This is the first book to introduce the irrational elliptic function series, providing a theoretical treatment for the smooth and discontinuous system and opening a new branch of applied mathematics. The discovery of the smooth and discontinuous (SD) oscillator and the SD attractors discussed in this book represents a further milestone in nonlinear dynamics, following on the discovery of the Ueda attractor in 1961 and Lorenz attractor in 1963. This particular system bears significant similarities to the Duffing oscillator, exhibiting the standard dynamics governed by the hyperbolic structure associated with the stationary state of the double well. However, there is a substantial departure in nonlinear dynamics from standard dynamics at the discontinuous stage. The constructed irrational elliptic function series, which offers a way to directly approach the nature dynamics analytically for both smooth and discontinuous behaviours including the unperturbed periodic motions and the perturbed chaotic attractors without any truncation, is of particular interest. Readers will also gain a deeper understanding of the actual nonlinear phenomena by means of a simple mechanical model: the theory, methodology, and the applications in various interlinked disciplines of sciences and engineering. This book offers a valuable resource for researchers, professionals and postgraduate students in mechanical engineering, non-linear dynamics, and related areas, such as nonlinear modelling in various fields of mathematics, physics and the engineering sciences.

This textbook serves as an introduction to groups, rings, fields, vector and tensor spaces, algebras, topological spaces, differentiable manifolds and Lie groups --- mathematical structures which are foundational to modern theoretical physics. It is aimed primarily at undergraduate students in physics and mathematics with no previous background in these topics. Applications to physics --- such as the metric tensor of special relativity, the symplectic structures associated with Hamilton's equations and the Generalized Stokes's Theorem --- appear at appropriate places in the text. Worked examples, end-of-chapter problems (many with hints and some with answers) and guides to further reading make this an excellent book for self-study. Upon completing this book the reader will be well prepared to delve more deeply into advanced texts and specialized monographs in theoretical physics or mathematics.

This book introduces new models based on R-calculus and theories of belief revision for dealing with large and changing data. It extends R-calculus from first-order logic to propositional logic, description logics, modal logic and logic programming, and from minimal change semantics to subset minimal change, pseudo-subformula minimal change and deduction-based minimal change (the last two minimal changes are newly defined). And it proves soundness and completeness theorems with respect to the minimal changes in these logics. To make R-calculus computable, an approximate R-calculus is given which uses finite injury priority method in recursion theory. Moreover, two applications of R-calculus are given to default theory and semantic inheritance networks. This book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners in the field of logic. Also it is very useful for all those who are interested in data, digitization and correctness and consistency of information, in modal logics, non monotonic logics, decidable/undecidable logics, logic programming, description logics, default logics and semantic inheritance networks.

This book presents the best papers from the 2nd International Conference on Mathematical Research for Blockchain Economy (MARBLE) 2020, held in Vilamoura, Portugal. 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. Blockchain Technology has been considered as the most fundamental and revolutionising invention since the Internet. Every year, thousands of blockchain projects are launched and circulated in the market, and there is a tremendous wealth of blockchain applications, from finance to healthcare, education, media, logistics and more. However, due to theoretical and technical barriers, most of these applications are impractical for use in a real-world business context. The papers in this book reveal the challenges and limitations, such as scalability, latency, privacy and security, and showcase solutions and developments to overcome them.

This book involves ideas/results from the topics of mathematical, information, and data sciences, in connection with the main research interests of Professor Pardo that can be summarized as Information Theory with Applications to Statistical Inference. This book is a tribute to Professor Leandro Pardo, who has chaired the Department of Statistics and OR of the Complutense University in Madrid, and he has been also President of the Spanish Society of Statistics and Operations Research. In this way, the contributions have been structured into three parts, which often overlap to a greater or lesser extent, namely Trends in Mathematical Sciences (Part I) Trends in Information Sciences (Part II) Trends in Data Sciences (Part III) The contributions gathered in this book have offered either new developments from a theoretical and/or computational and/or applied point of view, or reviews of recent literature of outstanding developments. They have been applied through nice examples in climatology, chemistry, economics, engineering, geology, health sciences, physics, pandemics, and socioeconomic indicators. Consequently, the intended audience of this book is mainly statisticians, mathematicians, computer scientists, and so on, but users of these disciplines as well as experts in the involved applications may certainly find this book a very interesting read.

This book formulates the kinematical conservation laws (KCL), analyses them and presents their applications to various problems in physics. Finally, it addresses one of the most challenging problems in fluid dynamics: finding successive positions of a curved shock front. The topics discussed are the outcome of collaborative work that was carried out mainly at the Indian Institute of Science, Bengaluru, India. The theory presented in the book is supported by referring to extensive numerical results. The book is organised into ten chapters. Chapters 1-4 offer a summary of and briefly discuss the theory of hyperbolic partial differential equations and conservation laws. Formulation of equations of a weakly nonlinear wavefront and those of a shock front are briefly explained in Chapter 5, while Chapter 6 addresses KCL theory in space of arbitrary dimensions. The remaining chapters examine various analyses and applications of KCL equations ending in the ultimate goal-propagation of a three-dimensional curved shock front and formation, propagation and interaction of kink lines on it.

This special issue collects selected contributions (excluding general lectures) of a Symposium on "Micro to MACRO Mathematical Modelling in Soil Mechanics", which took place at the University of Reggio Calabria, Italy, from May 29th to June 1st, 2018. The Symposium provided an opportunity to enhance the scientific debate on the construction of mathematical models for the description of the physical behaviour of soils, as well as on the suggestions provided by the micro-mechanical observation of the matter. The focus was on the comparison between the appropriateness of models and the need of mathematics to obtain rigorous results, which involves know-how from applied mathematical physics, geotechnical engineering and mechanics of solids. The contributions were selected by the Editors and the other Members of the Scientific Committee of the Symposium: Gianfranco Capriz (Pisa, Roma), Claudio di Prisco (Milan), Wolfgang Ehlers (Stuttgart), James T. Jenkins (Cornell), Stefan Luding (Twente), David Muir Wood (Dundee), Kenichi Soga (Berkeley).

This book presents a unified study of dynamically coupled systems involving a rigid body and an ideal fluid flow from the perspective of Lagrangian and Hamiltonian mechanics. It compiles theoretical investigations on the topic of dynamically coupled systems using a framework grounded in Kirchhoff's equations. The text achieves a balance between geometric mechanics, or the modern theories of reduction of Lagrangian and Hamiltonian systems, and classical fluid mechanics, with a special focus on the applications of these principles. Following an introduction to Kirchhoff's equations of motion, the book discusses several extensions of Kirchhoff's work, particularly related to vortices. It addresses the equations of motions of these systems and their Lagrangian and Hamiltonian formulations. The book is suitable to mathematicians, physicists and engineers with a background in Lagrangian and Hamiltonian mechanics and theoretical fluid mechanics. It includes a brief introductory overview of geometric mechanics in the appendix.

What are the principles that keep our society together? This question is even more difficult to answer than the long-standing question, what are the forces that keep our world together. However, the social challenges of humanity in the 21st century ranging from the financial crises to the impacts of globalization, require us to make fast progress in our understanding of how society works, and how our future can be managed in a resilient and sustainable way. This book can present only a few very first steps towards this ambitious goal. However, based on simple models of social interactions, one can already gain some surprising insights into the social, ``macro-level'' outcomes and dynamics that is implied by individual, ``micro-level'' interactions. Depending on the nature of these interactions, they may imply the spontaneous formation of social conventions or the birth of social cooperation, but also their sudden breakdown. This can end in deadly crowd disasters or tragedies of the commons (such as financial crises or environmental destruction). Furthermore, we demonstrate that classical modeling approaches (such as representative agent models) do not provide a sufficient understanding of the self-organization in social systems resulting from individual interactions. The consideration of randomness, spatial or network interdependencies, and nonlinear feedback effects turns out to be crucial to get fundamental insights into how social patterns and dynamics emerge. Given the explanation of sometimes counter-intuitive phenomena resulting from these features and their combination, our evolutionary modeling approach appears to be powerful and insightful. The chapters of this book range from a discussion of the modeling strategy for socio-economic systems over experimental issues up the right way of doing agent-based modeling. We furthermore discuss applications ranging from pedestrian and crowd dynamics over opinion formation, coordination, and cooperation up to conflict, and also address the response to information, issues of systemic risks in society and economics, and new approaches to manage complexity in socio-economic systems. Selected parts of this book had been previously published in peer reviewed journals.

Despite major advances in healthcare over the past century, the successful treatment of cancer has remained a significant challenge, and cancers are the second leading cause of death worldwide behind cardiovascular disease. Early detection and survival are important issues to control cancer. The development of quantitative methods and computer technology has facilitated the formation of new models in medical and biological sciences. The application of mathematical modelling in solving many real-world problems in medicine and biology has yielded fruitful results. In spite of advancements in instrumentations technology and biomedical equipment, it is not always possible to perform experiments in medicine and biology for various reasons. Thus, mathematical modelling and simulation are viewed as viable alternatives in such situations, and are discussed in this book. The conventional diagnostic techniques of cancer are not always effective as they rely on the physical and morphological appearance of the tumour. Early stage prediction and diagnosis is very difficult with conventional techniques. It is well known that cancers are involved in genome level changes. As of now, the prognosis of various types of cancer depends upon findings related to the data generated through different experiments. Several machine learning techniques exist in analysing the data of expressed genes; however, the recent results related with deep learning algorithms are more accurate and accommodative, as they are effective in selecting and classifying informative genes. This book explores the probabilistic computational deep learning model for cancer classification and prediction.

This is the first single volume monograph that systematically summarizes the recent progress in using non-Fourier heat conduction theories to deal with the multiphysical behaviour of smart materials and structures. The book contains six chapters and starts with a brief introduction to Fourier and non-Fourier heat conduction theories. Non-Fourier heat conduction theories include Cattaneo-Vernotte, dual-phase-lag (DPL), three-phase-lag (TPL), fractional phase-lag, and nonlocal phase-lag heat theories. Then, the fundamentals of thermal wave characteristics are introduced through reviewing the methods for solving non-Fourier heat conduction theories and by presenting transient heat transport in representative homogeneous and advanced heterogeneous materials. The book provides the fundamentals of smart materials and structures, including the background, application, and governing equations. In particular, functionally-graded smart structures made of piezoelectric, piezomagnetic, and magnetoelectroelastic materials are introduced as they represent the recent development in the industry. A series of uncoupled thermal stress analyses on one-dimensional structures are also included. The volume ends with coupled thermal stress analyses of one-dimensional homogenous and heterogeneous smart piezoelectric structures considering different coupled thermopiezoelectric theories. Last but not least, fracture behavior of smart structures under thermal disturbance is investigated and the authors propose directions for future research on the topic of multiphysical analysis of smart materials.

This book introduces and develops the mathematical models used to describe crane dynamics, and explores established and emerging control methods employed for industrial cranes. It opens with a general introduction to the design and structure of various crane types including gantry cranes, rotary cranes, and mobile cranes currently being used for material handling processes. Mathematical models describing their dynamics for control purposes are developed via two different modeling approaches: lumped-mass and distributed parameter models. Control strategies applicable to real industrial problems are then discussed, including open-loop control, feedback control, boundary control, and hybrid control strategies. Finally, based on the methods covered in the book, future research directions are proposed for the advancement of crane technologies. This book can be used by graduate students, engineers, and researchers in the material handling industry including those working in warehouses, manufacturing, construction sites, ship building, seaports, container terminals, nuclear power plants, and in offshore engineering.

Introduction to the Theory of Optimization in Euclidean Space is intended to provide students with a robust introduction to optimization in Euclidean space, demonstrating the theoretical aspects of the subject whilst also providing clear proofs and applications. Students are taken progressively through the development of the proofs, where they have the occasion to practice tools of differentiation (Chain rule, Taylor formula) for functions of several variables in abstract situations. Throughout this book, students will learn the necessity of referring to important results established in advanced Algebra and Analysis courses. Features Rigorous and practical, offering proofs and applications of theorems Suitable as a textbook for advanced undergraduate students on mathematics or economics courses, or as reference for graduate-level readers Introduces complex principles in a clear, illustrative fashion

This textbook deals with engineering, science, technical, legal, financial, ICT, logistics and people management topics necessary for managing engineered assets such as all man-made tools, gadgets, buildings, equipment, machines, infrastructure, large-scale physical and industrial facilities and systems which pervade all sectors of industry. By coalescing concepts, principles, practices, and practical issues from the relevant multi-disciplines, the book addresses the body of knowledge required for managing engineered assets in the 4IR and Society 5.0 era and beyond. The book is written for: Scholars and students who intend to strengthen or acquire knowledge about the concepts, principles, and practice of managing engineered assets; Managers of engineered assets in both the public and private sectors who aim to improve asset management practice for their organisational purposes and missions; Policymakers and regulators in order to improve policymaking, governance, assessment and evaluation frameworks on the management of engineered assets; The broader audience concerned about the sustainable management of engineered assets that constitute our built environment and provide the means for industry and livelihood.

This book addresses one of the most important unsolved problems in artificial intelligence: the task of learning, in an unsupervised manner, from massive quantities of spatiotemporal visual data that are available at low cost. The book covers important scientific discoveries and findings, with a focus on the latest advances in the field. Presenting a coherent structure, the book logically connects novel mathematical formulations and efficient computational solutions for a range of unsupervised learning tasks, including visual feature matching, learning and classification, object discovery, and semantic segmentation in video. The final part of the book proposes a general strategy for visual learning over several generations of student-teacher neural networks, along with a unique view on the future of unsupervised learning in real-world contexts. Offering a fresh approach to this difficult problem, several efficient, state-of-the-art unsupervised learning algorithms are reviewed in detail, complete with an analysis of their performance on various tasks, datasets, and experimental setups. By highlighting the interconnections between these methods, many seemingly diverse problems are elegantly brought together in a unified way. Serving as an invaluable guide to the computational tools and algorithms required to tackle the exciting challenges in the field, this book is a must-read for graduate students seeking a greater understanding of unsupervised learning, as well as researchers in computer vision, machine learning, robotics, and related disciplines.

Today the notion of the algorithm is familiar not only to mathematicians. It forms a conceptual base for information processing; the existence of a corresponding algorithm makes automatic information processing possible. The theory of algorithms (together with mathematical logic ) forms the the oretical basis for modern computer science (see [Sem Us 86]; this article is called "Mathematical Logic in Computer Science and Computing Practice" and in its title mathematical logic is understood in a broad sense including the theory of algorithms). However, not everyone realizes that the word "algorithm" includes a transformed toponym Khorezm. Algorithms were named after a great sci entist of medieval East, is al-Khwarizmi (where al-Khwarizmi means "from Khorezm"). He lived between c. 783 and 850 B.C. and the year 1983 was chosen to celebrate his 1200th birthday. A short biography of al-Khwarizmi compiled in the tenth century starts as follows: "al-Khwarizmi. His name is Muhammad ibn Musa, he is from Khoresm" (cited according to [Bul Rozen Ah 83, p.8]).

This book is the first one in which basic demographic models are rigorously formulated by using modern age-structured population dynamics, extended to study real-world population problems. Age structure is a crucial factor in understanding population phenomena, and the essential ideas in demography and epidemiology cannot be understood without mathematical formulation; therefore, this book gives readers a robust mathematical introduction to human population studies. In the first part of the volume, classical demographic models such as the stable population model and its linear extensions, density-dependent nonlinear models, and pair-formation models are formulated by the McKendrick partial differential equation and are analyzed from a dynamical system point of view. In the second part, mathematical models for infectious diseases spreading at the population level are examined by using nonlinear differential equations and a renewal equation. Since an epidemic can be seen as a nonlinear renewal process of an infected population, this book will provide a natural unification point of view for demography and epidemiology. The well-known epidemic threshold principle is formulated by the basic reproduction number, which is also a most important key index in demography. The author develops a universal theory of the basic reproduction number in heterogeneous environments. By introducing the host age structure, epidemic models are developed into more realistic demographic formulations, which are essentially needed to attack urgent epidemiological control problems in the real world.

In recent years the traditional subject of continuum mechanics has grown rapidly and many new techniques have emerged. This text provides a rigorous, yet accessible introduction to the basic concepts of the network approximation method and provides a unified approach for solving a wide variety of applied problems. As a unifying theme, the authors discuss in detail the transport problem in a system of bodies. They solve the problem of closely placed bodies using the new method of network approximation for PDE with discontinuous coefficients, developed in the 2000s by applied mathematicians in the USA and Russia. Intended for graduate students in applied mathematics and related fields such as physics, chemistry and engineering, the book is also a useful overview of the topic for researchers in these areas.

This volume covers many diverse topics related in varying degrees to mathematics in mind including the mathematical and topological structures of thought and communication. It examines mathematics in mind from the perspective of the spiral, cyclic and hyperlinked structures of the human mind in terms of its language, its thoughts and its various modes of communication in science, philosophy, literature and the arts including a chapter devoted to the spiral structure of the thought of Marshall McLuhan. In it, the authors examine the topological structures of hypertext, hyperlinking, and hypermedia made possible by the Internet and the hyperlinked structures that existed before its emergence. It also explores the cognitive origins of mathematical thinking of the human mind and its relation to the emergence of spoken language, and studies the emergence of mathematical notation and its impact on education. Topics addressed include: * The historical context of any topic that involves how mathematical thinking emerged, focusing on archaeological and philological evidence. * Connection between math cognition and symbolism, annotation and other semiotic processes. * Interrelationships between mathematical discovery and cultural processes, including technological systems that guide the thrust of cognitive and social evolution. * Whether mathematics is an innate faculty or forged in cultural-historical context * What, if any, structures are shared between mathematics and language

Includes over 250 solved problems to supplement graduate-level courses in fluid mechanics and turbomachinery. Enables students to practice applying key concepts of fluid mechanics and the governing conservation laws to solve real-world problems. Uses the physics-first approach, allowing for a good understanding of the problem physics and the results obtained. Covers problems on flowpath aerodynamics design. Covers problems on secondary air systems modeling of gas turbines.

This edited volume on data science features a variety of research ranging from theoretical to applied and computational topics. Aiming to establish the important connection between mathematics and data science, this book addresses cutting edge problems in predictive modeling, multi-scale representation and feature selection, statistical and topological learning, and related areas. Contributions study topics such as the hubness phenomenon in high-dimensional spaces, the use of a heuristic framework for testing the multi-manifold hypothesis for high-dimensional data, the investigation of interdisciplinary approaches to multi-dimensional obstructive sleep apnea patient data, and the inference of a dyadic measure and its simplicial geometry from binary feature data. Based on the first Women in Data Science and Mathematics (WiSDM) Research Collaboration Workshop that took place in 2017 at the Institute for Compuational and Experimental Research in Mathematics (ICERM) in Providence, Rhode Island, this volume features submissions from several of the working groups as well as contributions from the wider community. The volume is suitable for researchers in data science in industry and academia.

Modern life is increasingly relying on digital technology, which in turn runs on mathematics. However, this underlying math is hidden from us. That is mostly a good thing since we do not want to be solving equations and calculating fractions just to get things done in our everyday business. But the mathematical details do matter for anyone who wants to understand how stuff works, or wishes to create something new in the jungle of apps and algorithms. This book takes a look at the mathematical models behind weather forecasting, climate change prediction, artificial intelligence, medical imaging and computer graphics. The reader is expected to have only a curious mind; technical math skills are not needed for enjoying this text.

The book is devoted to intelligent design of structures as a novel kind of designing based on computational intelligence. The proposed methodology based on computational intelligence has some heuristic and learning attributes typical for natural intelligence. Computer models of the structures are built on the base of the finite element method (FEM), the boundary element method (BEM) or coupling of FEM and BEM. The short description of possible discrete models of structures using these methods is included in the Chapter 2. Various kinds of intelligent approaches using sequential, parallel, distributed, fuzzy and hybrid evolutionary, immune and particle swarm algorithms and neural computing are presented in Chapter 3. Different kinds of optimization such as shape, topology, size and material optimization for structures under static and dynamical mechanical and thermo-mechanical loadings, structures with cracks and composite structures are considered in Chapter 4. Multi-objective optimization for coupled problems is also taken into account. Several numerical examples illustrating these kinds of optimization are presented for 2-D (plane-stress or plane-strain, plates, shells) as well as 3-D structures. Chapter 5 is devoted to special problems related to solving inverse problems in which boundary conditions, defects such as voids or cracks and material characteristics, are unknown. Closing comments summarizing the book are presented in Chapter 6.

Many scientific and real-world problems that occur in science, engineering, and medicine can be represented in differential equations. There is a vital role for differential equations in studying the behavior of different types of real-world problems. Thus, it becomes crucial to know the existence uniqueness properties of differential equations and various methods of finding differential equation solutions in explicit form. It is also essential to know different kinds of differential equations in terms of eigenvalues, termed eigenvalue problems, and some special functions used in finding the solution to differential equations. The study of nonlinear problems also plays a significant role in different real-world situations. There is a necessity to know the behavior of solutions of nonlinear differential equations. Still, there are very few forms of differential equations whose solution can be found in explicit form. For the differential equations whose solutions cannot be found in explicit form, one has to study the properties of solutions of the given differential equation to guess an approximate solution of it. This book aims to introduce all the necessary topics of differential equations in one book so that laymen can easily understand the subject and apply it in their research areas. The novel approach used in this book is that I have introduced different analytical methods for finding the solution of differential equations with sufficient theorems, corollaries, and examples, and the geometrical interpretations in each topic. This textbook is intended to study the theory and methods of finding the explicit solutions to differential equations, wherever possible, and in the absence of finding explicit solutions. It is intended to study the properties of solutions to the given differential equations. This book is based on syllabi of the theory of differential equations prescribed for postgraduate students of mathematics and applied mathematics in different institutions and universities of India and abroad. This book will be helpful for competitive examinations as well.

Features Includes multiple case studies. Suitable for scientists and professionals working on methods for mosquito control. Provides a much-needed focal point for interdisciplinary discussion.