Anvendt matematik

One of the central highlights of this work is the exploration of the Yoneda lemma and its profound implications, during which intuitive explanations are provided, as well as detailed proofs, and specific examples. This book covers aspects of category theory often considered advanced in a clear and intuitive way, with rigorous mathematical proofs. It investigates universal properties, coherence, the relationship between categories and graphs, and treats monads and comonads on an equal footing, providing theorems, interpretations and concrete examples. Finally, this text contains an introduction to monoidal categories and to strong and commutative monads, which are essential tools in current research but seldom found in other textbooks.Starting Category Theory serves as an accessible and comprehensive introduction to the fundamental concepts of category theory. Originally crafted as lecture notes for an undergraduate course, it has been developed to be equally well-suited for individuals pursuing self-study. Most crucially, it deliberately caters to those who are new to category theory, not requiring readers to have a background in pure mathematics, but only a basic understanding of linear algebra.

This book presents fixed point theory, one of the crucial tools in applied mathematics, functional analysis, and topology, which has been used to solve distinct real-world problems in computer science, engineering, and physics. The authors begin with an overview of the extension of metric spaces. Readers are introduced to general fixed-point theorems while comparing and contrasting important and insignificant metric spaces. The book is intended to be self-contained and serves as a unique resource for researchers in various disciplines.

Vector Quantization, a pioneering discretization method based on nearest neighbor search, emerged in the 1950s primarily in signal processing, electrical engineering, and information theory. Later in the 1960s, it evolved into an automatic classification technique for generating prototypes of extensive datasets. In modern terms, it can be recognized as a seminal contribution to unsupervised learning through the k-means clustering algorithm in data science.In contrast, Functional Quantization, a more recent area of study dating back to the early 2000s, focuses on the quantization of continuous-time stochastic processes viewed as random vectors in Banach function spaces. This book distinguishes itself by delving into the quantization of random vectors with values in a Banach space¿a unique feature of its content. Its main objectives are twofold: first, to offer a comprehensive and cohesive overview of the latest developments as well as several new results in optimal quantization theory, spanning both finite and infinite dimensions, building upon the advancements detailed in Graf and Luschgy's Lecture Notes volume. Secondly, it serves to demonstrate how optimal quantization can be employed as a space discretization method within probability theory and numerical probability, particularly in fields like quantitative finance. The main applications to numerical probability are the controlled approximation of regular and conditional expectations by quantization-based cubature formulas, with applications to time-space discretization of Markov processes, typically Brownian diffusions, by quantization trees.While primarily catering to mathematicians specializing in probability theory and numerical probability, this monograph also holds relevance for data scientists, electrical engineers involved in data transmission, and professionals in economics and logistics who are intrigued by optimal allocation problems.

This revised book provides an accessible presentation of concepts from probability theory, statistical methods, the design of experiments, and statistical quality control. It is shaped by the experience of the two teachers teaching statistical methods and concepts to engineering students. Practical examples and end-of-chapter exercises are the highlights of the text, as they are purposely selected from different fields. Statistical principles discussed in the book have a great relevance in several disciplines like economics, commerce, engineering, medicine, health care, agriculture, biochemistry, and textiles to mention a few.Organised into 16 chapters, the revised book discusses four major topics¿probability theory, statistical methods, the design of experiments, and statistical quality control. A large number of students with varied disciplinary backgrounds need a course in basics of statistics, the design of experiments and statistical quality control at an introductory level to pursue their discipline of interest. No previous knowledge of probability or statistics is assumed, but an understanding of calculus is a prerequisite. The whole book also serves as a master level introductory course in all the three topics, as required in textile engineering or industrial engineering.

This book provides an introduction to classical celestial mechanics. It is based on lectures delivered by the authors over many years at both Padua University (MC) and V.N. Karazin Kharkiv National University (EB). The book aims to provide a mathematical description of the gravitational interaction of celestial bodies. The approach to the problem is purely formal. It allows the authors to write equations of motion and solve them to the greatest degree possible, either exactly or by approximate techniques, when there is no other way. The results obtained provide predictions that can be compared with the observations. Five chapters are supplemented by appendices that review certain mathematical tools, deepen some questions (so as not to interrupt the logic of the mainframe with heavy technicalities), give some examples, and provide an overview of special functions useful here, as well as in many other fields of physics. The authors also present the original investigation of torus potential. This book is aimed at senior undergraduate students of physics or astrophysics, as well as graduate students undertaking a master's degree or Ph.D.

Computation and Modeling for Fractional Order Systems provides readers with problem-solving techniques for obtaining exact and/or approximate solutions of governing equations arising in fractional dynamical systems presented using various analytical, semi-analytical, and numerical methods. Various analytical/semi-analytical/numerical methods are applied for solving real-life fractional order problems. The comprehensive descriptions of different recently developed fractional singular, non-singular, fractal-fractional, and discrete fractional operators, along with computationally efficient methods, are included for the reader to understand how these may be applied to real-world systems, and a wide variety of dynamical systems such as deterministic, stochastic, continuous, and discrete are addressed. Fractional calculus has gained increasing popularity and relevance over the last few decades, due to its well-established applications in various fields of science and engineering. It deals with the differential and integral operators with non-integral powers. Fractional differential equations are the pillar of various systems occurring in a wide range of science and engineering disciplines, namely physics, chemical engineering, mathematical biology, financial mathematics, structural mechanics, control theory, circuit analysis, and biomechanics, among others.

The volume includes a collection of peer-reviewed contributions from among those presented at the FNE, the main conference organized every two years by the Mexican Statistical Society (AME), and the 2020 AME Virtual Meeting. Statistical research in Latin America is prolific and research networks span both within and outside the region. As much of the work is typically carried out and published in Spanish, a large portion of the interested public is denied access to interesting findings, and the goal of this volume is therefore to provide access to selected works from Mexican collaborators and their international research networks to a wider audience. It may be especially attractive to academics interested in the latest methodological advances, while professionals from other disciplines may also find value in these new tools for data analysis. In 2021, the conference broadly focused on the interdisciplinary aspects of Statistics.

This book describes a new strategy for rehabilitation from injury and/or disease using Crucial Event Therapy. Recent studies have shown that individuals can recuperate more rapidly from surgery and other invasive procedures intended to correct the negative effects of disease or injury through the use of life support systems that operate at the body's natural biofrequencies. The same observation has been clinically shown to reverse the degenerative effects of neurodegenerative diseases such as Parkinson¿s and Alzheimer's Disease.Crucial Event Therapy describes medicine as the operational control of the functions of the human body treated as a network-of-networks, with 1/f-variable crucial events coding the dynamic states of health and disease through information flow within a network and information exchange between biomedical networks. A new way of thinking based on the statistics of Cortical Events is presented and the relevant literature is suitably referenced. This is anideal book for biophysicists and data scientists seeking to understand the connection of complexity measures for the study of consciousness with the clinical aspects of designing a rehabilitation strategy.

This book presents a selection of peer-reviewed contributions to the fifth Bayesian Young Statisticians Meeting, BaYSM 2021, held virtually due to the COVID-19 pandemic on 1-3 September 2021. Despite all the challenges of an online conference, the meeting provided a valuable opportunity for early career researchers, including MSc students, PhD students, and postdocs to connect with the broader Bayesian community.The proceedings highlight many different topics in Bayesian statistics, presenting promising methodological approaches to address important challenges in a variety of applications. The book is intended for a broad audience of people interested in statistics, and provides a series of stimulating contributions on theoretical, methodological, and computational aspects of Bayesian statistics.

This book explains the basic theory of Hilbert C*-module in detail, covering a wide range of applications from generalized index to module framework. At the center of the book, the Beurling-Deny criterion is characterized between operator valued Dirichlet forms and quantum Markov semigroups, hence opening a new field of quantum probability research. The general scope of the book includes: basic theory of Hilbert C*-modules; generalized indices and module frames; operator valued Dirichlet forms; and quantum Markov semigroups.This book will be of value to scholars and graduate students in the fields of operator algebra, quantum probability and quantum information.

This book gathers peer-reviewed contributions submitted to the 21st European Conference on Mathematics for Industry, ECMI 2021, which was virtually held online, hosted by the University of Wuppertal, Germany, from April 13th to April 15th, 2021. The works explore mathematics in a wide variety of applications, ranging from problems in electronics, energy and the environment, to mechanics and mechatronics. Topics covered include: Applied Physics, Biology and Medicine, Cybersecurity, Data Science, Economics, Finance and Insurance, Energy, Production Systems, Social Challenges, and Vehicles and Transportation.The goal of the European Consortium for Mathematics in Industry (ECMI) conference series is to promote interaction between academia and industry, leading to innovations in both fields. These events have attracted leading experts from business, science and academia, and have promoted the application of novel mathematical technologies to industry. They have also encouraged industrial sectors to share challenging problems where mathematicians can provide fresh insights and perspectives. Lastly, the ECMI conferences are one of the main forums in which significant advances in industrial mathematics are presented, bringing together prominent figures from business, science and academia to promote the use of innovative mathematics in industry.

This book discusses state-of-the-art stochastic optimization algorithms for distributed machine learning and analyzes their convergence speed. The book first introduces stochastic gradient descent (SGD) and its distributed version, synchronous SGD, where the task of computing gradients is divided across several worker nodes. The author discusses several algorithms that improve the scalability and communication efficiency of synchronous SGD, such as asynchronous SGD, local-update SGD, quantized and sparsified SGD, and decentralized SGD. For each of these algorithms, the book analyzes its error versus iterations convergence, and the runtime spent per iteration. The author shows that each of these strategies to reduce communication or synchronization delays encounters a fundamental trade-off between error and runtime.

In der Diskussion über Sprache in Bildungskontexten geht man davon aus, dass diese sogenannte ¿Bildungssprache¿ durch verschiedene grammatische und lexikalische Merkmale charakterisiert wird. Häufig wird außerdem angenommen, dass diese Merkmale für Schüler/-innen ¿ unter anderem und insbesondere solchen, die Deutsch als Zweitsprache erlernen ¿ schwierig und damit eine Hürde für erfolgreiches fachliches Lernen sein könnten. Der Band widmet sich in einer Reihe von Einzelstudien möglichen Zugängen zur empirischen Überprüfung dieser Annahmen.

Arbeitsbuch Stochastik (Einführung und Grundzüge der Maßtheorie)Dieses Arbeitsbuch enthält die Aufgaben, Hinweise, Lösungen und Lösungswege der Kapitel 2 bis 8 des Lehrbuchs Stochastik: Eine Einführung mit Grundzügen der Maßtheorie. Durch die Offenlegung der Lösungswege und der Lösungen ist das Werk bestens geeignet zum Selbststudium, zur Vorlesungsbegleitung und als Prüfungsvorbereitung.Das Werk umfasst mehr als 330 Übungsaufgaben, die in Verständnisfragen, Beweisaufgaben und Rechenaufgaben gegliedert sind, und ist in der vorliegenden zweiten Auflage auf die zweite Auflage des Hauptwerks angepasst.

This textbook provides a comprehensive overview of noncooperative and cooperative dynamic games involving uncertain parameter values, with the stochastic process being described by an event tree. Primarily intended for graduate students of economics, management science and engineering, the book is self-contained, as it defines and illustrates all relevant concepts originally introduced in static games before extending them to a dynamic framework. It subsequently addresses the sustainability of cooperative contracts over time and introduces a range of mechanisms to help avoid such agreements breaking down before reaching maturity. To illustrate the concepts discussed, the book provides various examples of how dynamic games played over event trees can be applied to environmental economics, management science, and engineering.

This book presents a new approach to computational musicology in which music becomes a computational entity based on human cognition, allowing us to calculate music like numbers. Does music have semantics? Can the meaning of music be revealed using symbols and described using language? The authors seek to answer these questions in order to reveal the essence of music. Chapter 1 addresses a very fundamental point, the meaning of music, while referring to semiotics, gestalt, Schenkerian analysis and cognitive reality. Chapter 2 considers why the 12-tone equal temperament came to be prevalent. This chapter serves as an introduction to the mathematical definition of harmony, which concerns the ratios of frequency in tonic waves. Chapter 3, "e;Music and Language,"e; explains the fundamentals of grammar theory and the compositionality principle, which states that the semantics of a sentence can be composed in parallel to its syntactic structure. In turn, Chapter 4 explains the most prevalent score notation - the Berklee method, which originated at the Berklee School of Music in Boston - from a different point of view, namely, symbolic computation based on music theory. Chapters 5 and 6 introduce readers to two important theories, the implication-realization model and generative theory of tonal music (GTTM), and explain the essence of these theories, also from a computational standpoint. The authors seek to reinterpret these theories, aiming at their formalization and implementation on a computer. Chapter 7 presents the outcomes of this attempt, describing the framework that the authors have developed, in which music is formalized and becomes computable. Chapters 8 and 9 are devoted to GTTM analyzers and the applications of GTTM. Lastly, Chapter 10 discusses the future of music in connection with computation and artificial intelligence.This book is intended both for general readers who are interested in music, and scientists whose research focuses on music information processing. In order to make the content as accessible as possible, each chapter is self-contained.

This book is devoted to the study of multivariate discrete q-distributions, which is greatly facilitated by existing multivariate q-sequences and q-functions. Classical multivariate discrete distributions are defined on a sequence of independent and identically distributed Bernoulli trials, with either being a success of a certain rank (level) or a failure. The author relaxes the assumption that the probability of success of a trial is constant by assuming that it varies geometrically with the number of trials and/or the number of successes. The latter is advantageous in the sense that it permits incorporating the experience gained from the previous trials and/or successes, which leads to multivariate discrete q-distributions. Furthermore, q-multinomial and negative q-multinomial formulae are obtained. Next, the book addresses q-multinomial and negative q-multinomial distributions of the first and second kind. The author also examines multiple q-Polya urn model, multivariate q-Polya and inverse q-Polya distributions. Presents definitions and theorems that highlight key concepts and worked examples to illustrate the various applicationsContains numerous exercises at varying levels of difficulty that consolidate the presented concepts and resultsIncludes hints and answers to all exercises via the appendix and is supplemented with an Instructor's Solution Manual

This book explores certain social and environmental drivers of sustainable economic growth for European Union countries (EU-27) and United Kingdom (UK) in the context of the UN 2030 Agenda for Sustainable Development. The author provides a comprehensive overview of the factors that impact and facilitate sustainable economic growth and discusses the complex set of factors involved in sustainable economic development. Special attention is given to quantitative frameworks and empirical modelling, with the main focus on panel data regression models and vector error correction model approach. Furthermore, the book develops ratings of sustainable economic growth for each of the explored countries, by employing data mining techniques such as principal component analysis. Also, the data envelopment analysis non-parametric methodology towards assessing sustainable economic growth is investigated, as well as the cluster analysis in order to classify the selected nations according to sustainable economic growth. The book appeals to policy-makers and academics targeting to learn more about the characteristics of sustainable economic growth.

This book goes into a detailed investigation of adapting artificial neural network (ANN) and structural equation modeling (SEM) techniques in marketing and consumer research. The aim of using a dual-stage SEM and ANN approach is to obtain linear and non-compensated relationships because the ANN method captures non-compensated relationships based on the black box technology of artificial intelligence. Hence, the ANN approach validates the results of the SEM method. In addition, such the novel emerging approach increases the validity of the prediction by determining the importance of the variables. Consequently, the number of studies using SEM-ANN has increased, but the different types of study cases that show customization of different processes in ANNs method combination with SEM are still unknown, and this aspect will be affecting to the generation results. Thus, there is a need for further investigation in marketing and consumer research. This book bridges the significant gap in this research area. The adoption of SEM and ANN techniques in social commerce and consumer research is massive all over the world. Such an expansion has generated more need to learn how to capture linear and non-compensatory relationships in such area. This book would be a valuable reading companion mainly for business and management students in higher academic organizations, professionals, policy-makers, and planners in the field of marketing. This book would also be appreciated by researchers who are keenly interested in social commerce and consumer research.

Based on over 15 years¿ experience in the design and delivery of successful first-year courses, this book equips undergraduates with the mathematical skills required for degree courses in economics, finance, management, and business studies. The book starts with a summary of basic skills and takes its readers as far as constrained optimisation helping them to become confident and competent in the use of mathematical tools and techniques that can be applied to a range of problems in economics and finance.Designed as both a course text and a handbook, the book assumes little prior mathematical knowledge beyond elementary algebra and is therefore suitable for students returning to mathematics after a long break. The fundamental ideas are described in the simplest mathematical terms, highlighting threads of common mathematical theory in the various topics.Features of the book include:a systematic approach: ideas are touched upon, introduced gradually and thenconsolidated through the use of illustrative examples;several entry points to accommodate differing mathematical backgrounds; numerous problems, with full solutions, and exercises to illustrate the theory and applications; key learning objectives and self-assessment questions provided for each chapter; full solutions to exercises, available to lecturers via the Springer Nature Extramaterial - Lecturer Material website. Vass Mavron is Emeritus Professor of Mathematics at Aberystwyth University. Tim Phillips is Professor of Applied Mathematics in the School of Mathematics at Cardiff University.

This third volume of the book series shows R-calculus is a Gentzen-typed deduction system which is non-monotonic, and is a concrete belief revision operator which is proved to satisfy the AGM postulates and the DP postulates. In this book, R-calculus is taken as Tableau-based/sequent-based/multisequent-based to preserve the satisfiability of the Theory/sequent/multisequent to revise, or sequent-based, to preserve the satisfiability of the sequent to revise. The R-calculi for Post and three-valued logic is given.  This book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners in the field of logic. 

This book is the first comprehensive guide to logic-based Benders decomposition (LBBD), a general and versatile method for breaking large, complex optimization problems into components that are small enough for practical solution. The author introduces logic-based Benders decomposition for optimization, which substantially generalizes the classical Benders method. It can reduce solution times by orders of magnitude and allows decomposition to be applied to a much wider variety of optimization problems. On the theoretical side, this book provides a full account of inference duality concepts that underlie LBBD, as well as a description of how LBBD can be combined with stochastic and robust optimization, heuristic methods, and decision diagrams. It also clarifies the connection between LBBD and combinatorial Benders cuts for mixed integer programming. On the practical side, it explains how LBBD has been applied to a rapidly growingvariety of problem domains. After describing basic theory, this book provides a comprehensive review of the rapidly growing literature that describes these applications, in each case explaining how LBBD is adapted to the problem at hand. In doing so this work provides a sourcebook of ideas for applying LBBD to new problems as they arise.

This book provides a comprehensive introduction to the foundations and frontiers of graph neural networks. In addition, the book introduces the basic concepts and definitions in graph representation learning and discusses the development of advanced graph representation learning methods with a focus on graph neural networks. The book providers researchers and practitioners with an understanding of the fundamental issues as well as a launch point for discussing the latest trends in the science. The authors emphasize several frontier aspects of graph neural networks and utilize graph data to describe pairwise relations for real-world data from many different domains, including social science, chemistry, and biology. Several frontiers of graph neural networks are introduced, which enable readers to acquire the needed techniques of advances in graph neural networks via theoretical models and real-world applications. 

Dieses Buch veranschaulicht zentrale mathematische Aspekte des Goldenen Schnittes: Es geht insbesondere auf geometrische und zahlentheoretische Zusammenhänge und Beispiele ein und macht weiterführende Betrachtungen und Verallgemeinerungen zugänglich.Das Buch richtet sich primär an Studierende, Schülerinnen und Schüler, Mathematiklehrpersonen und interessierte Laien. Es ist modular aufgebaut, so dass die einzelnen Kapitel unabhängig voneinander lesbar sind. Die Lektüre soll zu eigenen geometrischen Aktivitäten anregen. Dazu werden auch Tipps und Verfahrenshinweise aus dem handwerklich-kreativen Bereich gegeben.Ergänzende Animationen sind mit der SN More Media App abrufbar: einfach die SN More Media App kostenfrei herunterladen, ein Bild oder einen Link mit dem Play-Button scannen und sofort die Animation auf Smartphone oder Tablet ausspielen.

The book constitutes an introduction to stochastic calculus, stochastic differential equations and related topics such as Malliavin calculus. On the other hand it focuses on the techniques of stochastic integration and calculus via regularization initiated by the authors. The definitions relies on a smoothing procedure  of the integrator process, they generalize the usual Ito and Stratonovich integrals for Brownian motion but the integrator could also not be a semimartingale and the integrand is allowed to be anticipating. The resulting calculus requires a simple formalism: nevertheless it entails pathwise techniques even though it takes into account randomness.  It allows connecting different types of pathwise and non pathwise integrals such as Young, fractional, Skorohod integrals, enlargement of filtration and rough paths. The covariation, but also high order variations, play a fundamental role in the calculus via regularization, which can also be applied for irregular integrators. A large class of Gaussian processes, various generalizations of semimartingales such that Dirichlet and weak Dirichlet processes are revisited. Stochastic calculus via regularization has been successfully used in applications, for instance in robust finance and on modeling vortex filaments in turbulence. The book is addressed to PhD students and researchers in stochastic analysis and applications to various fields.

This book gathers contributions from the fourth edition of the Conference on "e;Philosophy and Theory of Artificial Intelligence"e; (PT-AI), held on 27-28th of September 2021 at Chalmers University of Technology, in Gothenburg, Sweden. It covers topics at the interface between philosophy, cognitive science, ethics and computing. It discusses advanced theories fostering the understanding of human cognition, human autonomy, dignity and morality, and the development of corresponding artificial cognitive structures, analyzing important aspects of the relationship between humans and AI systems, including the ethics of AI. This book offers a thought-provoking snapshot of what is currently going on, and what are the main challenges, in the multidisciplinary field of the philosophy of artificial intelligence. 

Die 3., ergänzte Auflage stellt auf breiter fachlicher Ebene einfache elementare zahlentheoretische Inhalte vor sowie Stoffkomplexe aus der analytischen und algebraischen Zahlentheorie. Das Lehrbuch bietet auf überschaubaren mathematischen Niveau einen leicht verständlichen Einstieg in ausgewählte Themen der Zahlentheorie und beschreibt aktuelle Forschungsergebnisse zum RSA-Algorithmus. Sämtliche Kapitel enthalten umfassende Beispiele, Übungsaufgaben mit Lösungen und ausführlich durchgerechnete Beweise, so dass es sich sehr gut zur Prüfungsvorbereitung eignet.

Das vorliegende Buch analysiert den zukünftigen Temperaturverlauf der Erdoberfläche mithilfe eines naturwissenschaftlichen Modells und gibt eine Übersicht über die Ursachen und Auswirkungen des Klimawandels. Der Inhalt umfasst außerdem relevante Daten und Fakten zu den Themen Kohlenstoffbudget, Demographie, Gletscher, Permafrost, Artenvielfalt, Mobilität und Extremwetter. Die rasche globale Reduzierung des CO2-Anstiegs auf Netto-Null ist eine dringende Notwendigkeit, um nachfolgenden Generationen ein menschenwürdiges Leben zu ermöglichen. Die Industriestaaten tragen als Hauptverursacher eine moralische Verantwortung, die erwähnte Reduzierung zügig umzusetzen und die Entwicklungsländer in diesem Prozess zu unterstützen. Das Buch richtet sich auch an Personen mit wenig Bezug zur Mathematik.Die Produktfamilie WissensExpress bietet Ihnen Lehr- und Lernbücher in kompakter Form. Die Bücher liefern schnell und verständlich fundiertes Wissen.