Computer. Hierzu werden die Computeralgebrasysteme MAPLE, MATHEMATICA, MATHCAD und MATLAB und das Tabellenkalkulationsprogramm EXCEL herangezogen und versionsunabh ngig erl utert.

Introduction to Probability with Texas Hold'em Examples illustrates both standard and advanced probability topics using the popular poker game of Texas Hold'em, rather than the typical balls in urns. The author uses students' natural interest in poker to teach important concepts in probability.

Exploring Geometry, Second Edition promotes student engagement with the beautiful ideas of geometry. Every major concept is introduced in its historical context and connects the idea with real-life. A system of experimentation followed by rigorous explanation and proof is central. Exploratory projects play an integral role in this text. Students develop a better sense of how to prove a result and visualize connections between statements, making these connections real. They develop the intuition needed to conjecture a theorem and devise a proof of what they have observed. Features: Second edition of a successful textbook for the first undergraduate course Every major concept is introduced in its historical context and connects the idea with real life Focuses on experimentation Projects help enhance student learning All major software programs can be used; free software from author

This book formally introduces synthetic differential topology, a natural extension of the theory of synthetic differential geometry which captures classical concepts of differential geometry and topology by means of the rich categorical structure of a necessarily non-Boolean topos and of the systematic use of logical infinitesimal objects in it. Beginning with an introduction to those parts of topos theory and synthetic differential geometry necessary for the remainder, this clear and comprehensive text covers the general theory of synthetic differential topology and several applications of it to classical mathematics, including the calculus of variations, Mather's theorem, and Morse theory on the classification of singularities. The book represents the state of the art in synthetic differential topology and will be of interest to researchers in topos theory and to mathematicians interested in the categorical foundations of differential geometry and topology.

For a brief time in history, it was possible to imagine that a sufficiently advanced intellect could, given sufficient time and resources, in principle understand how to mathematically prove everything that was true. They could discern what math corresponds to physical laws, and use those laws to predict anything that happens before it happens. That time has passed. Goedel's undecidability results (the incompleteness theorems), Turing's proof of non-computable values, the formulation of quantum theory, chaos, and other developments over the past century have shown that there are rigorous arguments limiting what we can prove, compute, and predict. While some connections between these results have come to light, many remain obscure, and the implications are unclear. Are there, for example, real consequences for physics - including quantum mechanics - of undecidability and non-computability? Are there implications for our understanding of the relations between agency, intelligence, mind, and the physical world? This book, based on the winning essays from the annual FQXi competition, contains ten explorations of Undecidability, Uncomputability, and Unpredictability. The contributions abound with connections, implications, and speculations while undertaking rigorous but bold and open-minded investigation of the meaning of these constraints for the physical world, and for us as humans.

The hybrid/heterogeneous nature of future microprocessors and large high-performance computing systems will result in a reliance on two major types of components: multicore/manycore central processing units and special purpose hardware/massively parallel accelerators. While these technologies have numerous benefits, they also pose substantial performance challenges for developers, including scalability, software tuning, and programming issues. Researchers at the Forefront Reveal Results from Their Own State-of-the-Art Work Edited by some of the top researchers in the field and with contributions from a variety of international experts, Scientific Computing with Multicore and Accelerators focuses on the architectural design and implementation of multicore and manycore processors and accelerators, including graphics processing units (GPUs) and the Sony Toshiba IBM (STI) Cell Broadband Engine (BE) currently used in the Sony PlayStation 3. The book explains how numerical libraries, such as LAPACK, help solve computational science problems; explores the emerging area of hardware-oriented numerics; and presents the design of a fast Fourier transform (FFT) and a parallel list ranking algorithm for the Cell BE. It covers stencil computations, auto-tuning, optimizations of a computational kernel, sequence alignment and homology, and pairwise computations. The book also evaluates the portability of drug design applications to the Cell BE and illustrates how to successfully exploit the computational capabilities of GPUs for scientific applications. It concludes with chapters on dataflow frameworks, the Charm++ programming model, scan algorithms, and a portable intracore communication framework. Explores the New Computational Landscape of Hybrid Processors By offering insight into the process of constructing and effectively using the technology, this volume provides a thorough and practical introduction to the area of hybrid computing. It discusses introductory concepts and simple examples of parallel computing, logical and performance debugging for parallel computing, and advanced topics and issues related to the use and building of many applications.

This book provides an organized exposition of the current state of the theory of commutative semigroup cohomology, a theory which was originated by the author and has matured in the past few years. The work contains a fundamental scientific study of questions in the theory. The various approaches to commutative semigroup cohomology are compared. The problems arising from definitions in higher dimensions are addressed. Computational methods are reviewed. The main application is the computation of extensions of commutative semigroups and their classification. Previously the components of the theory were scattered among a number of research articles. This work combines all parts conveniently in one volume. It will be a valuable resource for future students of and researchers in commutative semigroup cohomology and related areas.

Gerhard Gentzen is best known for his development of the proof systems of natural deduction and sequent calculus, central in many areas of logic and computer science today. Another noteworthy achievement is his resolution of the embarrassing situation created by Goedel's incompleteness results, especially the second one about the unprovability of consistency of elementary arithmetic. After these successes, Gentzen dedicated the rest of his short life to the main problem of Hilbert's proof theory, the question of the consistency of analysis. He was arrested in the summer of 1945 with other professors of the German University of Prague and died soon afterward of starvation in a prison cell. Attempts at locating his lost manuscripts failed at the time, but several decades later, two slim folders of shorthand notes were found. In this volume, Jan von Plato gives an overview of Gentzen's life and scientific achievements, based on detailed archival and systematic studies, and essential for placing the translations of shorthand manuscripts that follow in the right setting. The materials in this book are singular in the way they show the birth and development of Gentzen's central ideas and results, sometimes in a well-developed form, and other times as flashes into the anatomy of the workings of a unique mind.

Elements of Mathematics takes readers on a fascinating tour that begins in elementary mathematics--but, as John Stillwell shows, this subject is not as elementary or straightforward as one might think. Not all topics that are part of today's elementary mathematics were always considered as such, and great mathematical advances and discoveries had to occur in order for certain subjects to become "elementary." Stillwell examines elementary mathematics from a distinctive twenty-first-century viewpoint and describes not only the beauty and scope of the discipline, but also its limits. From Gaussian integers to propositional logic, Stillwell delves into arithmetic, computation, algebra, geometry, calculus, combinatorics, probability, and logic. He discusses how each area ties into more advanced topics to build mathematics as a whole. Through a rich collection of basic principles, vivid examples, and interesting problems, Stillwell demonstrates that elementary mathematics becomes advanced with the intervention of infinity. Infinity has been observed throughout mathematical history, but the recent development of "reverse mathematics" confirms that infinity is essential for proving well-known theorems, and helps to determine the nature, contours, and borders of elementary mathematics. Elements of Mathematics gives readers, from high school students to professional mathematicians, the highlights of elementary mathematics and glimpses of the parts of math beyond its boundaries.

This survey of computability theory offers the techniques and tools that computer scientists (as well as mathematicians and philosophers studying the mathematical foundations of computing) need to mathematically analyze computational processes and investigate the theoretical limitations of computing. Beginning with an introduction to the mathematisation of "mechanical process" using URM programs, this textbook explains basic theory such as primitive recursive functions and predicates and sequence-coding, partial recursive functions and predicates, and loop programs. Advanced chapters cover the Ackerman function, Tarski's theorem on the non-representability of truth, Goedel's incompleteness and Rosser's incompleteness theorems, two short proofs of the incompleteness theorem that are based on Lob's deliverability conditions, Church's thesis, the second recursion theorem and applications, a provably recursive universal function for the primitive recursive functions, Oracle computations and various classes of computable functionals, the Arithmetical hierarchy, Turing reducibility and Turing degrees and the priority method, a thorough exposition of various versions of the first recursive theorem, Blum's complexity, Hierarchies of primitive recursive functions, and a machine-independent characterisation of Cobham's feasibly computable functions.