Anvendt matematik

This thesis deals with storage systems that are organized in last-in-first-out stacks. This approach for storing items is common, for example, in container terminals, and is therefore of great practical interest as well as high relevance in the literature. Furthermore, optimization problems that may arise in this context are presented and addressed by developing novel mathematical model formulations and customized solution methods.

This book publishes select papers presented at the 4th International Conference on Frontiers in Industrial and Applied Mathematics (FIAM-2021), held at the Sant Longowal Institute of Engineering and Technology, Longowal, Punjab, India, from 21¿22 December 2021. Most of the papers deal with mathematical theory embedded with its applications to engineering and sciences. This book illustrates numerical simulation of scientific problems and the state-of-the-art research in industrial and applied mathematics, including various computational and modeling techniques with case studies and concrete examples. Graduate students and researchers, who are interested in real applications of mathematics in the areas of computational and theoretical fluid dynamics, solid mechanics, optimization and operations research, numerical analysis, bio-mathematics, fuzzy, control and systems theory, dynamical systems and nonlinear analysis, algebra and approximation theory, will find the book useful.

Petri nets model concurrent and distributed systems where active components communicate through the production and absorption of various kinds of resources. Although the dynamic properties of such systems may be very complex, they may sometimes be connected to the static structure of a Petri net. Many properties are decidable, but their complexity may be huge. It is often opportune to restrict oneself to classes of systems, to partial algorithms, and to similar but simpler properties. Instead of analysing a given system, it is also possible to search for a system satisfying some desired properties by construction. This comprehensive textbook/reference presents and discusses these issues in-depth in the context of one of the most fundamental Petri net models, called place/transition nets. The presentation is fortified by means of many examples and worked exercises. Among topics addressed: ¿ In which order may actions may be generated and scheduled? ¿ What states and configurations may be reached in a concurrent system? ¿ Which interesting classes of systems can be analysed relatively efficiently? ¿ Is it possible to synthesise a system of some class from its behaviour? ¿ How can systems be represented algebraically, compositionally, and concisely? This unique text, based on introductory as well as on advanced courses on distributed systems, will serve as an invaluable guide for students and (future) researchers interested in theoretical¿as well as in practical¿aspects of Petri nets and related system models. Eike Best has been a full professor (now retired) affiliated to Carl von Ossietzky Universität Oldenburg, Germany. Raymond Devillers has been a full professor (now retired) affiliated to Université Libre de Bruxelles, Belgium. The authors have a long record as collaborators in the fields of Petri nets and the semantics of concurrency.

This textbook introduces quantitative methods in operations management, based on operational research. Written for undergraduate and graduate students as well as practitioners, this book serves as a valuable compendium of essential tools for project planning, control, and strategic decision-making.Drawing from the expertise of both experienced scientists and seasoned practical managers, the descriptions of each tool are a harmonious blend of theoretical insights and real-world applicability. With a focus on accessibility, the authors have thoughtfully combined abstract concepts with easy-to-follow examples and detailed case studies.Readers will benefit from the abundance of well-explained recommendations and practical problem-solving approaches, where the book offers guidance on how to solve presented issues by using commercial software. Whether one seeks to refine project management, optimize operations, or make strategic choices, this book equips readers with theknowledge and proficiency required to excel in the dynamic field of operations management.

These are the proceedings of the 27th International Conference on Domain Decomposition Methods in Science and Engineering, which was held in Prague, Czech Republic, in July 2022.Domain decomposition methods are iterative methods for solving the often very large systems of equations that arise when engineering problems are discretized, frequently using finite elements or other modern techniques. These methods are specifically designed to make effective use of massively parallel, high-performance computing systems.The book presents both theoretical and computational advances in this domain, reflecting the state of art in 2022.

This book focuses on Krylov subspace methods for solving linear systems, which are known as one of the top 10 algorithms in the twentieth century, such as Fast Fourier Transform and Quick Sort (SIAM News, 2000). Theoretical aspects of Krylov subspace methods developed in the twentieth century are explained and derived in a concise and unified way. Furthermore, some Krylov subspace methods in the twenty-first century are described in detail, such as the COCR method for complex symmetric linear systems, the BiCR method, and the IDR(s) method for non-Hermitian linear systems.The strength of the book is not only in describing principles of Krylov subspace methods but in providing a variety of applications: shifted linear systems and matrix functions from the theoretical point of view, as well as partial differential equations, computational physics, computational particle physics, optimizations, and machine learning from a practical point of view.The book is self-contained in that basic necessary concepts of numerical linear algebra are explained, making it suitable for senior undergraduates, postgraduates, and researchers in mathematics, engineering, and computational science. Readers will find it a useful resource for understanding the principles and properties of Krylov subspace methods and correctly using those methods for solving problems in the future.

This book is an introduction to machine learning, with a strong focus on the mathematics behind the standard algorithms and techniques in the field, aimed at senior undergraduates and early graduate students of Mathematics. There is a focus on well-known supervised machine learning algorithms, detailing the existing theory to provide some theoretical guarantees, featuring intuitive proofs and exposition of the material in a concise and precise manner. A broad set of topics is covered, giving an overview of the field. A summary of the topics covered is: statistical learning theory, approximation theory, linear models, kernel methods, Gaussian processes, deep neural networks, ensemble methods and unsupervised learning techniques, such as clustering and dimensionality reduction. This book is suited for students who are interested in entering the field, by preparing them to master the standard tools in Machine Learning. The reader will be equipped to understand the main theoretical questions of the current research and to engage with the field.

Statistik und Wahrscheinlichkeit ¿ leicht gemachtist ein Lehr- und Nachschlagewerkfür Schule, Studium und Beruf.Das Buch ist zum Selbststudium geeignet.Alle wichtigen Begriffe, Regeln und Methodenwerden in verständlicher Form dargestellt,in Handlungsanweisungen übertragen undan Beispielen erläutertJedes Kapitel derDatenanalyseStatistikRegressionKombinatorikWahrscheinlichkeitDichte- und VerteilungsfunktionenTestkonzeptionHypothesentestsBayes-Statistikwird durch Übungsaufgaben mitvollständigem Lösungsweg komplettiert.

Unlock the secrets of the universe with Schrödinger Equation - Fundamental Aspects and Potential Applications. Delve into the heart of quantum mechanics, where matter, energy, and mathematics intertwine in a dance of profound discovery. This essential volume introduces you to the spectral theory of the Schrödinger equation, offering a sturdy foundation to explore its enigmatic depths. Discover the fascinating world of scattering theory, unraveling the intricacies of quantum interactions, while the principles of quantization and Feynman path integrals reveal the mechanics of quantum systems. With a fresh perspective, we explore relative entropy methods and transformation theory, unveiling their significance in crafting singular diffusion processes akin to Schrödinger equations. This well-organized and accessible book caters to a diverse audience, from students and researchers to professionals in functional analysis, probability theory, and quantum dynamics. Within these pages, yoüll uncover the profound wonders of the Schrödinger equation and its vast potential in science, engineering, and technology. Embark on a journey through the quantum cosmos and let your understanding of the universe expand as you explore the quantum realm. Welcome to a world where matter and energy dance to the tune of Schrödinger¿s equation, a world filled with infinite possibilities and extraordinary insights.

Sequences and the de Bruijn Graph: Properties, Constructions, and Applications explores the foundations of theoretical mathematical concepts and their important applications to computer science, electrical engineering, and bioinformatics. The book introduces the various concepts, ideas, and techniques associated with the use of the de Bruijn Graph, providing comprehensive coverage of sequence classification, one-dimensional and two-dimensional properties, constructions, and interconnection networks. This book is suitable for researchers, graduate students, professors, and professionals working in the fields of applied mathematics, electrical engineering, computer science, and bioinformatics. The de Bruijn graph was defined in 1946 to enumerate the number of closed sequences where each n-tuple appears exactly once as a window in a sequence. Through the years, the graph and its sequences have found numerous applications - in space technology, wireless communication, cryptography, parallel computation, genome assembly, DNA storage, and microbiome research, among others.

This book presents a new way of thinking about quantum mechanics and machine learning by merging the two. Quantum mechanics and machine learning may seem theoretically disparate, but their link becomes clear through the density matrix operator which can be readily approximated by neural network models, permitting a formulation of quantum physics in which physical observables can be computed via neural networks. As well as demonstrating the natural affinity of quantum physics and machine learning, this viewpoint opens rich possibilities in terms of computation, efficient hardware, and scalability. One can also obtain trainable models to optimize applications and fine-tune theories, such as approximation of the ground state in many body systems, and boosting quantum circuits¿ performance. The book begins with the introduction of programming tools and basic concepts of machine learning, with necessary background material from quantum mechanics and quantum information also provided. This enables the basic building blocks, neural network models for vacuum states, to be introduced. The highlights that follow include: non-classical state representations, with squeezers and beam splitters used to implement the primary layers for quantum computing; boson sampling with neural network models; an overview of available quantum computing platforms, their models, and their programming; and neural network models as a variational ansatz for many-body Hamiltonian ground states with applications to Ising machines and solitons. The book emphasizes coding, with many open source examples in Python and TensorFlow, while MATLAB and Mathematica routines clarify and validate proofs. This book is essential reading for graduate students and researchers who want to develop both the requisite physics and coding knowledge to understand the rich interplay of quantum mechanics and machine learning.

Dive into Stellar Mastery: Uncover the Universe's Secrets with Revolutionary Mathematical Insights.Are you captivated by the vastness of our universe? Intrigued by the patterns and phenomena that govern our skies? Brace yourself for a groundbreaking expedition that delves deep into the heart of celestial dynamics. This work is more than just a book-it's an invitation to explore a world where traditional norms are challenged, and innovative perspectives are celebrated. Astronomer amateurs and undergrad students alike will find themselves enthralled by the methodical dissection of long-established methodologies. By sidestepping the widely accepted 'stellar constant', this work introduces readers to a fresh, unparalleled approach to understanding the universe's harmonious rhythm.Discover the intricate dance between solar mass and solar radius. Revel in the beauty of their interdependent relationship and its pivotal role in demarcating circumstellar habitable zones across an array of stellar hosts. And as if this intellectual voyage wasn't fascinating enough, the book illuminates the significance of surface temperature-a critical variable long overlooked in these pivotal calculations. Towards its finale, readers are treated to a captivating discourse, a juxtaposition of unique conversions and Newton's famed equation on orbital periods. This masterful blend crafts an algorithm that, for the first time, offers an indirect route to discern a star system's solar mass, presenting a fresh perspective on celestial mechanics. For the curious minds and those unafraid to challenge the status quo, this work is a beacon of innovation and discovery. Whether you're a seasoned astronomer, an undergrad in pursuit of knowledge, or simply a seeker of the universe's truths, this book promises an enthralling journey of astronomical revelations. Step into a realm where stars align in patterns yet uncharted. Dive deep, look up, and let the universe unveil its secrets.

This book provides a systematic presentation of the major results in the field of the theory of k-out-of-n systems obtained in recent years and their applications for the reliability assessment of high-altitude unmanned platforms. Mathematical models, methods, and algorithms, presented in the book, will make a significant contribution to the development of reliability theory and the theoretical foundations of unmanned UAV-based aerial communications networks in the framework of the concept of creating the 5G and beyond networks. The book gives a description of new mathematical methods and approaches (based on decomposable semi-regenerative processes, simulation and machine learning methods, and inventory models) to the study of the complex k-out-of-n systems, which makes it possible to carry out numerical calculations of reliability indicators. Organized into five chapters, each chapter begins with a summary of the main definitions andresults contained in the chapter. The content of this book is based on the original results developed by the authors, many of which appear for the first time in book form.

Large numbers of studies of the KdV equation have appeared since the pioneering paper by Gardner, Greene, Kruskal, and Miura in 1967. Most of those works have employed the inverse spectral method for 1D Schrödinger operators or an advanced Fourier analysis. Although algebraic approaches have been discovered by HirotäSato and Marchenko independently, those have not been fully investigated and analyzed. The present book offers a new approach to the study of the KdV equation, which treats decaying initial data and oscillating data in a unified manner. The author¿s method is to represent the tau functions introduced by HirotäSato and developed by Segal¿Wilson later in terms of the Weyl¿Titchmarsh functions (WT functions, in short) for the underlying Schrödinger operators. The main result is stated by a class of WT functions satisfying some of the asymptotic behavior along a curve approaching the spectrum of the Schrödinger operators at +¿ in an order of -(n-1/2)for the nth KdV equation. This class contains many oscillating potentials (initial data) as well as decaying ones. Especially bounded smooth ergodic potentials are included, and under certain conditions on the potentials, the associated Schrödinger operators have dense point spectrum. This provides a mathematical foundation for the study of the soliton turbulence problem initiated by Zakharov, which was the author¿s motivation for extending the class of initial data in this book. A large class of almost periodic potentials is also included in these ergodic potentials. P. Deift has conjectured that any solutions to the KdV equation starting from nearly periodic initial data are almost periodic in time. Therefore, our result yields a foundation for this conjecture. For the reader¿s benefit, the author has included here (1) a basic knowledge of direct and inverse spectral problem for 1D Schrödinger operators, including the notion of the WT functions; (2)Satös Grassmann manifold method revised by Segal¿Wilson; and (3) basic results of ergodic Schrödinger operators.

This concise and rigorous textbook introduces students to continuum thermodynamics, combining a complete treatment of the subject with practical applications to material modelling. It presents mathematical prerequisites and the foundations of continuum mechanics, then introduces more advanced topics such as theories for the investigation of material models. Taking the student step-by-step through the subject, it allows full understanding of the theory and how it relates to real-world practical applications. Packed with examples and illustrations to describe complex concepts and mathematical derivations, and including end-of-chapter problems with helpful hints, this is the ideal, accessible introduction to continuum thermodynamics for senior undergraduate and graduate students in mechanical, aeronautical and civil engineering.

This book keeps an eye in the direction of applications of advanced and high performance scientific computing in describing the behavior of natural and constructed systems, e.g. chaos, bifurcation, fractal, Lyapunov exponent, period doubling, Poincaré map, strange attractor etc. With the aid of powerful computers the modem theory of chaos and its geometry, the fractals, and attractors are developed. The concepts of object oriented computing are introduced early in the text and steadily expanded as one progresses through the chapters. The beginning of each chapter is of an introductory nature, followed by practical applications, the discussion of numerical results, theoretical investigations on nonlinear stability and convergence.This is the first complete introduction to process modelling and computing that fully integrates software tools ¿ enabling professionals and students to master critical techniques hands on through computer simulations based on the popular MATLAB environment. The book offers a simple tool for all those oscillations that are travelling through the world, helping them discover its hidden beauty.Many applications as well as results of computer simulations are presented. The center of concern is set on existing as well as emerging continuous methods of investigations useful for researchers, engineers and practitioners active in many and often interdisciplinary fields, where physics, electrochemistry, biology and medicine play a key role. Coverage includes:¿ Dynamic behavior of nonlinear systems,¿ Fundamental descriptions of processes exhibiting nonlinear oscillations,¿ Mechanism and function of structures of nonlinear oscillations¿ patterns,¿ Analysis of dynamical oscillations in electric circuits and systems,¿ Artificial intelligence models of natural systems,¿ Nonlinear oscillations in chemistry, biologyand medicine,¿ Oscillations in mechanics and transport systems,¿ Oscillations in fractional-order systems,¿ Energy harvesting systems from the surrounding environment.With an insatiable appetite for exploring the surrounding world and doing research, this book can help readers quickly find ways to use new computers and facilitate the quest for greater knowledge and understanding of reality. The reach of novelty of the book ranges from new mathematical ideas to motivating questions and science issues in many subject areas.

This book contains papers presented at the 2nd International Conference on Cognitive based Information Processing and Applications (CIPA) in Changzhou, China, from September 22 to 23, 2022. The book is divided into a 2-volume series and the papers represent the various technological advancements in network information processing, graphics and image processing, medical care, machine learning, smart cities. It caters to postgraduate students, researchers, and practitioners specializing and working in the area of cognitive-inspired computing and information processing.

This book presents the best papers from the 4th International Conference on Mathematical Research for Blockchain Economy (MARBLE) 2023, held in London, UK. While most blockchain conferences and forums are dedicated to business applications, product development, or Initial Coin Offering (ICO) launches, this conference focused on the mathematics behind blockchain to bridge the gap between practice and theory.The book spans the divide between theoretical promise and practical reality in blockchain technology and explores the challenges hindering its real-world integration across diverse sectors, offering comprehensive insights into issues like scalability, security, and privacy.

This contributed volume explores innovative research in the modeling, simulation, and control of crowd dynamics. Chapter authors approach the topic from the perspectives of mathematics, physics, engineering, and psychology, providing a comprehensive overview of the work carried out in this challenging interdisciplinary research field. The volume begins with an overview of analytical problems related to crowd modeling. Attention is then given to the importance of considering the social and psychological factors that influence crowd behavior ¿ such as emotions, communication, and decision-making processes ¿ in order to create reliable models. Finally, specific features of crowd behavior are explored, including single-file traffic, passenger movement, modeling multiple groups in crowds, and the interplay between crowd dynamics and the spread of disease.Crowd Dynamics, Volume 4 is ideal for mathematicians, engineers, physicists, and other researchers working in the rapidly growing field of modeling and simulation of human crowds.