Topology and Approximate Fixed Points
This book examines in detail approximate fixed point theory in different classes of topological spaces for general classes of maps. It offers a comprehensive treatment of the subject that is up-to-date, self-contained, and rich in methods, for a wide variety of topologies and maps. Content includes known and recent results in topology (with proofs), as well as recent results in approximate fixed point theory.This work starts with a set of basic notions in topological spaces. Special attention is given to topological vector spaces, locally convex spaces, Banach spaces, and ultrametric spaces. Sequences and function spaces-and fundamental properties of their topologies-are also covered. The reader will find discussions on fundamental principles, namely the Hahn-Banach theorem on extensions of linear (bounded) functionals; the Banach open mapping theorem; the Banach-Steinhaus uniform boundedness principle; and Baire categories, including some applications. Also included are weak topologies and their properties, in particular the theorems of Eberlein-Smulian, Goldstine, Kakutani, James and Grothendieck, reflexive Banach spaces, l_{1}- sequences, Rosenthal's theorem, sequential properties of the weak topology in a Banach space and weak* topology of its dual, and the Fr矇chet-Urysohn property.The subsequent chapters cover various almost fixed point results, discussing how to reach or approximate the unique fixed point of a strictly contractive mapping of a spherically complete ultrametric space. They also introduce synthetic approaches to fixed point problems involving regular-global-inf functions. The book finishes with a study of problems involving approximate fixed point property on an ambient space with different topologies.By providing appropriate background and up-to-date research results, this book can greatly benefit graduate students and mathematicians seeking to advance in topology and fixed point theory.
Functional Analysis
This textbook presents the principles of functional analysis in a clear and concise way. The first three chapters describe the general notions of distance, integral, and norm, as well as their relations. Fundamental examples are provided in the three chapters that follow: Lebesgue spaces, dual spaces, and Sobolev spaces. Two subsequent chapters develop applications to capacity theory and elliptic problems. In particular, the isoperimetric inequality and the P籀lya-Szegő and Faber-Krahn inequalities are proved by purely functional methods. The epilogue contains a sketch of the history of functional analysis in relation to integration and differentiation. Starting from elementary analysis and introducing relevant research, this work is an excellent resource for students in mathematics and applied mathematics. The second edition of Functional Analysis includes several improvements as well as the addition of supplementary material. Specifically, the coverage of advanced calculus and distribution theory has been completely rewritten and expanded. New proofs, theorems, and applications have been added as well for readers to explore.
Singularly Perturbed Problems
This book collects papers from the Special Issue "Singularly Perturbed Problems: Asymptotic Analysis and Approximate Solution", published in Axioms. These papers cover different aspects of singular perturbation theory and its applications: axiomatic approach in the analytic theory of singular perturbations; asymptotic solution of various types of singularly perturbed integral-differential and integral equations with weakly and rapidly varying kernels of the integral operators; propagation of two-dimensional periodic perturbations in a viscous continuously stratified fluid; asymptotic analysis of the stochastic linear-quadratic optimal control problem with two fast timescales in the dynamics; asymptotic solution of singularly perturbed Cauchy problem for different types of differential equations with "simple" turning points; asymptotic analysis of the complete Euclidean space controllability for different types of singularly perturbed differential systems with time delays; asymptotic solution of singularly perturbed systems in the critical case by the orthogonal projector method; application of the direct scheme method to asymptotic solution of one class of optimal control problems with three-tempo state variables; asymptotic analysis and solution of a cheap control linear quadratic zero-sum differential game; analysis of asymptotic behavior of the solutions for one class of singularly perturbed Neumann boundary value problems .
Calculus of One Variable
This book is designed to serve as a textbook for courses offered to undergraduate and graduate students enrolled in Mathematics. The first edition of this book was published in 2015. As there is a demand for the next edition, it is quite natural to take note of the several suggestions received from the users of the earlier edition over the past six years. This is the prime motivation for bringing out a revised second edition with a thorough revision of all the chapters. The book provides a clear understanding of the basic concepts of differential and integral calculus starting with the concepts of sequences and series of numbers, and also introduces slightly advanced topics such as sequences and series of functions, power series, and Fourier series which would be of use for other courses in mathematics for science and engineering programs. The salient features of the book are - precise definitions of basic concepts; several examples for understanding the concepts and for illustrating the results; includes proofs of theorems; exercises within the text; a large number of problems at the end of each chapter as home-assignments. The student-friendly approach of the exposition of the book would be of great use not only for students but also for the instructors. The detailed coverage and pedagogical tools make this an ideal textbook for students and researchers enrolled in a mathematics course.
Complex Variables
Complex Variables: A Physical Approach with Applications, Second Edition offers a notable revision. The emphasis remains on theory and practice. The first part of the text focuses on the fundamental concepts. The author then moves on to a detailed look at how complex variables are used in the real world.
Statistical Evidence
This book redresses the balance, explaining why science has clung to a defective methodology despite its well-known defects. After examining the strengths and weaknesses of the work of Neyman and Pearson and the Fisher paradigm, the author proposes an alternative paradigm.
Combinatorics
Bijective proofs are some of the most elegant and powerful techniques in all of mathematics. Suitable for readers without prior background in algebra or combinatorics, the book presents an introduction to enumerative and algebraic combinatorics emphasizing bijective methods.
Introduction to Probability with R
This text presents R programs and animations to provide an intuitive yet rigorous understanding of how to model natural phenomena from a probabilistic point of view. Each chapter includes a short biographical note about a contributor to probability theory, exercises, and selected answers. Ancillary material is accessible online.
Sports Math
Can you really keep your eye on the ball? How is massive data collection changing sports?Sports science courses are growing in popularity. The author's course at Roanoke College is a mix of physics, physiology, mathematics, and statistics. Many students of both genders find it exciting to think about sports. Sports problems are easy to create and state, even for students who do not live sports 24/7. Sports are part of their culture and knowledge base, and the opportunity to be an expert on some area of sports is invigorating. This should be the primary reason for the growth of mathematics of sports courses: the topic provides intrinsic motivation for students to do their best work.From the Author: "The topics covered in Sports Science and Sports Analytics courses vary widely. To use a golfing analogy, writing a book like this is like hitting a drive at a driving range; there are many directions you can go without going out of bounds. At the driving range, I pick out a small target to focus on, and that is what I have done here. I have chosen a sample of topics I find very interesting. Ideally, users of this book will have enough to choose from to suit whichever version of a sports course is being run.""The book is very appealing to teach from as well as to learn from. Students seem to have a growing interest in ways to apply traditionally different areas to solve problems. This, coupled with an enthusiasm for sports, makes Dr. Minton's book appealing to me."--Kevin Hutson, Furman University
Bayesian Analysis for Population Ecology
Emphasizing model choice and model averaging, this book presents Bayesian methods for analyzing complex ecological data. Providing a basic introduction to Bayesian methods, the book includes detailed descriptions of methods that deal with covariate data and covers techniques at the forefront of research, such as model discrimination and model av
Statistical Methods for Spatial Data Analysis
Statistical Methods for Spatial Data Analysis is a comprehensive treatment of statistical theory and methods for spatial data analysis, employing a model-based and frequentist approach that emphasizes the spatial domain. The authors deliver an outstanding treatment of semivariogram estimation and modeling, spatial analysis in the s
Principles of Fourier Analysis
Strikingly different from typical presentations, Principles of Fourier Analysis provides an introduction to and comprehensive overview of the mathematical theory of Fourier analysis as it is used in applications in engineering, science, and mathematics.
The Mathematics of Politics
It is because mathematics is often misunderstood, it is commonlybelieved it has nothing to say about politics. The high schoolexperience with mathematics, for so many the lasting impressionof the subject, suggests that mathematics is the study of numbers, operations, formulas, and manipulations of symbols. Thosebelieving this is the extent of mathematics might conclude mathematics has no relevance to politics. This book counters this impression. The second edition of this popular book focuses on mathematical reasoningabout politics. In the search for ideal ways to make certain kindsof decisions, a lot of wasted effort can be averted if mathematics can determine thatfinding such an ideal is actually impossible in the first place.In the first three parts of this book, we address the following threepolitical questions: (1) Is there a good way to choose winners of elections?(2) Is there a good way to apportion congressional seats?(3) Is there a good way to make decisions in situations of conflict anduncertainty?In the fourth and final part of this book, we examine the ElectoralCollege system that is used in the United States to select a president.There we bring together ideas that are introduced in each of the threeearlier parts of the book.
Understanding Real Analysis
This book is a one-semester text for an introduction to real analysis. The author's primary aims are to develop ideas already familiar from elementary calculus in a rigorous manner and to help students deeply understand some basic but crucial mathematical ideas.
Dependence Modeling with Copulas
This book covers recent advances in the field, including vine copula modeling of high-dimensional data. The author develops vine copula models and generalizations, discusses other multivariate constructions and parametric copula families, and presents dependence and tail properties to assist readers in copula model selection. He also covers infe
Non-Smooth and Complementarity-Based Distributed Parameter Systems
Rectifiability
Rectifiable sets, measures, currents and varifolds are foundational concepts in geometric measure theory. The last four decades have seen the emergence of a wealth of connections between rectifiability and other areas of analysis and geometry, including deep links with the calculus of variations and complex and harmonic analysis. This short book provides an easily digestible overview of this wide and active field, including discussions of historical background, the basic theory in Euclidean and non-Euclidean settings, and the appearance of rectifiability in analysis and geometry. The author avoids complicated technical arguments and long proofs, instead giving the reader a flavour of each of the topics in turn while providing full references to the wider literature in an extensive bibliography. It is a perfect introduction to the area for researchers and graduate students, who will find much inspiration for their own research inside. This title is also available as open access on Cambridge Core.
Homological Methods in Banach Space Theory
Many researchers in geometric functional analysis are unaware of algebraic aspects of the subject and the advances they have permitted in the last half century. This book, written by two world experts on homological methods in Banach space theory, gives functional analysts a new perspective on their field and new tools to tackle its problems. All techniques and constructions from homological algebra and category theory are introduced from scratch and illustrated with concrete examples at varying levels of sophistication. These techniques are then used to present both important classical results and powerful advances from recent years. Finally, the authors apply them to solve many old and new problems in the theory of (quasi-) Banach spaces and outline new lines of research. Containing a lot of material unavailable elsewhere in the literature, this book is the definitive resource for functional analysts who want to know what homological algebra can do for them.
The ASQ Certified Six Sigma Black Belt Handbook, Fourth Edition
Fully updated to reflect the 2022 ASQ Certified Six Sigma Black Belt (CSSBB) Body of Knowledge (BoK), The ASQ Certified Six Sigma Black Belt Handbook, Fourth Edition is ideal for candidates studying for the CSSBB examination. This comprehensive reference focuses on the core areas of organization-wide planning and deployment, team management, and each of the DMAIC project phases. The fourth edition of this handbook offers thorough explanations of statistical concepts in a straightforward way. It also reflects the latest technology and applications of Six Sigma and lean tools. Updates you will find in the fourth edition include: New topics and tools, such as return on investment calculations, the roles of coaching and finance in projects, process-decision program charts, interrelationship digraphs, A3 analysis, maturity models, key behavior indicators, and audit MSA A new chapter on risk analysis and managementRevamped statistics sectionsNew tables, figures, and examples to help illustrate key points
Models and Methods for Quantum Condensation and Fluids
The Institute for Mathematical Sciences at the National University of Singapore hosted a thematic program on Quantum and Kinetic Problems: Modeling, Analysis, Numerics and Applications from September 2019 to March 2020. As an important part of the program, tutorials and special lectures were given by leading experts in the fields for participating graduate students and junior researchers. This invaluable volume collects six expanded lecture notes with self-contained tutorials. The coverage includes mathematical models and numerical methods for multidimensional solitons in linear and nonlinear potentials; Bose-Einstein condensation (BEC) with dipole-dipole interaction, higher order interaction and spin-orbit coupling; classical and quantum turbulence; and molecular dynamics process based on the first-principle in quantum chemistry.This volume serves to inspire graduate students and researchers who will embark into original research work in these fields.
The Big Bang of Numbers
Our universe has multiple origin stories, from religious creation myths to the Big Bang of scientists. But if we leave those behind and start from nothing--no matter, no cosmos, not even empty space--could we create a universe using only math? Irreverent, richly illustrated, and boundlessly creative, The Big Bang of Numbers invites us to try.In this new mathematical origin story, mathematician and novelist Manil Suri creates a natural progression of ideas needed to design our world, starting with numbers and continuing through geometry, algebra, and beyond. He reveals the secret lives of real and imaginary numbers, teaches them to play abstract games with real-world applications, discovers unexpected patterns that connect humble lifeforms to enormous galaxies, and explores mathematical underpinnings for randomness and beauty. With evocative examples ranging from multidimensional crochet to the Mona Lisa's asymmetrical smile, as well as ingenious storytelling that helps illuminate complex concepts like infinity and relativity, The Big Bang of Numbers charts a playful, inventive course to existence. Mathematics, Suri shows, might best be understood not as something we invent to explain Nature, but as the source of all creation, whose directives Nature tries to obey as best she can.Offering both striking new perspectives for math aficionados and an accessible introduction for anyone daunted by calculation, The Big Bang of Numbers proves that we can all fall in love with math.
Games Businesses Play
Game theory has come to dominate industrial organization economics, but business strategists continue to debate its usefulness. So far, empirical work on the application of game theory to business strategy has been too limited to force a consensus. As a (partial) remedy, Games Businesses Play uses detailed case studies of competitive interaction to explore the uses and limits of game theory as a tool for business strategists. Because they are analytical rather than descriptive, the case studies are not typical teaching cases. The cases are paired with customized game-theoretic models that cover a wide range of commitment decisions, from short-run commitments such as price to longer-run commitments such as capacity expansion and reduction, product and process innovation, and battles for market share. A variety of quantitative and qualitative techniques are used to test the models' predictions on case data. In addition the book sheds light on a number of other issues important to strategic management, including the resource-based view of the firm and the emergent theory of dynamic capabilities.
Computational Genomics with R
This book has fundamental theoretical and practical aspects of data analysis, useful for beginners and experienced researchers that are looking for a recipe or an analysis approach. Since R has many packages, even experienced researchers look for how particular functions are used in an analysis workflow.
Real Analysis
This book provides a resolution to the "bridging-the-gap problem." The book not only presents the fundamental theorems of real analysis, but also shows the reader how to compose and produce the proofs of these theorems.
Stochastic Processes in Cell Biology
Sensing the environment.- Intracellular pattern formation and reaction-diffusion processes.- Statistical mechanics and dynamics of polymers and membranes.- Self-organization and assembly of cellular structures.- Dynamics and regulation of the cytoskeleton.- Bacterial population growth and collective behavior.- Stochastic reaction-diffusion processes.
Neural Networks are Homeomorphisms
This book is an introductory guide for data scientists to learn the mathematical principles behind the most well-known AI algorithms. The author proposes two original theoretical concepts: the accordion theory and the recurrent third iteration theory. He then applies them to real cases. This work covers topics of higher mathematics from algebraic topology and spectral theory to functional analysis and ergodic theory. These concepts are fundamental to understanding AI concepts and algorithms. This deepens both practitioners' and managers' knowledge of mathematical modeling and assists them to engage with specialized literature. More importantly this book will help them to formally write their own ideas and research.
Study of Linear and Nonlinear Models with Mathematica
The book is devoted to the problems of modeling physical systems and fields using the tools and capabilities of the 'Mathematica' software package. In the process of teaching classical courses in mechanics and mathematical physics, one often has to overcome significant difficulties associated with the cumbersomeness of the mathematical apparatus, which more than once distracts from the essence of the problems under consideration. The use of the 'Mathematica' package, which has a rich set of analytical and graphic tools, makes the presentation of classic issues related to modeling and interpretation of physical processes much more transparent. This package enables the visualization of both analytical solutions of nonlinear differential equations and solutions obtained in the form of infinite series or special functions.The textbook consists of two parts that can be studied independently of each other. The first part deals with the issues of nonlinear mechanics and the theory of oscillations. The second part covers linear problems of classical mathematical physics and nonlinear evolution models describing, inter alia, transport phenomena and propagation of waves. The book contains the codes of programs written in the 'Mathematica' package environment. Supplementary materials of programs illustrating and often complementing the presented material are available on the publisher's website.
Spatial Dynamics Models in the Life Sciences and the Role of Feedback in Robust Developments
Basic mathematical techniques for partial differential equations (PDE) with applications to the life sciences form an integral part of the core curriculum for programs in mathematical biology. Yet, students in such a program with an undergraduate training in biology are typically deficient in any exposure to PDE. This volume starts with simple first order PDE and progresses through higher order equations and systems but with interesting applications, even at the level of a single first order PDE with constant coefficients.Similar to the two previous volumes by the author, another unique feature of the book is highlighting the scientific theme(s) of interest for the biological phenomena being modelled and analysed. In addition to temporal evolution of a biological phenomenon, its limiting equilibrium states and their stability, the possibility of locational variations leads to a study of additional themes such as (signal and wave) propagation, spatial patterning and robustness. The requirement that biological developments are relatively insensitive to sustained environmental changes provides an opportunity to examine the issue of feedback and robustness not encountered in the previous two volumes of this series.
Classical Lie Algebras at Infinity
Originating from graduate topics courses given by the first author, this book functions as a unique text-monograph hybrid that bridges a traditional graduate course to research level representation theory. The exposition includes an introduction to the subject, some highlights of the theory and recent results in the field, and is therefore appropriate for advanced graduate students entering the field as well as research mathematicians wishing to expand their knowledge. The mathematical background required varies from chapter to chapter, but a standard course on Lie algebras and their representations, along with some knowledge of homological algebra, is necessary. Basic algebraic geometry and sheaf cohomology are needed for Chapter 10. Exercises of various levels of difficulty are interlaced throughout the text to add depth to topical comprehension.The unifying theme of this book is the structure and representation theory of infinite-dimensional locally reductive Lie algebras and superalgebras. Chapters 1-6 are foundational; each of the last 4 chapters presents a self-contained study of a specialized topic within the larger field. Lie superalgebras and flag supermanifolds are discussed in Chapters 3, 7, and 10, and may be skipped by the reader.
Cofinally Complete Metric Spaces and Related Functions
The monograph targets a huge variety of characterizations of cofinally complete metric spaces. These spaces are studied in terms of several properties of some classes of functions between metric spaces that are stronger than the continuous functions such as Cauchy-regular, uniformly continuous, strongly uniformly continuous, and various Lipschitz-type functions. There is one chapter that is dedicated to studying cofinally complete metric spaces in terms of hyperspace and function space topologies. Along with that, various characterizations are studied in terms of geometric functionals, sequences, Cantor-type conditions, etc. The study of such spaces is interesting as well as it has nice connections with various other branches of mathematics such as convex analysis, optimization theory, fixed point theory, functional analysis and approximation theory. But until now, there has been no textbook or research monograph which presents the entire theory of these spaces in a comprehensive way. The study of the aforesaid spaces and their variants is still a vibrant area of research, and many prominent researchers are working in this area.The book is targeted at researchers as well as graduate students interested in real functions, analysis on metric spaces, topology, and the aforementioned. Since the monograph often discusses various properties of Lipschitz-type functions, it would be of interest to people interested in PDEs as well.
Geometry of Deep Learning
The focus of this book is on providing students with insights into geometry that can help them understand deep learning from a unified perspective. Rather than describing deep learning as an implementation technique, as is usually the case in many existing deep learning books, here, deep learning is explained as an ultimate form of signal processing techniques that can be imagined. To support this claim, an overview of classical kernel machine learning approaches is presented, and their advantages and limitations are explained. Following a detailed explanation of the basic building blocks of deep neural networks from a biological and algorithmic point of view, the latest tools such as attention, normalization, Transformer, BERT, GPT-3, and others are described. Here, too, the focus is on the fact that in these heuristic approaches, there is an important, beautiful geometric structure behind the intuition that enables a systematic understanding. A unified geometric analysis to understand the working mechanism of deep learning from high-dimensional geometry is offered. Then, different forms of generative models like GAN, VAE, normalizing flows, optimal transport, and so on are described from a unified geometric perspective, showing that they actually come from statistical distance-minimization problems.Because this book contains up-to-date information from both a practical and theoretical point of view, it can be used as an advanced deep learning textbook in universities or as a reference source for researchers interested in acquiring the latest deep learning algorithms and their underlying principles. In addition, the book has been prepared for a codeshare course for both engineering and mathematics students, thus much of the content is interdisciplinary and will appeal to students from both disciplines.
Stochastic Processes in Cell Biology
Introduction.- Random walks and Brownian motion.- Protein receptors and ion channels.- Molecular motors.- Stochastic gene expression and regulatory networks.- Diffusive transport.- Active transport.- The WKB method, path integrals, and large deviations.- Probability theory and martingales.
Protecting Privacy Through Homomorphic Encryption
This book summarizes recent inventions, provides guidelines and recommendations, and demonstrates many practical applications of homomorphic encryption. This collection of papers represents the combined wisdom of the community of leading experts on Homomorphic Encryption. In the past 3 years, a global community consisting of researchers in academia, industry, and government, has been working closely to standardize homomorphic encryption. This is the first publication of whitepapers created by these experts that comprehensively describes the scientific inventions, presents a concrete security analysis, and broadly discusses applicable use scenarios and markets. This book also features a collection of privacy-preserving machine learning applications powered by homomorphic encryption designed by groups of top graduate students worldwide at the Private AI Bootcamp hosted by Microsoft Research.The volume aims to connect non-expert readers with thisimportant new cryptographic technology in an accessible and actionable way. Readers who have heard good things about homomorphic encryption but are not familiar with the details will find this book full of inspiration. Readers who have preconceived biases based on out-of-date knowledge will see the recent progress made by industrial and academic pioneers on optimizing and standardizing this technology. A clear picture of how homomorphic encryption works, how to use it to solve real-world problems, and how to efficiently strengthen privacy protection, will naturally become clear.
Numerical Methods and Optimization
This text, covering a very large span of numerical methods and optimization, is primarily aimed at advanced undergraduate and graduate students. A background in calculus and linear algebra are the only mathematical requirements. The abundance of advanced methods and practical applications will be attractive to scientists and researchers working in different branches of engineering. The reader is progressively introduced to general numerical methods and optimization algorithms in each chapter. Examples accompany the various methods and guide the students to a better understanding of the applications. The user is often provided with the opportunity to verify their results with complex programming code. Each chapter ends with graduated exercises which furnish the student with new cases to study as well as ideas for exam/homework problems for the instructor. A set of programs made in Matlab(TM) is available on the author's personal website and presents both numerical and optimization methods.
The Elements of Hawkes Processes
Hawkes processes are studied and used in a wide range of disciplines: mathematics, social sciences, and earthquake modelling, to name a few. This book presents a selective coverage of the core and recent topics in the broad field of Hawkes processes. It consists of three parts. Parts I and II summarise and provide an overview of core theory (including key simulation methods) and inference methods, complemented by a selection of recent research developments and applications. Part III is devoted to case studies in seismology and finance that connect the core theory and inference methods to practical scenarios. This book is designed primarily for applied probabilists, statisticians, and machine learners. However, the mathematical prerequisites have been kept to a minimum so that the content will also be of interest to undergraduates in advanced mathematics and statistics, as well as machine learning practitioners. Knowledge of matrix theory with basics of probability theory, including Poisson processes, is considered a prerequisite. Colour-blind-friendly illustrations are included.
Fundamentals of Statistical Thinking
Written for students with basic experience in college algebra and applied calculus, Fundamentals of Statistical Thinking: Tools and Applications familiarizes readers with fundamental concepts in statistical thinking in order to prepare them for specialized management courses such as econometrics and quantitative analysis. The book is organized into four sections, each of which focuses on a common tool used in application. Chapters 1 through 4 discuss data analysis and summaries, with an emphasis on descriptive statistics and visualization. In Chapters 5 through 8 students learn about probability models and sampling distributions. Chapters 9 and 10 deal with statistical inferences, while Chapters 11 and 12 provide further applications for categorical data and simple linear regression models. Graphical illustrations support the written text and each chapter concludes with a visual summary. Rooted in over ten years of classroom experience at both the undergraduate and graduate levels, Fundamentals of Statistical Thinking helps readers understand the importance of the main technical tools of statistical decision making, and explains when they can most appropriately be used for applied studies.
Foundations of Quantitative Finance Book II: Probability Spaces and Random Variables
Every financial professional wants and needs an advantage. A firm foundation in advanced mathematics can translate into dramatic advantages to professionals willing to obtain it. Many are not-and that is the advantage these books offer the astute reader.
Mathematical Puzzle Tales from Mount Olympus
This book uses fascinating tales from Greek Mythology as the background for introducing mathematics puzzles to the general public. A background in high school mathematics will be ample preparation for using this book, and it should appeal to anyone who enjoys puzzles and recreational mathematics.
Fuzzy Natural Logic in IFSA-EUSFLAT 2021
The present book contains five papers accepted and published in the Special Issue, "Fuzzy Natural Logic in IFSA-EUSFLAT 2021", of the journal Mathematics (MDPI). These papers are extended versions of the contributions presented in the conference "The 19th World Congress of the International Fuzzy Systems Association and the 12th Conference of the European Society for Fuzzy Logic and Technology jointly with the AGOP, IJCRS, and FQAS conferences", which took place in Bratislava (Slovakia) from September 19 to September 24, 2021.Fuzzy Natural Logic (FNL) is a system of mathematical fuzzy logic theories that enables us to model natural language terms and rules while accounting for their inherent vagueness and allows us to reason and argue using the tools developed in them. FNL includes, among others, the theory of evaluative linguistic expressions (e.g., small, very large, etc.), the theory of fuzzy and intermediate quantifiers (e.g., most, few, many, etc.), and the theory of fuzzy/linguistic IF-THEN rules and logical inference. The papers in this Special Issue use the various aspects and concepts of FNL mentioned above and apply them to a wide range of problems both theoretically and practically oriented.This book will be of interest for researchers working in the areas of fuzzy logic, applied linguistics, generalized quantifiers, and their applications.
A History of Mechanics
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Continuum, and Other Types of Serial Order, With an Introduction to Cantor's Transfinite Numbers
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Census of England and Wales, 1911 (10 Edward 7 and 1 George 5, ch. 27); Volume 1
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Lectures on the Theory of Elliptic Functions; Volume I
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
An Elementary Course of Infinitesimal Calculus
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Report On The Census Of Porto Rico, 1899
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
