- Table View
- List View
Functions of Least Gradient (Monographs in Mathematics #110)
by José M. Mazón Wojciech GórnyThis book is devoted to the least gradient problem and its variants. The least gradient problem concerns minimization of the total variation of a function with prescribed values on the boundary of a Lipschitz domain. It is the model problem for studying minimization problems involving functionals with linear growth. Functions which solve the least gradient problem for their own boundary data, which arise naturally in the study of minimal surfaces, are called functions of least gradient. The main part of the book is dedicated to presenting the recent advances in this theory. Among others are presented an Euler–Lagrange characterization of least gradient functions, an anisotropic counterpart of the least gradient problem motivated by an inverse problem in medical imaging, and state-of-the-art results concerning existence, regularity, and structure of solutions. Moreover, the authors present a surprising connection between the least gradient problem and the Monge–Kantorovich optimal transport problem and some of its consequences, and discuss formulations of the least gradient problem in the nonlocal and metric settings. Each chapter is followed by a discussion section concerning other research directions, generalizations of presented results, and presentation of some open problems. The book is intended as an introduction to the theory of least gradient functions and a reference tool for a general audience in analysis and PDEs. The readers are assumed to have a basic understanding of functional analysis and partial differential equations. Apart from this, the text is self-contained, and the book ends with five appendices on functions of bounded variation, geometric measure theory, convex analysis, optimal transport, and analysis in metric spaces.
Functions of Omega-Bounded Type: Basic Theory (Frontiers in Mathematics)
by Armen M. Jerbashian Joel E. RestrepoThe book gives the basic results of the theory of the spaces Apω of functions holomorphic in the unit disc, halfplane and in the finite complex plane, which depend on functional weights ω permitting any rate of growth of a function near the boundary of the domain. This continues and essentially improves M.M. Djrbashian's theory of spaces Apα (1945) of functions holomorphic in the unit disc, the English translation of the detailed and complemented version of which (1948) is given in Addendum to the book. Besides, the book gives the ω-extensions of M. M. Djrbashian's two factorization theories of functions meromorphic in the unit disc of 1945-1948 and 1966-1975 to classes of functions delta-subharmonic in the unit disc and in the half-plane.The book can be useful for a wide range of readers. It can be a good handbook for Master, PhD students and Postdoctoral Researchers for enlarging their knowledge and analytical methods, as well as a useful resource for scientists who want to extend their investigation fields.
Functions of Two Variables (Second Edition)
by Sean Dineen<p>Multivariate calculus, as traditionally presented, can overwhelm students who approach it directly from a one-variable calculus background. There is another way-a highly engaging way that does not neglect readers' own intuition, experience, and excitement. One that presents the fundamentals of the subject in a two-variable context and was set forth in the popular first edition of Functions of Two Variables. <p>The second edition goes even further toward a treatment that is at once gentle but rigorous, atypical yet logical, and ultimately an ideal introduction to a subject important to careers both within and outside of mathematics. The author's style remains informal and his approach problem-oriented. He takes care to motivate concepts prior to their introduction and to justify them afterwards, to explain the use and abuse of notation and the scope of the techniques developed. <p>Functions of Two Variables, Second Edition includes a new section on tangent lines, more emphasis on the chain rule, a rearrangement of several chapters, refined examples, and more exercises. It maintains a balance between intuition, explanation, methodology, and justification, enhanced by diagrams, heuristic comments, examples, exercises, and proofs.</p>
Functor Categories, Model Theory, Algebraic Analysis and Constructive Methods: FCMTCCT2 2022, Almería, Spain, July 11–15, Invited and Selected Contributions (Springer Proceedings in Mathematics & Statistics #450)
by Alexander MartsinkovskyThis volume comprises selected contributions by the participants of the second "Functor Categories, Model Theory, Algebraic Analysis and Constructive Methods" conference, which took place at the University of Almería, Spain, in July 2022.The conference was devoted to several seemingly unrelated fields: functor categories, model theory of modules, algebraic analysis (including linear control systems), and constructive category theory, to mention just a few. The fact that these fields are actually related is a very recent realization. The connections between these disciplines are changing in real time, and the goal of this volume is to provide an initial reference point for this emerging interdisciplinary field.Besides research articles, the volume includes two extended lectures: one on constructive methods in algebraic analysis and the other on the functorial approach to algebraic systems theory. Hence, in addition to its interestfor researchers, the volume will also be an invaluable resource for newcomers.
Fundamental and Applied Sciences in Asia: International Conference on Science Technology and Social Sciences (ICSTSS 2018)
by Nor Azizah Yacob Duratul Ain Tholibon Nor Yuziah Mohd Yunus Zadariana Jamil Syuhada Mohd TahirThis book gathers selected science and technology papers presented at the 2018 International Conference on Science Technology and Social Sciences (ICSTSS 2018), organised bi-annually by Universiti Teknologi MARA Pahang, Malaysia. Based on the theme “Redesigning Education for Industrial Revolution”, the papers in this book address a broad range of topics in the fundamental and applied sciences, including computer science, engineering, environmental and management, furniture, forestry, health and medicine, material science, mathematics, plantation and agrotechnology, sport science and statistics, covering theoretical, numerical and experimental studies. The book serves as a platform for disseminating research findings by academicians of local, regional and global prominence, as a catalyst to inspire positive innovations in the development of the region. It provides a significant point of reference for academicians and students: for academicians, it is a good source of information to conduct further research; for students, it is the latest point of reference on research conducted in their fields of study. The carefully reviewed papers intend to facilitate the creation of new knowledge through the exchange of ideas, strategies and innovations in various science and technology disciplines, and to contribute towards enhancing the learning environment.
Fundamental Aspects of Operational Risk and Insurance Analytics
by Marcelo G. Cruz Pavel V. Shevchenko Gareth W. PetersA one-stop guide for the theories, applications, andstatistical methodologies essential to operational riskProviding a complete overview of operational risk modeling andrelevant insurance analytics, Fundamental Aspects of OperationalRisk and Insurance Analytics: A Handbook of Operational Riskoffers a systematic approach that covers the wide range of topicsin this area. Written by a team of leading experts in the field,the handbook presents detailed coverage of the theories,applications, and models inherent in any discussion of thefundamentals of operational risk, with a primary focus on BaselII/III regulation, modeling dependence, estimation of risk models,and modeling the data elements.Fundamental Aspects of Operational Risk and Insurance Analytics:A Handbook of Operational Risk begins with coverage on the fourdata elements used in operational risk framework as well asprocessing risk taxonomy. The book then goes further in-depth intothe key topics in operational risk measurement and insurance, forexample diverse methods to estimate frequency and severity models.Finally, the book ends with sections on specific topics, such asscenario analysis; multifactor modeling; and dependence modeling. Aunique companion with Advances in Heavy Tailed Risk Modeling: AHandbook of Operational Risk, the handbook also features:Discussions on internal loss data and key risk indicators,which are both fundamental for developing a risk-sensitiveframeworkGuidelines for how operational risk can be inserted into afirm's strategic decisionsA model for stress tests of operational risk under the UnitedStates Comprehensive Capital Analysis and Review (CCAR)programA valuable reference for financial engineers, quantitativeanalysts, risk managers, and large-scale consultancy groupsadvising banks on their internal systems, the handbook is alsouseful for academics teaching postgraduate courses on themethodology of operational risk.
Fundamental Aspects of Plasma Chemical Physics
by Annarita Laricchiuta Domenico Bruno Mario CapitelliFundamental Aspects of Plasma Chemical Physics: Transport develops basic and advanced concepts of plasma transport to the modern treatment of the Chapman-Enskog method for the solution of the Boltzmann transport equation. The book invites the reader to consider actual problems of the transport of thermal plasmas with particular attention to the derivation of diffusion- and viscosity-type transport cross sections, stressing the role of resonant charge-exchange processes in affecting the diffusion-type collision calculation of viscosity-type collision integrals. A wide range of topics is then discussed including (1) the effect of non-equilibrium vibrational distributions on the transport of vibrational energy, (2) the role of electronically excited states in the transport properties of thermal plasmas, (3) the dependence of transport properties on the multitude of Saha equations for multi-temperature plasmas, and (4) the effect of the magnetic field on transport properties. Throughout the book, worked examples are provided to clarify concepts and mathematical approaches. This book is the second of a series of three published by the Bari group on fundamental aspects of plasma chemical physics. The first book, Fundamental Aspects of Plasma Chemical Physics: Thermodynamics, is dedicated to plasma thermodynamics; and the third, Fundamental Aspects of Plasma Chemical Physics: Kinetics, deals with plasma kinetics.
Fundamental Concepts for New Clinical Trialists (Chapman & Hall/CRC Biostatistics Series #77)
by Scott Evans Naitee TingFundamental Concepts for New Clinical Trialists describes the core scientific concepts of designing, data monitoring, analyzing, and reporting clinical trials as well as the practical aspects of trials not typically discussed in statistical methodology textbooks. The first section of the book provides background information about clinical trials. I
Fundamental Concepts of Abstract Algebra
by Gertrude EhrlichA text in abstract algebra for undergraduate mathematics majors, this volume contains enough material for a two-semester course. It presents extensive coverage of set theory, groups, rings, modules, vector spaces, and fields. Examples, definitions, theorems, and proofs appear throughout, along with numerous practice exercises at the end of each section. 1991 edition.
Fundamental Concepts of Geometry (Dover Books on Mathematics)
by Bruce E. MeserveFundamental Concepts of Geometry demonstrates in a clear and lucid manner the relationships of several types of geometry to one another. This highly regarded work is a superior teaching text, especially valuable in teacher preparation, as well as providing an excellent overview of the foundations and historical evolution of geometrical concepts. Professor Meserve (University of Vermont) offers students and prospective teachers the broad mathematical perspective gained from an elementary treatment of the fundamental concepts of mathematics. The clearly presented text is written on an undergraduate (or advanced secondary-school) level and includes numerous exercises and a brief bibliography. An indispensable taddition to any math library, this helpful guide will enable the reader to discover the relationships among Euclidean plane geometry and other geometries; obtain a practical understanding of "proof"; view geometry as a logical system based on postulates and undefined elements; and appreciate the historical evolution of geometric concepts.
Fundamental Discrete Structures (University Texts in the Mathematical Sciences)
by V. Ravichandran Atul Kumar RazdanThis book serves as a core text in discrete mathematics. It discusses topics such as symbolic logic, enumerative combinatorics, algebraic structures, graph theory, and related applications to computer science and other allied subjects. The presentation of related concepts is suitable for sophomore, junior, and senior-level undergraduate students. Exercises provided at the end of each chapter are designed to help the reader have an active learning experience throughout the study.
Fundamental Groups and Covering Spaces
by Elon Lages LimaThis introductory textbook describes fundamental groups and their topological soul mates, the covering spaces. The author provides several illustrative examples that touch upon different areas of mathematics, but in keeping with the books introductory aim, they are all quite elementary. Basic concepts are clearly defined, proofs are complete, and n
Fundamental Math and Physics for Scientists and Engineers
by Hannah Yevick David YevickThis text summarizes the core undergraduate physics curriculum together with the mathematics frequently encountered in engineering and physics calculations, focusing on content relevant to practical applications.Covers major undergraduate physics topics including the complete Physics GRE subject examination syllabusOverview of key results in undergraduate applied mathematics and introduces scientific programmingPresents simple, coherent derivations and illustrations of fundamental concepts
Fundamental Mathematical Analysis (Springer Undergraduate Mathematics Series)
by Robert MagnusThis textbook offers a comprehensive undergraduate course in real analysis in one variable. Taking the view that analysis can only be properly appreciated as a rigorous theory, the book recognises the difficulties that students experience when encountering this theory for the first time, carefully addressing them throughout.Historically, it was the precise description of real numbers and the correct definition of limit that placed analysis on a solid foundation. The book therefore begins with these crucial ideas and the fundamental notion of sequence. Infinite series are then introduced, followed by the key concept of continuity. These lay the groundwork for differential and integral calculus, which are carefully covered in the following chapters. Pointers for further study are included throughout the book, and for the more adventurous there is a selection of "nuggets", exciting topics not commonly discussed at this level. Examples of nuggets include Newton's method, the irrationality of π, Bernoulli numbers, and the Gamma function.Based on decades of teaching experience, this book is written with the undergraduate student in mind. A large number of exercises, many with hints, provide the practice necessary for learning, while the included "nuggets" provide opportunities to deepen understanding and broaden horizons.
Fundamental Mathematical Modeling of Additive Manufacturing (Springer Tracts in Additive Manufacturing)
by Juha Jeronen Tero Tuovinen Matti KurkiThis book elucidates the fundamental thermomechanical behaviour inherent in the 3D printing process within a laser-based powder bed fusion (L-PBF) system. It presents foundational concepts and provides in-depth derivations of the governing equations. The analysis encompasses arbitrary anisotropic linear viscoelastic materials, accounting for thermal effects. The authors leverage the theory of axially moving materials, a framework previously employed in the analysis of production processes within the process industry. They introduce a coordinate frame that moves in tandem with the printing laser, adopting an Eulerian perspective towards the in-motion solid. Designed for graduate students and researchers, this book is poised to foster a profound comprehension and spur innovative technological advancements in the realm of additive manufacturing.
Fundamental Mathematical Structures of Quantum Theory: Spectral Theory, Foundational Issues, Symmetries, Algebraic Formulation
by Valter MorettiThis textbook presents in a concise and self-contained way the advanced fundamental mathematical structures in quantum theory. It is based on lectures prepared for a 6 months course for MSc students. The reader is introduced to the beautiful interconnection between logic, lattice theory, general probability theory, and general spectral theory including the basic theory of von Neumann algebras and of the algebraic formulation, naturally arising in the study of the mathematical machinery of quantum theories. Some general results concerning hidden-variable interpretations of QM such as Gleason's and the Kochen-Specker theorems and the related notions of realism and non-contextuality are carefully discussed. This is done also in relation with the famous Bell (BCHSH) inequality concerning local causality.Written in a didactic style, this book includes many examples and solved exercises.The work is organized as follows. Chapter 1 reviews some elementary facts and properties of quantum systems. Chapter 2 and 3 present the main results of spectral analysis in complex Hilbert spaces. Chapter 4 introduces the point of view of the orthomodular lattices' theory. Quantum theory form this perspective turns out to the probability measure theory on the non-Boolean lattice of elementary observables and Gleason's theorem characterizes all these measures. Chapter 5 deals with some philosophical and interpretative aspects of quantum theory like hidden-variable formulations of QM. The Kochen-Specker theorem and its implications are analyzed also in relation BCHSH inequality, entanglement, realism, locality, and non-contextuality. Chapter 6 focuses on the algebra of observables also in the presence of superselection rules introducing the notion of von Neumann algebra. Chapter 7 offers the idea of (groups of) quantum symmetry, in particular, illustrated in terms of Wigner and Kadison theorems. Chapter 8 deals with the elementary ideas and results of the so called algebraic formulation of quantum theories in terms of both *-algebras and C*-algebras.This book should appeal to a dual readership: on one hand mathematicians that wish to acquire the tools that unlock the physical aspects of quantum theories; on the other physicists eager to solidify their understanding of the mathematical scaffolding of quantum theories.
Fundamental Number Theory with Applications
by Richard A. MollinAn update of the most accessible introductory number theory text available, Fundamental Number Theory with Applications, Second Edition presents a mathematically rigorous yet easy-to-follow treatment of the fundamentals and applications of the subject. The substantial amount of reorganizing makes this edition clearer and more elementary in i
Fundamental Physics and Physics Education Research (Springer Proceedings In Physics Ser. #145)
by Burra G. Sidharth Jesús Carnicer Murillo Marisa Michelini Carmen PereaThis book highlights selected contributions presented at the 15th annual international symposium Frontiers of Fundamental Physics (FFP15), with the aim of informing readers about the most important recent advances in fundamental physics and physics education research. The FFP series offers a platform for physicists from around the world to present their latest theories and findings. The latest symposium was held in Orihuela, Spain and covered diverse fields of research, including gravitation, astronomy and astrophysics, physics of complex systems, high-energy physics, and mathematical physics. Considerable attention was also paid to physics education research, teacher education in physics, and the popularization of physics. In a knowledge-based society, research into fundamental physics plays a vital role in both the advancement of human knowledge and the development of new technologies. Presenting valuable new peer-reviewed contributions submitted from 15 countries, this book will appeal to a broad audience of scholars and researchers.
The Fundamental Rules of Risk Management
by Nigel LewisThe consequences of taking on risk can be ruinous to personal finances, professional careers, corporate survivability, and even nation states. Yet many risk managers do not have a clear understanding of the basics. Requiring no statistical or mathematical background, The Fundamental Rules of Risk Management gives you the knowledge to successfully h
Fundamental Solutions of Linear Partial Differential Operators
by Norbert Ortner Peter WagnerThis monograph provides the theoretical foundations needed for the construction of fundamental solutions and fundamental matrices of (systems of) linear partial differential equations. Many illustrative examples also show techniques for finding such solutions in terms of integrals. Particular attention is given to developing the fundamentals of distribution theory, accompanied by calculations of fundamental solutions. The main part of the book deals with existence theorems and uniqueness criteria, the method of parameter integration, the investigation of quasihyperbolic systems by means of Fourier and Laplace transforms, and the representation of fundamental solutions of homogeneous elliptic operators with the help of Abelian integrals. In addition to rigorous distributional derivations and verifications of fundamental solutions, the book also shows how to construct fundamental solutions (matrices) of many physically relevant operators (systems), in elasticity, thermoelasticity, hexagonal/cubic elastodynamics, for Maxwell's system and others. The book mainly addresses researchers and lecturers who work with partial differential equations. However, it also offers a valuable resource for students with a solid background in vector calculus, complex analysis and functional analysis.
Fundamental Statistical Concepts and Techniques in the Biological and Environmental Sciences: With jamovi
by A. Bradley DuthieFundamental Statistical Concepts and Techniques in the Biological and Environmental Sciences: With jamovi is an introductory textbook for learning statistics. It starts with the very basics and prioritises helping the reader to develop a conceptual understanding of statistics, and apply the most fundamental statistical tools. New concepts are introduced with examples designed to be familiar to the reader, serving as a useful starting point for exploring more abstract concepts.Key Features: Designed to be accessible for students learning statistics in biological and environmental sciences. Utilizes the statistical software jamovi to explore new concepts. Prioritizes good statistical judgement over adherence to protocols. This book will be useful to students beginning their study of statistical concepts in biological and environmental sciences, whilst also acting as an insightful resource for teachers using jamovi in the classroom. Fundamental Statistical Concepts and Techniques in the Biological and Environmental Sciences: With jamovi is a valuable resource for anyone who wishes to understand and apply statistical techniques commonly used in the biological and environmental sciences.
Fundamental Statistical Inference: A Computational Approach (Wiley Series in Probability and Statistics)
by Marc S. PaolellaA hands-on approach to statistical inference that addresses the latest developments in this ever-growing field This clear and accessible book for beginning graduate students offers a practical and detailed approach to the field of statistical inference, providing complete derivations of results, discussions, and MATLAB programs for computation. It emphasizes details of the relevance of the material, intuition, and discussions with a view towards very modern statistical inference. In addition to classic subjects associated with mathematical statistics, topics include an intuitive presentation of the (single and double) bootstrap for confidence interval calculations, shrinkage estimation, tail (maximal moment) estimation, and a variety of methods of point estimation besides maximum likelihood, including use of characteristic functions, and indirect inference. Practical examples of all methods are given. Estimation issues associated with the discrete mixtures of normal distribution, and their solutions, are developed in detail. Much emphasis throughout is on non-Gaussian distributions, including details on working with the stable Paretian distribution and fast calculation of the noncentral Student's t. An entire chapter is dedicated to optimization, including development of Hessian-based methods, as well as heuristic/genetic algorithms that do not require continuity, with MATLAB codes provided. The book includes both theory and nontechnical discussions, along with a substantial reference to the literature, with an emphasis on alternative, more modern approaches. The recent literature on the misuse of hypothesis testing and p-values for model selection is discussed, and emphasis is given to alternative model selection methods, though hypothesis testing of distributional assumptions is covered in detail, notably for the normal distribution. Presented in three parts—Essential Concepts in Statistics; Further Fundamental Concepts in Statistics; and Additional Topics—Fundamental Statistical Inference: A Computational Approach offers comprehensive chapters on: Introducing Point and Interval Estimation; Goodness of Fit and Hypothesis Testing; Likelihood; Numerical Optimization; Methods of Point Estimation; Q-Q Plots and Distribution Testing; Unbiased Point Estimation and Bias Reduction; Analytic Interval Estimation; Inference in a Heavy-Tailed Context; The Method of Indirect Inference; and, as an appendix, A Review of Fundamental Concepts in Probability Theory, the latter to keep the book self-contained, and giving material on some advanced subjects such as saddlepoint approximations, expected shortfall in finance, calculation with the stable Paretian distribution, and convergence theorems and proofs.
Fundamental Statistics for the Behavioral Sciences 8th Edition
by David C. HowellFUNDAMENTAL STATISTICS FOR THE BEHAVIORAL SCIENCES focuses on providing the context of statistics in behavioral research, while emphasizing the importance of looking at data before jumping into a test. This practical approach provides readers with an understanding of the logic behind the statistics, so they understand why and how certain methods are used--rather than simply carry out techniques by rote. Readers move beyond number crunching to discover the meaning of statistical results and appreciate how the statistical test to be employed relates to the research questions posed by an experiment. An abundance of real data and research studies provide a real-life perspective and help you understand concepts as you learn about the analysis of data.
Fundamental Statistics for the Social and Behavioral Sciences
by Howard T. TokunagaFundamental Statistics for the Social and Behavioral Sciences, Second Edition places statistics within the research process, illustrating how they are used to answer questions and test ideas. Students learn not only how to calculate statistics, but also how to interpret and communicate the results of statistical analyses in light of a study’s research hypothesis. Featuring accessible writing and well-integrated research examples, the book gives students a greater understanding of how research studies are conceived, conducted, and communicated. New and Proven Features Updated data sets and research examples address real-world issues and topics across the social and behavioral sciences, illustrating the use of statistical procedures to test research questions and hypotheses. Significantly expanded discussion of linear and multiple regression and correlation now gives regression its own separate chapter. Thorough presentation of formulas, hand calculations, and the presentation of visual data enable mastery of key techniques and prove especially helpful in flipped or online classes. In-chapter learning checks and end-of-chapter exercises give students an opportunity to continually assess their understanding. Screenshots of statistical calculations using IBM® SPSS® Statistics at the end of chapters help students learn to use SPSS software and interpret output. Original SAGE videos for each chapter, featuring author Howard K. Tokunaga, bring concepts to life and appeal to diverse learners.
Fundamental Statistics for the Social and Behavioral Sciences
by Howard T. TokunagaFundamental Statistics for the Social and Behavioral Sciences, Second Edition places statistics within the research process, illustrating how they are used to answer questions and test ideas. Students learn not only how to calculate statistics, but also how to interpret and communicate the results of statistical analyses in light of a study’s research hypothesis. Featuring accessible writing and well-integrated research examples, the book gives students a greater understanding of how research studies are conceived, conducted, and communicated. New and Proven Features Updated data sets and research examples address real-world issues and topics across the social and behavioral sciences, illustrating the use of statistical procedures to test research questions and hypotheses. Significantly expanded discussion of linear and multiple regression and correlation now gives regression its own separate chapter. Thorough presentation of formulas, hand calculations, and the presentation of visual data enable mastery of key techniques and prove especially helpful in flipped or online classes. In-chapter learning checks and end-of-chapter exercises give students an opportunity to continually assess their understanding. Screenshots of statistical calculations using IBM® SPSS® Statistics at the end of chapters help students learn to use SPSS software and interpret output. Original SAGE videos for each chapter, featuring author Howard K. Tokunaga, bring concepts to life and appeal to diverse learners.