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الصفحة 25
Galois Theory
Classical Galois theory is a subject generally acknowledged to be one of the most central and beautiful areas in pure mathematics. This text develops the subject systematically and from the beginning, requiring of the reader only basic facts about polynomials and a good knowledge of linear algebra.The book discusses Galois theory in considerable generality, treating fields of characteristic zero and of positive characteristic with consideration of both separable and inseparable extensions, but with a particular emphasis on algebraic extensions of the field of rational numbers. While most of the book is concerned with finite extensions, it concludes with a discussion of the algebraic closure and of infinite Galois extensions.
Galileo Galilei - When the World Stood Still
"I, Galileo, son of the late Vincenzio Galilei, Florentine, aged seventy years ...kneeling before you Most Eminent and Reverend Lord Cardinals ...I abjure, curse, detest the aforesaid errors and heresies."The mathematician and physicist Galileo Galilei is one of the most famous scientists of all times. The story of his life and times, of his epoch-making experiments and discoveries, of his stubbornness and pride, of his patrons in the house of Medici, of his enemies and friends in their struggle for truth - all is brought vividly to life in this book. Atle Næss has written a gripping account of one of the great figures in European history.
Galerkin Finite Element Methods for Parabolic Problems
This book provides insight in the mathematics of Galerkin finite element method as applied to parabolic equations. The approach is based on first discretizing in the spatial variables by Galerkin's method, using piecewise polynomial trial functions, and then applying some single step or multistep time stepping method. The concern is stability and error analysis of approximate solutions in various norms, and under various regularity assumptions on the exact solution.
Fuzzy set approach to multidimensional poverty measurement
This volume brings together advanced thinking on the multidimensional measurement of poverty, including the theoretical background, applications to cross-sections using contemporary European examples, and longitudinal aspects of multidimensional fuzzy poverty analysis that pay particular attention to the transitory, or impermanent, conditions that often occur during transitions to market economies.
Fuzzy Probability and Statistics
This book combines material from our previous books FP (Fuzzy Probabilities: New Approach and Applications,Physica-Verlag, 2003) and FS (Fuzzy Statistics, Springer, 2004), plus has about one third new results. From FP we have material on basic fuzzy probability, discrete (fuzzy Poisson,binomial) and continuous (uniform, normal, exponential) fuzzy random variables. From FS we included chapters on fuzzy estimation and fuzzy hypothesis testing related to means, variances, proportions, correlation and regression. New material includes fuzzy estimators for arrival and service rates, and the uniform distribution, with applications in fuzzy queuing theory. Also, new to this book, is three chapters on fuzzy maximum entropy (imprecise side conditions) estimators producing fuzzy distributions and crisp discrete/continuous distributions.
Fuzzy probabilities : New approach and applications
In probability and statistics we often have to estimate probabilities and parameters in probability distributions using a random sample. Instead of using a point estimate calculated from the data we propose using fuzzy numbers which are constructed from a set of confidence intervals. In probability calculations we apply constrained fuzzy arithmetic because probabilities must add to one. Fuzzy random variables have fuzzy distributions. A fuzzy normal random variable has the normal distribution with fuzzy number mean and variance. Applications are to queuing theory, Markov chains, inventory control, decision theory and reliability theory.
Fuzzy multi-criteria decision making : Theory and applications with recent developments
In trying to make a satisfactory decision when imprecise and multicriteria situations are involved, a decision maker has to use a fuzzy multicriteria decision making method. Fuzzy Multi-Criteria Decision Making (MCDM) presents fuzzy multiattribute and multiobjective decision-making methodologies by distinguished MCDM researchers. In summarizing the concepts and results of the most popular fuzzy multicriteria methods, using numerical examples, this work examines all the fuzzy multicriteria methods recently developed, such as fuzzy AHP, fuzzy TOPSIS, interactive fuzzy multiobjective stochastic linear programming, fuzzy multiobjective dynamic programming, grey fuzzy multiobjective optimization, fuzzy multiobjective geometric programming, and more.
Fuzzy logic with engineering applications
With numerous examples and end-of-chapter problems, this book is essential reading for graduates and senior undergraduate students in civil, chemical, mechanical and electrical engineering as wells as researchers and practitioners working with fuzzy logic in industry.
Fuzzy Logic in Action : Applications in Epidemiology and Beyond
The volume addresses the most significant topics in the broad areas of epidemiology, mathematical modeling and uncertainty, embodying them within the framework of fuzzy set and dynamic systems theory.
Fuzzy Applications in Industrial Engineering
After an introductory chapter explaining the recent status of fuzzy sets in IE, this volume involves application chapters on the major seven areas of IE to which fuzzy set theory can contribute. These major application areas are Control and Reliability, Engineering Economics and Investment Analysis, Group and Multi-criteria Decision-making, Human Factors Engineering and Ergonomics, Manufacturing Systems and Technology Management, Optimization Techniques, and Statistical Decision-making. Under these major areas, every chapter includes didactic numerical applications.
Fundamentals of statistics with fuzzy data
This research monograph presents basic foundational aspects for a theory of statistics with fuzzy data, together with a set of practical applications. Fuzzy data are modeled as observations from random fuzzy sets. Theories of fuzzy logic and of random closed sets are used as basic ingredients in building statistical concepts and procedures in the context of imprecise data, including coarse data analysis. The monograph also aims at motivating statisticians to look at fuzzy statistics to enlarge the domain of applicability of statistics in general.
Fundamentals of image data mining : Analysis, features, classification and retrieval
Presents a comprehensive review of the essentials of image data mining, and the latest cutting-edge techniques used in the field. The coverage spans all aspects of image analysis and understanding, offering deep insights into areas of feature extraction, machine learning, and image retrieval. The theoretical coverage is supported by practical mathematical models and algorithms, utilizing data from real-world examples and experiments. Topics and features: Describes essential tools for image mining, covering Fourier transforms, Gabor filters, and contemporary wavelet transforms / Develops many new exercises (most with MATLAB code and instructions) / Includes review summaries at the end of each chapter / Analyses state-of-the-art models, algorithms, and procedures for image mining / Integrates new sections on pre-processing, discrete cosine transform, and statistical inference and testing / Demonstrates how features like color, texture, and shape can be mined or extracted for image representation / Applies powerful classification approaches: Bayesian classification, support vector machines, neural / networks, and decision trees / Implements imaging techniques for indexing, ranking, and presentation, as well as database visualization
Fundamentals of Data Mining in Genomics and Proteomics
The book presents key analytical techniques used to analyze genomic and proteomic data by detailing their underlying principles, merits and limitations. An important goal of this text is to provide a highly intuitive and conceptual (as opposed to intricate mathematical) account of the discussed methodologies. This treatment will enable readers with interest in analysis of genomic and proteomic data to quickly learn and appreciate the essential properties of relevant data mining methodologies without recourse to advanced mathematics.
Fundamentals of clinical research : Bridging medicine, statistics and operations
The scope of clinical research is to evaluate the effect of a treatment on the evolution of a disease in the human species.The treatment can be pharmacological, surgical, psychological/behavioral or organizational/logistic. The disease, intended as an impairment of a state of well-being or a condition capable of provoking such impairment over time, can be universally accepted as such (e.g. a cancer or a bone fracture) or perceived as such only by limited groups of individuals in a given cultural context (e.g. hair loss or weight gain). The course of the disease that ones wishes to change can be the one with no intervention or, more frequently, the one observed with the available treatment. The evaluation of the effect of a treatment on the course of a disease is a lengthy process, which progresses in increasingly complex stages.
Fundamentals of Artificial Intelligence
Fundamentals of Artificial Intelligence introduces the foundations of present day AI and provides coverage to recent developments in AI such as Constraint Satisfaction Problems, Adversarial Search and Game Theory, Statistical Learning Theory, Automated Planning, Intelligent Agents, Information Retrieval, Natural Language & Speech Processing, and Machine Vision. The book features a wealth of examples and illustrations, and practical approaches along with the theoretical concepts. It covers all major areas of AI in the domain of recent developments. The book is intended primarily for students who major in computer science at undergraduate and graduate level but will also be of interest as a foundation to researchers in the area of AI.
Fundamentals of analytical toxicology : Clinical and forensic ; 2nd ed.
An integrated introduction to the analysis of drugs, poisons, and other foreign compounds in biological and related specimens. Assuming only basic knowledge of analytical chemistry, this invaluable guide helps trainee analytical toxicologists understand the principles and practical skills involved in detecting, identifying, and measuring a broad range of compounds in various biological samples. Clear, easy-to-read chapters provide detailed information on topics including sample collection and preparation, spectrophotometric and luminescence techniques, liquid and gas-liquid chromatography, and mass spectrometry including hyphenated techniques. Focuses on analytical, statistical, and pharmacokinetic principles / Describes basic methodology, including colour tests and immunoassay and enzyme-based assays / Outlines laboratory operations, such as method validation, quality assessment, staff training, and laboratory accreditation / Follows IUPAC nomenclature for chemical names and recommended International Non-proprietary Name (rINN) for drugs and pesticides / Includes discussion of 'designer drugs' (novel pharmaceutical substances NPS)
Fundamentals and Methods of Machine and Deep Learning : Algorithms, Tools, and Applications
provides a practical approach by explaining the concepts of machine learning and deep learning algorithms, evaluation of methodology advances, and algorithm demonstrations with applications. In recent research studies, they are regarded as one of the disruptive technologies that will transform our future life, business, and the global economy. The recent explosion of digital data in a wide variety of domains, including science, engineering, Internet of Things, biomedical, healthcare, and many business sectors, has declared the era of big data, which cannot be analysed by classical statistics but by the more modern, robust machine learning and deep learning techniques. Since machine learning learns from data rather than by programming hard-coded decision rules, an attempt is being made to use machine learning to make computers that are able to solve problems like human experts in the field.
Functions of a-Bounded Type in the Half-Plane
This is a unique book related to the theory of functions of a-bounded type in the half-plane of the complex plane, which is constructed by application of the Liouville integro-differential operator. In addition, the book contains improvements of several results such as the Phragmen-Lindelof Principle and Nevanlinna Factorization in the Half-Plane, and offers a new, equivalent definition of the classical Hardy spaces in the half-plane. The last chapter of the book presents an application of the constructed theory as well as M.M.Djrbashian’s theory of Nevanlinna type classes in the disc in the spectral theory of linear operators. This is a solution of a problem repeatedly stated by M.G.Krein and being of special interest for a long time.
Functions de variable réelle : Théorie élémentaire = Real variable functions : Elementary theory
The Mathematics Elements of Nicolas BOURBAKI aim to provide a rigorous, systematic presentation without prerequisites of mathematics from their foundations. This Book is the fourth of the treaty; it is devoted to the basics of real analysis. It includes the chapters: Derivatives; Primitive and integral; Elementary functions; Differential equations ; Local study of functions; Generalized Taylorian developments. Euler-Maclaurin summation formula; The gamma function. It also contains historical notes.
Functionalized Nanoscale Materials, Devices and Systems
The primary objective of the NATO Advanced Study Institute (ASI) titled “Functionalized Nanoscale Materials, Devices, and Systems for Chem. -Bio Sensors, Photonics, and Energy Generation and Storage” was to present a contemporary and comprehensive overview of the field of nanostructured materials and devices and its applications in chem. -bio sensors, nanophotonics, and energy generation and storage devices. The study has become one of the most promising disciplines in science and technology, as it aims at the fundamental understanding of new physical, che- cal, and biological properties of systems and the technological advances arising from their exploration. Such systems are intermediate in size, between the isolated atoms and molecules and bulk material, where the unique transitional characteristics between the two can be understood, controlled, and manipulated.
