Mathematical Game Theory
What is a game? Classically, a game is perceived as something played by human beings. Its mathematical analysis is human-centered, explores the structures of particular games, economic or social environments and tries to model supposedly 'rational' human behavior in search of appropriate 'winning strategies'. This point of view places game theory into a very special scientific corner where mathematics, economics and psychology overlap and mingle.This book takes a novel approach to the subject. Its focus is on mathematical models that apply to game theory in particular but exhibit a universal character and thus extend the scope of game theory considerably.This textbook addresses anyone interested in a general game-theoretic view of the world. The reader should have mathematical knowledge at the level of a first course in real analysis and linear algebra. However, possibly more specialized aspects are further elaborated and pointers to relevant supplementary literature are given. Moreover, many examples invite the reader to participate 'actively' when going through the material. The scope of the book can be covered in one course on Mathematical Game Theory at advanced undergraduate or graduate level.
Numerical Analysis and Computational Mathematics
Mathematical modeling is an active area of applied mathematics. At its beginning, engineers were the main practitioners of this area of mathematics, developing mathematical models to solve engineering problems in natural sciences. However, analysis methods and models in social sciences are similar to those of nature sciences, including engineering, with the only difference being that instead of using principles of the nature, one uses principles or theories from experts of such social sciences. Models based on ordinary or partial differential equations describe a wide variety of phenomena such as sound, heat, diffusion, electrostatics, electrodynamics, fluid dynamics, elasticity, or quantum mechanics, for example. Further, stochastic models have recently received increasing attention. Obviously, some of these types of complex problems also require a deep analysis of the tools utilized to solve these situations. In this collection, we will attempt to integrate models, methods, and also applications, not only in the scope of traditional natural sciences, but also opening the scope to education and other social sciences. Theory and data-driven models, even in a synergy that gives rise to producing fertile, multidisciplinary, and hybrid models, can be considered.
Fractional Derivative Modeling in Mechanics and Engineering
This textbook highlights the theory of fractional calculus and its wide applications in mechanics and engineering. It describes in details the research findings in using fractional calculus methods for modeling and numerical simulation of complex mechanical behavior. It covers the mathematical basis of fractional calculus, the relationship between fractal and fractional calculus, unconventional statistics and anomalous diffusion, typical applications of fractional calculus, and the numerical solution of the fractional differential equation. It also includes latest findings, such as variable order derivative, distributed order derivative and its applications. Different from other textbooks in this subject, the book avoids lengthy mathematical demonstrations, and presents the theories in close connection to the applications in an easily readable manner. This textbook is intended for students, researchers and professionals in applied physics, engineering mechanics, and applied mathematics. It is also of high reference value for those in environmental mechanics, geotechnical mechanics, biomechanics, and rheology.
Cambridge Lower Secondary Complete Mathematics 8 Student Book 2nd Edition Set
Graphs and Combinatorial Optimization: From Theory to Applications
This book highlights new and original contributions on Graph Theory and Combinatorial Optimization both from the theoretical point of view and from applications in all fields. The book chapters describe models and methods based on graphs, structural properties, discrete optimization, network optimization, mixed-integer programming, heuristics, meta-heuristics, math-heuristics, and exact methods as well as applications. The book collects selected contributions from the CTW2020 international conference (18th Cologne-Twente Workshop on Graphs and Combinatorial Optimization), held online on September 14-16, 2020. The conference was organized by IASI-CNR with the contribution of University of Roma Tre, University Roma Tor Vergata, and CNRS-LIX and with the support of AIRO. It is addressed to researchers, PhD students, and practitioners in the fields of Graph Theory, Discrete Mathematics, Combinatorial Optimization, and Operations Research.
Robust Microelectronic Devices
Integrated electronic circuits have influenced our society over the past decades and have become an indispensable part of our daily lives. To maintain this development and ensure benefits for decades to come, continuous further development of electronic chips is necessary. These developments include improving their performance and universality and exploiting the full potential of microelectronic technologies. An important issue for all microelectronic devices is their robustness, i.e., the high performant and reliable function, which is the key for long-term failure safe and stable operation of complex electrical circuits and applications. In real devices, the high-performant and stable operation becomes limited by various physical effects, such as bias temperature instabilities, stress-induced leakage currents, etc. A continuous improvement of the physical understanding of such effects is essential for further optimization of silicon transistors and the improvement of the performance of emerging technologies such as devices based on wide bandgap materials like SiC or GaN as well as for novel 2D transistors. The publications published in this special issue cover various aspects of robust electronic devices and are just as diverse as the field of research itself.
Basic Abstract Algebra: Exercises and Solutions
This book is mainly intended for first-year University students who undertake a basic abstract algebra course, as well as instructors. It contains the basic notions of abstract algebra through solved exercises as well as a 'True or False' section in each chapter. Each chapter also contains an essential background section, which makes the book easier to use.
Mathematical Modeling of the Human Brain
This open access book bridges common tools in medical imaging and neuroscience with the numerical solution of brain modelling PDEs. The connection between these areas is established through the use of two existing tools, FreeSurfer and FEniCS, and one novel tool, the SVM-Tk, developed for this book. The reader will learn the basics of magnetic resonance imaging and quickly proceed to generating their first FEniCS brain meshes from T1-weighted images. The book's presentation concludes with the reader solving a simplified PDE model of gadobutrol diffusion in the brain that incorporates diffusion tensor images, of various resolution, and complex, multi-domain, variable-resolution FEniCS meshes with detailed markings of anatomical brain regions. After completing this book, the reader will have a solid foundation for performing patient-specific finite element simulations of biomechanical models of the human brain.
Basic Abstract Algebra
This book is mainly intended for first-year University students who undertake a basic abstract algebra course, as well as instructors. It contains the basic notions of abstract algebra through solved exercises as well as a 'True or False' section in each chapter. Each chapter also contains an essential background section, which makes the book easier to use.
Fractal Analysis: Basic Concepts and Applications
The aim of this book is to provide a basic and self-contained introduction to the ideas underpinning fractal analysis. The book illustrates some important applications issued from real data sets, real physical and natural phenomena as well as real applications in different fields, and consequently, presents to the readers the opportunity to implement fractal analysis in their specialties according to the step-by-step guide found in the book.Besides advanced undergraduate students, graduate students and senior researchers, this book may also serve scientists and research workers from industrial settings, where fractals and multifractals are required for modeling real-world phenomena and data, such as finance, medicine, engineering, transport, images, signals, among others.For the theorists, rigorous mathematical developments are established with necessary prerequisites that make the book self-containing. For the practitioner often interested in model building and analysis, we provide the cornerstone ideas.
Nonlinear Analysis and Global Optimization
This contributed volume discusses aspects of nonlinear analysis in which optimization plays an important role, as well as topics which are applied to the study of optimization problems. Topics include set-valued analysis, mixed concave-convex sub-superlinear Schroedinger equation, Schroedinger equations in nonlinear optics, exponentially convex functions, optimal lot size under the occurrence of imperfect quality items, generalized equilibrium problems, artificial topologies on a relativistic spacetime, equilibrium points in the restricted three-body problem, optimization models for networks of organ transplants, network curvature measures, error analysis through energy minimization and stability problems, Ekeland variational principles in 2-local Branciari metric spaces, frictional dynamic problems, norm estimates for composite operators, operator factorization and solution of second-order nonlinear difference equations, degenerate Kirchhoff-type inclusion problems, and more.
The Krasnosel’skiĭ-Mann Iterative Method
This brief explores the Krasnosel'skiĭ-Man (KM) iterative method, which has been extensively employed to find fixed points of nonlinear methods.
Chemotaxis Modeling of Autoimmune Inflammation
This book is directed to the computer-based modeling of chemotaxis inflammation, typically resulting from an infection by a pathogen (e.g., bacteria, viruses). The book has particular relevance to the coronavirus pandemic since long-Covid neurological impairment may be the result of brain inflammation.
Rank-Based Methods for Shrinkage and Selection
Rank-Based Methods for Shrinkage and Selection A practical and hands-on guide to the theory and methodology of statistical estimation based on rank Robust statistics is an important field in contemporary mathematics and applied statistical methods. Rank-Based Methods for Shrinkage and Selection: With Application to Machine Learning describes techniques to produce higher quality data analysis in shrinkage and subset selection to obtain parsimonious models with outlier-free prediction. This book is intended for statisticians, economists, biostatisticians, data scientists and graduate students. Rank-Based Methods for Shrinkage and Selection elaborates on rank-based theory and application in machine learning to robustify the least squares methodology. It also includes: Development of rank theory and application of shrinkage and selection Methodology for robust data science using penalized rank estimators Theory and methods of penalized rank dispersion for ridge, LASSO and Enet Topics include Liu regression, high-dimension, and AR(p) Novel rank-based logistic regression and neural networks Problem sets include R code to demonstrate its use in machine learning
Number Names; The Magic Square Divination of Cai Chen 蔡沈 (1167-1230)
In his Master Plan Cai Chen (1167-1230) created an original divination manual based on the Yijing and keyed it to an intricate series of 81 matrixes with the properties of "magic squares." Previously unrecognized, Cai's work is a milestone in the history of mathematics, and, in introducing it, this book dramatically expands our understanding of the Chinese number theory practiced by the "Image and Number" school within Confucian philosophy. Thinkers of that leaning devised graphic arrays of the binary figures called "trigrams" and "hexagrams" in the Yijing as a way of exploring the relationship between the random draws of divination and the classic's readings. Cai adapted this perspective to his 81 matrix series, which he saw as tracing the recurring temporal cycles of the natural world. The architecture of the matrix series is echoed in the language of his divination texts, which he called "number names"--hence, the book's title. This book will appeal to those interested in philosophy, the history of science and mathematics, and Chinese intellectual history. The divination text has significant literary as well as philosophical dimensions, and its audience lies both among specialists in these fields and with a general readership interested in recreational mathematics and topics like divination, Taiji, and Fengshui.
Visualizing Linear Models
This book provides a visual and intuitive coverage of the core theory of linear models. Designed to develop fluency with the underlying mathematics and to build a deep understanding of the principles, it's an excellent basis for a one-semester course on statistical theory and linear modeling for intermediate undergraduates or graduate students. Three chapters gradually develop the essentials of linear model theory. They are each preceded by a review chapter that covers a foundational prerequisite topic. This classroom-tested work explores two distinct and complementary types of visualization: the "observations picture" and the "variables picture." To improve retention of material, this book is supplemented by a bank of ready-made practice exercises for students. These are available for digital or print use.
Periodic Monopoles and Difference Modules
This book studies a class of monopoles defined by certain mild conditions, called periodic monopoles of generalized Cherkis-Kapustin (GCK) type. It presents a classification of the latter in terms of difference modules with parabolic structure, revealing a kind of Kobayashi-Hitchin correspondence between differential geometric objects and algebraic objects. It also clarifies the asymptotic behaviour of these monopoles around infinity.The theory of periodic monopoles of GCK type has applications to Yang-Mills theory in differential geometry and to the study of difference modules in dynamical algebraic geometry. A complete account of the theory is given, including major generalizations of results due to Charbonneau, Cherkis, Hurtubise, Kapustin, and others, and a new and original generalization of the nonabelian Hodge correspondence first studied by Corlette, Donaldson, Hitchin and Simpson.This work will be of interest to graduate students and researchers in differential and algebraic geometry, as well as in mathematical physics.
Applied Mathematics for Environmental Problems
This book contains some contributions presented at the Applied Mathematics for Environmental Problems minisymposium during the International Congress on Industrial and Applied Mathematics (ICIAM) held July 15-19, 2019 in Valencia, Spain. The first paper addresses a simplified physical wildfire spread model, based on partial differential equations solved with finite element methods and integrated into a GIS to provide a useful and efficient tool. The second paper focuses on one of the causes of the unpredictable behavior of wildfire, fire-spotting, through a statistical approach. The third paper addresses low -level wind shear which represents one of the most relevant hazards during aircraft takeoff and landing. It presents an experimental wind shear alert system that is based on predicting wind velocities obtained from the Harmonie-Arome model. The last paper addresses the environmental impact of oil reservoirs. It presents high-order hybridizable discontinuous Galerkin formulation combined with high-order diagonally implicit Runge-Kutta schemes to solve one-phase and two-phase flow problems through porous media. All the contributions collected in this volume are interesting examples of how mathematics and numerical modelling are effective tools in the field of environmental problems.
Ligeti's Macroharmonies
In the third and final book of his iconic piano etudes Gy繹rgy Ligeti charts a new path relative to the rest of his musical output, representing a significant arrival in a composer's oeuvre known for its stylistic transformations. This monograph is the first dedicated study of these capstone works, investigating them through a novel lens of statistical-graphical analysis that illuminates their compositional uniqueness as well as broader questions regarding the perception of stability in musical texture.With nearly 200 graphical illustrations and a detailed commentary, this examination reveals the unique manner in which Ligeti treads between tonality and atonality--a key idea in his late style--and the centrality of processes related to broader scale areas (or "macroharmony") in articulating structures and narratives. The analytical techniques developed here are a powerful tool for investigating macroharmonic stability that can be applied to a wide range of repertoire beyond these works.This book is intended for graduate-level and professional music theorists, musicologists, performers and mathematicians.
Geometrical Theory of Analytic Functions
The book contains papers published in the Mathematics Special Issue, entitled "Geometrical Theory of Analytic Functions". Fifteen papers devoted to the study concerning complex-valued functions of one variable present new outcomes related to special classes of univalent functions, differential equations in view of geometric function theory, quantum calculus and its applications in geometric function theory, operators and special functions associated with differential subordination and superordination theories and starlikeness, and convexity criteria.
Smart Materials and Devices for Energy Harvesting
This book is devoted to energy harvesting from smart materials and devices. It focusses on the latest available techniques recently published by researchers all over the world.Energy Harvesting allows otherwise wasted environmental energy to be converted into electric energy, such as vibrations, wind and solar energy.It is a common experience that the limiting factor for wearable electronics, such as smartphones or wearable bands, or for wireless sensors in harsh environments, is the finite energy stored in onboard batteries. Therefore, the answer to the battery "charge or change" issue is energy harvesting because it converts the energy in the precise location where it is needed. In order to achieve this, suitable smart materials are needed, such as piezoelectrics or magnetostrictives. Moreover, energy harvesting may also be exploited for other crucial applications, such as for the powering of implantable medical/sensing devices for humans and animals.Therefore, energy harvesting from smart materials will become increasingly important in the future. This book provides a broad perspective on this topic for researchers and readers with both physics and engineering backgrounds.
Information Retrieval and Natural Language Processing
This book gives a comprehensive view of graph theory in informational retrieval (IR) and natural language processing(NLP). This book provides number of graph techniques for IR and NLP applications with examples. It also provides understanding of graph theory basics, graph algorithms and networks using graph. The book is divided into three parts and contains nine chapters. The first part gives graph theory basics and graph networks, and the second part provides basics of IR with graph-based information retrieval. The third part covers IR and NLP recent and emerging applications with case studies using graph theory. This book is unique in its way as it provides a strong foundation to a beginner in applying mathematical structure graph for IR and NLP applications. All technical details that include tools and technologies used for graph algorithms and implementation in Information Retrieval and Natural Language Processing with its future scope are explained in a clear and organized format.
Optimal Quantification and Symmetry
This book offers a unique new look at the familiar quantification theory from the point of view of mathematical symmetry and spatial symmetry. Symmetry exists in many aspects of our life--for instance, in the arts and biology as an ingredient of beauty and equilibrium, and more importantly, for data analysis as an indispensable representation of functional optimality. This unique focus on symmetry clarifies the objectives of quantification theory and the demarcation of quantification space, something that has never caught the attention of researchers.Mathematical symmetry is well known, as can be inferred from Hirschfeld's simultaneous linear regressions, but spatial symmetry has not been discussed before, except for what one may infer from Nishisato's dual scaling. The focus on symmetry here clarifies the demarcation of quantification analysis and makes it easier to understand such a perennial problem as that of joint graphical display in quantification theory. The new framework will help advance the frontier of further developments of quantification theory. Many numerical examples are included to clarify the details of quantification theory, with a focus on symmetry as its operational principle. In this way, the book is useful not only for graduate students but also for researchers in diverse areas of data analysis.
Inverse Optimal Control and Inverse Noncooperative Dynamic Game Theory
This book presents a novel unified treatment of inverse problems in optimal control and noncooperative dynamic game theory. It provides readers with fundamental tools for the development of practical algorithms to solve inverse problems in control, robotics, biology, and economics. The treatment involves the application of Pontryagin's minimum principle to a variety of inverse problems and proposes algorithms founded on the elegance of dynamic optimization theory. There is a balanced emphasis between fundamental theoretical questions and practical matters. The text begins by providing an introduction and background to its topics. It then discusses discrete-time and continuous-time inverse optimal control. The focus moves on to differential and dynamic games and the book is completed by consideration of relevant applications. The algorithms and theoretical results developed in Inverse Optimal Control and Inverse Noncooperative Dynamic Game Theory provide new insights into information requirements for solving inverse problems, including the structure, quantity, and types of state and control data. These insights have significant practical consequences in the design of technologies seeking to exploit inverse techniques such as collaborative robots, driver-assistance technologies, and autonomous systems. The book will therefore be of interest to researchers, engineers, and postgraduate students in several disciplines within the area of control and robotics.
Computational Optimizations for Machine Learning
The present book contains the 10 articles finally accepted for publication in the Special Issue "Computational Optimizations for Machine Learning" of the MDPI journal Mathematics, which cover a wide range of topics connected to the theory and applications of machine learning, neural networks and artificial intelligence. These topics include, among others, various types of machine learning classes, such as supervised, unsupervised and reinforcement learning, deep neural networks, convolutional neural networks, GANs, decision trees, linear regression, SVM, K-means clustering, Q-learning, temporal difference, deep adversarial networks and more.It is hoped that the book will be interesting and useful to those developing mathematical algorithms and applications in the domain of artificial intelligence and machine learning as well as for those having the appropriate mathematical background and willing to become familiar with recent advances of machine learning computational optimization mathematics, which has nowadays permeated into almost all sectors of human life and activity.
Spatial Networks
This book provides a complete introduction into spatial networks. It offers the mathematical tools needed to characterize these structures and how they evolve in time and presents the most important models of spatial networks.The book puts a special emphasis on analyzing complex systems which are organized under the form of networks where nodes and edges are embedded in space. In these networks, space is relevant, and topology alone does not contain all the information. Characterizing and understanding the structure and the evolution of spatial networks is thus crucial for many different fields, ranging from urbanism to epidemiology.This subject is therefore at the crossroad of many fields and is of potential interest to a broad audience comprising physicists, mathematicians, engineers, geographers or urbanists. In this book, the author has expanded his previous book ("Morphogenesis of Spatial Networks") to serve as a textbook and reference on this topic for a wide range of students and professional researchers.
Fuzzy Sets in Business Management, Finance, and Economics
This book collects fifteen papers published in s Special Issue of Mathematics titled "Fuzzy Sets in Business Management, Finance, and Economics", which was published in 2021. These paper cover a wide range of different tools from Fuzzy Set Theory and applications in many areas of Business Management and other connected fields. Specifically, this book contains applications of such instruments as, among others, Fuzzy Set Qualitative Comparative Analysis, Neuro-Fuzzy Methods, the Forgotten Effects Algorithm, Expertons Theory, Fuzzy Markov Chains, Fuzzy Arithmetic, Decision Making with OWA Operators and Pythagorean Aggregation Operators, Fuzzy Pattern Recognition, and Intuitionistic Fuzzy Sets. The papers in this book tackle a wide variety of problems in areas such as strategic management, sustainable decisions by firms and public organisms, tourism management, accounting and auditing, macroeconomic modelling, the evaluation of public organizations and universities, and actuarial modelling.We hope that this book will be useful not only for business managers, public decision-makers, and researchers in the specific fields of business management, finance, and economics but also in the broader areas of soft mathematics in social sciences. Practitioners will find methods and ideas that could be fruitful in current management issues. Scholars will find novel developments that may inspire further applications in the social sciences.
Resolvability In Soft Topological Spaces
In this book, we used the concept of soft sets and we studied the soft sets theory as an analytical study and dividing the kinds to four families, to make a comparison between them and identify similarities and differences among them, then we chooses one of these families to be the focus of our work is the fourth family, all of this in order to we get the concepts of the resolvability and irresolvability in soft topological spaces .
Einstein's Violin
Music brings great joy to many of us. But its other benefits often go underappreciated. Numerous studies and historical anecdotes highlight how powerfully music alters the human mind. Two characteristics drive most of music's cognitive benefits: It builds a faster highway between the right and left sides of the brain, enabling greater cooperation between the logical and the creative. It also creates a vast mesh of connectivity within the brain, like a microcosm of the World Wide Web. In a fascinating study, Douglas Wadle celebrates the juxtaposition of art and science while examining music's influence on humanity's understanding of our place in the universe. Tracing the millennia-old love affair between music and science, Wadle chronicles the surprising ubiquity of musical training among history's greatest thinkers. He shines a spotlight on the intertwining stories of pattern and form and how they complement one another in our search for creativity and insight. Einstein's Violin relies on extensive research to tell the story of how music impacts the pattern recognition software in our brains, facilitating more creative problem solving. Without digression into technical treatise, it focuses on the historical stories that best display music's beautiful interaction with mind and universe.
Einstein's Violin
Music brings great joy to many of us. But its other benefits often go underappreciated. Numerous studies and historical anecdotes highlight how powerfully music alters the human mind. Two characteristics drive most of music's cognitive benefits: It builds a faster highway between the right and left sides of the brain, enabling greater cooperation between the logical and the creative. It also creates a vast mesh of connectivity within the brain, like a microcosm of the World Wide Web. In a fascinating study, Douglas Wadle celebrates the juxtaposition of art and science while examining music's influence on humanity's understanding of our place in the universe. Tracing the millennia-old love affair between music and science, Wadle chronicles the surprising ubiquity of musical training among history's greatest thinkers. He shines a spotlight on the intertwining stories of pattern and form and how they complement one another in our search for creativity and insight. Einstein's Violin relies on extensive research to tell the story of how music impacts the pattern recognition software in our brains, facilitating more creative problem solving. Without digression into technical treatise, it focuses on the historical stories that best display music's beautiful interaction with mind and universe.
Theoretical Computer Science for the Working Category Theorist
Using basic category theory, this Element describes all the central concepts and proves the main theorems of theoretical computer science. Category theory, which works with functions, processes, and structures, is uniquely qualified to present the fundamental results of theoretical computer science. In this Element, readers will meet some of the deepest ideas and theorems of modern computers and mathematics, such as Turing machines, unsolvable problems, the P=NP question, Kurt G繹del's incompleteness theorem, intractable problems, cryptographic protocols, Alan Turing's Halting problem, and much more. The concepts come alive with many examples and exercises.
Quasi-Interpolation
Quasi-interpolation is one of the most useful and often applied methods for the approximation of functions and data in mathematics and applications. Its advantages are manifold: quasi-interpolants are able to approximate in any number of dimensions, they are efficient and relatively easy to formulate for scattered and meshed nodes and for any number of data. This book provides an introduction into the field for graduate students and researchers, outlining all the mathematical background and methods of implementation. The mathematical analysis of quasi-interpolation is given in three directions, namely on the basis (spline spaces, radial basis functions) from which the approximation is taken, on the form and computation of the quasi-interpolants (point evaluations, averages, least squares), and on the mathematical properties (existence, locality, convergence questions, precision). Learn which type of quasi-interpolation to use in different contexts and how to optimise its features to suit applications in physics and engineering.
Surveys in Geometry I
The volume consists of a set of surveys on geometry in the broad sense. The goal is to present a certain number of research topics in a non-technical and appealing manner.The topics surveyed include spherical geometry, the geometry of finite-dimensional normed spaces, metric geometry (Bishop--Gromov type inequalities in Gromov-hyperbolic spaces), convexity theory and inequalities involving volumes and mixed volumes of convex bodies, 4-dimensional topology, Teichm羹ller spaces and mapping class groups actions, translation surfaces and their dynamics, and complex higher-dimensional geometry.Several chapters are based on lectures given by their authors to middle-advanced level students and young researchers. The whole book is intended to be an introduction to current research trends in geometry.
Non-Smooth and Complementarity-Based Distributed Parameter Systems
Theoretical Computer Science and Discrete Mathematics
This book includes 15 articles published in the Special Issue "Theoretical Computer Science and Discrete Mathematics" of Symmetry (ISSN 2073-8994). This Special Issue is devoted to original and significant contributions to theoretical computer science and discrete mathematics. The aim was to bring together research papers linking different areas of discrete mathematics and theoretical computer science, as well as applications of discrete mathematics to other areas of science and technology. The Special Issue covers topics in discrete mathematics including (but not limited to) graph theory, cryptography, numerical semigroups, discrete optimization, algorithms, and complexity.
Recent Advances and Future Trends in Nanophotonics
Nanophotonics has emerged as a multidisciplinary frontier of science and engineering. Due to its high potential to contribute to breakthroughs in many areas of technology, nanophotonics is capturing the interest of many researchers from different fields.This Special Issue of Applied Sciences on "Recent advances and future trends in nanophotonics" aims to give an overview on the latest developments in nanophotonics and its roles in different application domains. Topics of discussion include, but are not limited to, the exploration of new directions of nanophotonic science and technology that enable technological breakthroughs in high-impact areas mainly regarding diffraction elements, detection, imaging, spectroscopy, optical communications, and computing.
Geometric Transformations
This textbook teaches the transformations of plane Euclidean geometry through problems, offering a transformation-based perspective on problems that have appeared in recent years at mathematics competitions around the globe, as well as on some classical examples and theorems. It is based on the combined teaching experience of the authors (coaches of several Mathematical Olympiad teams in Brazil, Romania and the USA) and presents comprehensive theoretical discussions of isometries, homotheties and spiral similarities, and inversions, all illustrated by examples and followed by myriad problems left for the reader to solve. These problems were carefully selected and arranged to introduce students to the topics by gradually moving from basic to expert level. Most of them have appeared in competitions such as Mathematical Olympiads or in mathematical journals aimed at an audience interested in mathematics competitions, while some are fundamental facts of mathematics discussed in the framework of geometric transformations. The book offers a global view of the geometric content of today's mathematics competitions, bringing many new methods and ideas to the attention of the public.Talented high school and middle school students seeking to improve their problem-solving skills can benefit from this book, as well as high school and college instructors who want to add nonstandard questions to their courses. People who enjoy solving elementary math problems as a hobby will also enjoy this work.
Comic Sections Plus
Comic Sections Plus is a revised and greatly expanded edition of the hugely popular book Comic Sections, published by Boole Press in 1993, and now long out of print. It is the biggest (and best!) compendium of material ever published relating to mathematical jokes, anecdotes, humour, wit and wisdom. The author writes: Much of Comic Sections Plus is devoted to 'anecjokes', that is, stories, jokes and anecdotes about mathematics and mathematicians, or jokes with a mathematical or logical content. I firmly believe that such material is not necessarily flippant, but has a serious if not essential role to play in the study, understanding, and popularisation of mathematics. Mathematics and humour are actually closely related and we can easily find structural links between the theorem and the joke. The mathematical problem and the facetious riddle have a lot in common too, and logic is undoubtedly a connecting link; mathematics is regarded as ultra-logical, while humour is often ultra-illogical, turning logic on its head. One rarely meets the legendary 'absentminded mathematician' in reality and in fact the level of appreciation of humour among mathematicians seems to be quite high, at least as great as that of any other profession. This is perhaps because mathematicians are quick to spot logical fallacies and also have to endure a considerable amount of jokes and humour, often made by other scientists. In addition, humour can be an excellent aid to teaching mathematics, as long as it is used skilfully and carefully. Historically, there have been several mathematical humorists, humorous mathematicians, and people with a foot in both camps. We may cite Lewis Carroll, Stephen Leacock, Tom Lehrer, Martin Gardner, Charles Babbage, John Paulos, Paul Erdos, Leo Moser, James Clerk Maxwell and John Horton Conway. This book draws on the contributions of these great luminaries, but also features the amusing blunders of the 'geniuses' at the other end of the spectrum of mathematical talent. Sadly, mathematics has the reputation of being the least popular and most difficult subject in school and college. We really cannot afford this state of affairs to continue, because mathematics is essential to virtually all human activity, since it is the basis of all organised knowledge. Perhaps the problem is that the subject has always been taken too seriously. Comic Sections Plus is an attempt to lighten mathematics, to make it more enjoyable, and above all to humanise it.
Journal of Applied Logics. The IfCoLog Journal of Logics and their Applications, Volume 9, Issue 1, January 2022. Special issue
The Journal of Applied Logics- IfCoLog Journal of Logics and their Applications (FLAP) covers all areas of pure and applied logic, broadly construed. All papers published are free open access, and available via the College Publications website. This Journal is open access, puts no limit on the number of pages of any article, puts no limit on the number of papers in an issue and puts no limit on the number of issues per year. We insist only on a very high academic standard, and will publish issues as they come.
tp1.3 A continuing inquiry into the Foundations of the Science of Physics
This book, tp1.3, continues a dialog between the three friends, started in tp1.1 and tp1.2, on the foundations of the science of Physics. Having encountered numerous surprises in defining algebras, the friends have elected to continue on to a calculus for three dimensional vectors The friends start by considering whether the set of vectors may harbor a topology. Having found so, they next consider how limits may be defined for such a topology. They quickly arrive at many such: directional limits, omni-directional limits, limits of the first quadrant, limits in the first quadrant, limits in sections, limits along vectorial curves.From each of these limits arises the many definitions of derivatives for the set of vectors. Derivatives may be defined with reference to the underlying field or to the set of vectors itself. Since reference to the underlying field implicates order, these derivatives are called process. Process may occur in a direction, along a curve specified by the field or along a curve defined in set of vectors itself. Derivatives may also be defined with reference to the set of vectors itself, and so relinquish order. These possibilities enable the definition of three other derivatives, namely: divergences, curls, and gradients. These many possibilities are elaborated in their respective contexts. In the context of first quadrant gradients, a definition of the gradient of a vectorial function is defined which becomes a unifying concept for non-process differentiation. Some specific first quadrant results are given. The friends then turn to differentiation in a section. They find such differentiation occupies a central position between quadrant differentiation on the one hand and directional differentiation on the other.Finally the friends produce a table of sums and productsThe friends then turn to vectorial integration, finding they can continue on a path similar to differentiation. First, directional integrals, then process integration along curves. The integration of divergences, curls and gradients are called invergences, incurls, and ingradients respectively. The friends consider integration of functions incorporating step functions where they find interesting results.How, the friends wonder, does one integrate over regions? The answer comes from defining vector measures in the set of vectors. Integration over measurable set then becomes possible. They also pursue results of local integration of local derivatives. And step functions? For the local context, two new step functions are defined: point, and local step functions. In each context results are obtained which are extensions of the fundamental theorem of integral calculus. With step functions, the results are extended to function with a finite number of step discontinuities.With measurable sets comes surfaces. The friends consider derivatives and integrals over the surfaces. They find the development leads to an analysis of the Divergence Theorem.
An Introduction to the Mathematical Theory of Inverse Problems
This graduate-level textbook introduces the reader to the area of inverse problems, vital to many fields including geophysical exploration, system identification, nondestructive testing, and ultrasonic tomography. It aims to expose the basic notions and difficulties encountered with ill-posed problems, analyzing basic properties of regularization methods for ill-posed problems via several simple analytical and numerical examples. The book also presents three special nonlinear inverse problems in detail: the inverse spectral problem, the inverse problem of electrical impedance tomography (EIT), and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness, and continuous dependence on parameters. Ultimately, the text discusses theoretical results as well as numerical procedures for the inverse problems, including many exercises and illustrations to complement coursework in mathematics and engineering. This updated text includes a new chapter on the theory of nonlinear inverse problems in response to the field's growing popularity, as well as a new section on the interior transmission eigenvalue problem which complements the Sturm-Liouville problem and which has received great attention since the previous edition was published.
Algebra: A Comprehensive Course
Algebra is primarily concerned with the study of mathematical symbols as well as the rules that operate such symbols. It is applied in most of the sub-domains within mathematics. Algebra makes use of letters to denote numerical values. Some of the major branches of algebra are elementary algebra and abstract algebra. Elementary algebra focuses on the study of variables and polynomials. Abstract algebra studies the abstraction such as groups, rings and fields as well as elementary equation solving. It is applied in the study of various fields such as algebraic topology and algebraic number theory. This book is compiled in such a manner, that it will provide in-depth knowledge about the theory and practice of algebra. Some of the diverse topics covered herein address the varied branches that fall under this category. Coherent flow of topics, student-friendly language and extensive use of examples make this book an invaluable source of knowledge.
Directed Quantities in Electrodynamics
This monograph explores classical electrodynamics from a geometrical perspective with a clear visual presentation throughout. Featuring over 200 figures, readers will delve into the definitions, properties, and uses of directed quantities in classical field theory. With an emphasis on both mathematical and electrodynamic concepts, the author's illustrative approach will help readers understand the critical role directed quantities play in physics and mathematics. Chapters are organized so that they gradually scale in complexity, and carefully guide readers through important topics. The first three chapters introduce directed quantities in three dimensions with and without the metric, as well as the development of the algebra and analysis of directed quantities. Chapters four through seven then focus on electrodynamics without the metric, such as the premetric case, waves, and fully covariant four-dimensional electrodynamics. Complementing the book's careful structure, exercises are included throughout for readers seeking further opportunities to practice the material. Directed Quantities in Electrodynamics will appeal to students, lecturers, and researchers of electromagnetism. It is particularly suitable as a supplement to standard textbooks on electrodynamics.
Deep Learning in Multi-Step Prediction of Chaotic Dynamics
The book represents the first attempt to systematically deal with the use of deep neural networks to forecast chaotic time series. Differently from most of the current literature, it implements a multi-step approach, i.e., the forecast of an entire interval of future values. This is relevant for many applications, such as model predictive control, that requires predicting the values for the whole receding horizon. Going progressively from deterministic models with different degrees of complexity and chaoticity to noisy systems and then to real-world cases, the book compares the performances of various neural network architectures (feed-forward and recurrent). It also introduces an innovative and powerful approach for training recurrent structures specific for sequence-to-sequence tasks. The book also presents one of the first attempts in the context of environmental time series forecasting of applying transfer-learning techniques such as domain adaptation.
