Boolean Functions

Special functions, natural generalizations of the elementary functions, have been studied for centuries. The greatest mathematicians, among them Euler, Gauss, Legendre, Eisenstein, Riemann, and Ramanujan, have laid the foundations for this beautiful and useful area of mathematics. This treatise presents an overview of special functions, focusing primarily on hypergeometric functions and the associated hypergeometric series, including Bessel functions and classical orthogonal polynomials, using the basic building block of the gamma function. In addition to relatively new work on gamma and beta functions, such as Selberg's multidimensional integrals, many important but relatively unknown nineteenth century results are included. Other topics include q-extensions of beta integrals and of hypergeometric series, Bailey chains, spherical harmonics, and applications to combinatorial problems. The authors provide organizing ideas, motivation, and historical background for the study and applica

Special functions, natural generalizations of the elementary functions, have been studied for centuries. The greatest mathematicians, among them Euler, Gauss, Legendre, Eisenstein, Riemann, and Ramanujan, have laid the foundations for this beautiful and useful area of mathematics. This treatise presents an overview of special functions, focusing primarily on hypergeometric functions and the associated hypergeometric series, including Bessel functions and classical orthogonal polynomials, using the basic building block of the gamma function. In addition to relatively new work on gamma and beta functions, such as Selberg's multidimensional integrals, many important but relatively unknown nineteenth century results are included. Other topics include q-extensions of beta integrals and of hypergeometric series, Bailey chains, spherical harmonics, and applications to combinatorial problems. The authors provide organizing ideas, motivation, and historical background for the study and applica

This book gives an introduction to theories of computability from a mathematically sophisticated point of view. It treats not only 'the' theory of computability (created by Alan Turing and others in the 1930s), but also a variety of other theories (of Boolean functions, automata and formal languages). These are addressed from the classical perspective of their generation by grammars and from the modern perspective as rational cones. The treatment of the classical theory of computable functions and relations takes the form of a tour through basic recursive function theory, starting with an axiomatic foundation and developing the essential methods in order to survey the most memorable results of the field. This authoritative account by one of the leading lights of the subject will prove exceptionally useful reading for graduate students, and researchers in theoretical computer science and mathematics.

Two volumes of a classic 5-volume work inone handy edition. Part I considers general foundations of the theory of functions; Part II stresses special functions and characteristic, important typ

Contains the various principal special functions in common use and their basic properties and manipulations. Discusses expansions of functions in infinite series and infinite product and the asymptoti

The major thrust of this book is the analysis of pointwise behavior of Sobolev functions of integer order and BV functions (functions whose partial derivatives are measures with finite total variation

Turn Excel into an unstoppable data-and number-crunching machine Microsoft Excel is the Swiss Army knife of apps. With over 470 built-in functions and countless custom formulas, the program can help make you the smartest guy or gal in any room. And now that it's been supercharged with Copilot—Microsoft's AI-powered helper—it's even easier to produce accurate and useful results anywhere, anytime.Best of all, it doesn't take an advanced degree in mathematics or data science to take full advantage of Excel's functionality. Just grab a copy of this latest edition of Excel Formulas & Functions For Dummies and get a flying start on the Excel functions and formulas that power up your data superpowers. With this book, you'll: Learn to create and use hundreds of formulas and functions, correct common mistakes, and make calculationsDiscover how to analyze data and calculate statistics, and even work with dates and timesUse the ever-evolving, AI-powered Copilot to expand Excel's functionality

The term weakly differentiable functions in the title refers to those inte grable functions defined on an open subset of Rn whose partial derivatives in the sense of distributions are either Lr functi

Tau functions are a central tool in the modern theory of integrable systems. This volume provides a thorough introduction, starting from the basics and extending to recent research results. It covers a wide range of applications, including generating functions for solutions of integrable hierarchies, correlation functions in the spectral theory of random matrices and combinatorial generating functions for enumerative geometrical and topological invariants. A self-contained summary of more advanced topics needed to understand the material is provided, as are solutions and hints for the various exercises and problems that are included throughout the text to enrich the subject matter and engage the reader. Building on knowledge of standard topics in undergraduate mathematics and basic concepts and methods of classical and quantum mechanics, this monograph is ideal for graduate students and researchers who wish to become acquainted with the full range of applications of the theory of tau f

An illustrated journey through the past, present, and future of artificial intelligence, from popular science author Cliff Pickover.From medieval robots and Boolean algebra to facial recognition, arti

This book presents high-quality original contributions on positive systems, including those with positivity in compartmental switched systems, Markovian jump systems, Boolean networks, interval observ

Generalized Trigonometric and Hyperbolic Functions highlights, to those in the area of generalized trigonometric functions, an alternative path to the creation and analysis of these classes of functio

Viral Polymerases: Structures, Functions and Roles as Antiviral Drug Targets presents in-depth study information on the structure and functions of polymerases and their roles in the lifecycle of virus

This monograph presents an intuitive theory of trial wave functions for strongly interacting fermions in fractional quantum Hall states. The correlation functions for the proposed fermion interactions

"Quotations from Jewish scriptures play a crucial role in the Letter to the Romans. The Rhetorical Functions of Scriptural Quotations in Romans explores their rhetorical functions in Paul's argumentat

This book is a comprehensive guide to qualitative comparative analysis (QCA) using R. Using Boolean algebra to implement principles of comparison used by scholars engaged in the qualitative study of

This book introduces and develops new algebraic methods to work with relations, often conceived as Boolean matrices, and applies them to topology. Although these objects mirror the matrices that appea

For courses in precalculus. Ties concepts together using a functions approach The Concepts Through Functions Series introduces functions at the start of each text, and maintains a co

Designed for the three-semester engineering calculus course, CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, 7th Edition, continues to offer instructors and students innovative teaching and learning resourc

Complexity theory aims to understand and classify computational problems, especially decision problems, according to their inherent complexity. This book uses new techniques to expand the theory for use with counting problems. The authors present dichotomy classifications for broad classes of counting problems in the realm of P and NP. Classifications are proved for partition functions of spin systems, graph homomorphisms, constraint satisfaction problems, and Holant problems. The book assumes minimal prior knowledge of computational complexity theory, developing proof techniques as needed and gradually increasing the generality and abstraction of the theory. This volume presents the theory on the Boolean domain, and includes a thorough presentation of holographic algorithms, culminating in classifications of computational problems studied in exactly solvable models from statistical mechanics.

Executive Functions in Children's Everyday Lives captures the diversity and complexity of the executive system that underlies children's everyday life experiences. Acquisition of executive functions,

Periphyton: Functions and Application in Environmental Remediation presents a systematic overview of a wide variety of periphyton functions and applications in environmental remediation, providing rea

Fractal Functions, Fractal Surfaces, and Wavelets, Second Edition, is the first systematic exposition of the theory of local iterated function systems, local fractal functions and fractal surfaces, an

The subject of special functions is often presented as a collection of disparate results, rarely organized in a coherent way. This book emphasizes general principles that unify and demarcate the subjects of study. The authors' main goals are to provide clear motivation, efficient proofs, and original references for all of the principal results. The book covers standard material, but also much more. It shows how much of the subject can be traced back to two equations - the hypergeometric equation and confluent hypergeometric equation - and it details the ways in which these equations are canonical and special. There is extended coverage of orthogonal polynomials, including connections to approximation theory, continued fractions, and the moment problem, as well as an introduction to new asymptotic methods. There are also chapters on Meijer G-functions and elliptic functions. The final chapter introduces Painlevé transcendents, which have been termed the 'special functions of the twenty-

A sequel to his frequently cited Cost and Production Functions (1953), this book offers a unified, comprehensive treatment of these functions which underlie the economic theory of production.The appro

Linear Circuit Transfer Functions: A Tutorial Guide to Fast Analytical Techniques teaches readers how to determine transfer functions of linear passive and active circuits by applying Fast Analytical

The Woods Hole trace formula is a Lefschetz fixed-point theorem for coherent cohomology on algebraic varieties. It leads to a version of the sheaves-functions dictionary of Deligne, relating characteristic-p-valued functions on the rational points of varieties over finite fields to coherent modules equipped with a Frobenius structure. This book begins with a short introduction to the homological theory of crystals of Böckle and Pink with the aim of introducing the sheaves-functions dictionary as quickly as possible, illustrated with elementary examples and classical applications. Subsequently, the theory and results are expanded to include infinite coefficients, L-functions, and applications to special values of Goss L-functions and zeta functions. Based on lectures given at the Morningside Center in Beijing in 2013, this book serves as both an introduction to the Woods Hole trace formula and the sheaves-functions dictionary, and to some advanced applications on characteristic p zeta v

Computer-Hardware Evaluation of Mathematical Functions provides a thorough up-to-date understanding of the methods used in computer hardware for the evaluation of mathematical functions: reciprocals,

The description for this book, Analytic Functions, will be forthcoming.

Ridge functions are a rich class of simple multivariate functions which have found applications in a variety of areas. These include partial differential equations (where they are sometimes termed 'plane waves'), computerised tomography, projection pursuit in the analysis of large multivariate data sets, the MLP model in neural networks, Waring's problem over linear forms, and approximation theory. Ridge Functions is the first book devoted to studying them as entities in and of themselves. The author describes their central properties and provides a solid theoretical foundation for researchers working in areas such as approximation or data science. He also includes an extensive bibliography and discusses some of the unresolved questions that may set the course for future research in the field.

This book presents basic theory on static Green's functions in general anisotropic magnetoelectroelastic media including detailed derivations based on the complex variable method, potential method, and integral transforms. Green's functions corresponding to the reduced cases are also presented including those in anisotropic and transversely isotropic piezoelectric and piezomagnetic media, and in purely anisotropic elastic, transversely isotropic elastic and isotropic elastic media. Problems include those in three-dimensional, (two-dimensional) infinite, half, and biomaterial spaces (planes). While the emphasis is on the Green's functions related to the line and point force, those corresponding to the important line and point dislocation are also provided and discussed. This book provides a comprehensive derivation and collection of the Green's functions in the concerned media, and as such, it is an ideal reference book for researchers and engineers, and a textbook for both students in

This second edition systematically leads readers through the process of developing Green's functions for ordinary and partial differential equations. In addition to exploring the classical problems in

A sequel to his frequently cited Cost and Production Functions (1953), this book offers a unified, comprehensive treatment of these functions which underlie the economic theory of production.The appro

Diversity and Functions of GABA Receptors: A Tribute to Hanns Mohler, Part B, a new volume ofAdvances in Pharmacology, presents the diversity and functions of GABA Receptors. The volume looks at resea

Elegant and concise, this text explores properties of meromorphic functions, Picard theorem, harmonic and subharmonic functions, applications, and boundary behavior of the Riemann mapping function for

Now with new introductory material, Charles Ragin’s The Comparative Method proposes a synthetic new strategy, based on an application of Boolean algebra that, by combining the strengths of both qualit

This monograph summarizes the special functions needed in the performance analysis of wireless communications systems.On the basis of special Gaussian and Owen functions, the methodology for the calcu

This book is aimed at the approximation of set-valued functions with compact sets in an Euclidean space as values. The interest in set-valued functions is rather new. Such functions arise in various m

Describes how to conduct both basic and advanced searches on the Internet, providing information on the history of internet searching, using boolean search terms, and evaluating the content of search

This book provides a complete and exhaustive study of the Green’s functions. Professor Cabada first proves the basic properties of Green's functions and discusses the study of nonlinear boundary value