From the Foreword by Marshall Fisher, The Wharton School, University of Pennsylvania: As generation of academics and practitioners follows generation, it is worthwhile to compile long views of the research and practice in the past to shed light on research and practice going forward. This collection of peer-reviewed articles is intended to provide such a long view. This book contains a collection of chapters written by leading scholars/practitioners who have continued their efforts in developing and/or implementing innovative OR/MS tools for solving real world problems. In this book, the contributors share their perspectives about the past, present and future of OR/MS theoretical development, solution tools, modeling approaches, and applications. Specifically, this book collects chapters that offer insights about the following topics: * Survey articles taking a long view over the past two or more decades to arrive at the present state of the art while outlining ideas for future research. Surveys focus on use of a particular OR/MS approach, e.g., mathematical programming (LP, MILP, etc.) and solution methods for particular family of application, e.g., distribution system design, distribution planning system, health care. * Autobiographical or biographical accounts of how particular inventions (e.g., Structured Modeling) were made. These could include personal experiences in early development of OR/MS and an overview of what has happened since. * Development of OR/MS mathematical tools (e.g., stochastic programming, optimization theory). * Development of OR/MS in a particular industry sector such as global supply chain management. * Modeling systems for OR/MS and their development over time as well as speculation on future development (e.g., LINDO, LINGO, and What'sBest!) * New applications of OR/MS models (e.g., happiness) The target audience of this book is young researchers, graduate/advanced undergraduate students from OR/MS and related fields like computer science, engineering, and management as well as practitioners who want to understand how OR/MS modeling came about over the past few decades and what research topics or modeling approaches they could pursue in research or application.

This book deals with several types of multi-dimensional control problems in the face of data uncertainty for vector cases-multi-dimensional multi-objective control problem with uncertain objective functionals, uncertain constraint functionals, and uncertain objective as well as constraint functionals, uncertain multi-dimensional multi-objective control problem with semi-infinite constraints, uncertain dual multi-dimensional multi-objective variational control problem, and second-order PDE&PDI constrained robust optimization problem. The book provides the solution approaches-an exact l1 penalty function approach, modified objective approach, robust approach-in the simplest way to solve the recent developing optimization problems in the sense of uncertainty.

This book highlights a comprehensive introduction to the fundamental statistical mechanics underneath the inner workings of neural networks. The book discusses in details important concepts and techniques including the cavity method, the mean-field theory, replica techniques, the Nishimori condition, variational methods, the dynamical mean-field theory, unsupervised learning, associative memory models, perceptron models, the chaos theory of recurrent neural networks, and eigen-spectrums of neural networks, walking new learners through the theories and must-have skillsets to understand and use neural networks. The book focuses on quantitative frameworks of neural network models where the underlying mechanisms can be precisely isolated by physics of mathematical beauty and theoretical predictions. It is a good reference for students, researchers, and practitioners in the area of neural networks.

The second edition of this book brings together a cutting edge international team of contributors to critically review the current knowledge regarding the effectiveness of training interventions designed to improve cognitive functions in different target populations. Since the publication of the first volume, the field of cognitive research has rapidly evolved. There is substantial evidence that cognitive and physical training can improve cognitive performance, but these benefits seem to vary as a function of the type and the intensity of interventions and the way training-induced gains are measured and analyzed. This book will address the new topics in psychological research and aims to resolve some of the currently debated issues. This book offers a comprehensive overview of empirical findings and methodological approaches of cognitive training research in different cognitive domains (memory, executive functions, etc.), types of training (working memory training, video game training, physical training, etc.), age groups (from children to young and older adults), target populations (children with developmental disorders, aging workers, MCI patients etc.), settings (laboratory-based studies, applied studies in clinical and educational settings), and methodological approaches (behavioral studies, neuroscientific studies). Chapters feature theoretical models that describe the mechanisms underlying training-induced cognitive and neural changes. Cognitive Training: An Overview of Features and Applications, Second Edition will be of interest to researchers, practitioners, students, and professors in the fields of psychology and neuroscience.

This contributed volume investigates several mathematical techniques for the modeling and simulation of viral pandemics, with a special focus on COVID-19. Modeling a pandemic requires an interdisciplinary approach with other fields such as epidemiology, virology, immunology, and biology in general. Spatial dynamics and interactions are also important features to be considered, and a multiscale framework is needed at the level of individuals and the level of virus particles and the immune system. Chapters in this volume address these items, as well as offer perspectives for the future.

This book is the second of a set dedicated to the mathematical tools used in partial differential equations derived from physics. It presents the properties of continuous functions, which are useful for solving partial differential equations, and, more particularly, for constructing distributions valued in a Neumann space. The author examines partial derivatives, the construction of primitives, integration and the weighting of value functions in a Neumann space. Many of them are new generalizations of classical properties for values in a Banach space. Simple methods, semi-norms, sequential properties and others are discussed, making these tools accessible to the greatest number of students - doctoral students, postgraduate students - engineers and researchers, without restricting or generalizing the results.

This volume explores the connections between mathematical modeling, computational methods, and high performance computing, and how recent developments in these areas can help to solve complex problems in the natural sciences and engineering. The content of the book is based on talks and papers presented at the conference Modern Mathematical Methods and High Performance Computing in Science & Technology (M3HPCST), held at Inderprastha Engineering College in Ghaziabad, India in January 2020. A wide range of both theoretical and applied topics are covered in detail, including the conceptualization of infinity, efficient domain decomposition, high capacity wireless communication, infectious disease modeling, and more. These chapters are organized around the following areas: Partial and ordinary differential equations Optimization and optimal control High performance and scientific computing Stochastic models and statistics Recent Trends in Mathematical Modeling and High Performance Computing will be of interest to researchers in both mathematics and engineering, as well as to practitioners who face complex models and extensive computations.

Proceedings of the IIASA Workshop, November 30-December 4, 1987, Laxenburg, Austria

The main theme of this book is recent progress in structure-preserving algorithms for solving initial value problems of oscillatory differential equations arising in a variety of research areas, such as astronomy, theoretical physics, electronics, quantum mechanics and engineering. It systematically describes the latest advances in the development of structure-preserving integrators for oscillatory differential equations, such as structure-preserving exponential integrators, functionally fitted energy-preserving integrators, exponential Fourier collocation methods, trigonometric collocation methods, and symmetric and arbitrarily high-order time-stepping methods. Most of the material presented here is drawn from the recent literature. Theoretical analysis of the newly developed schemes shows their advantages in the context of structure preservation. All the new methods introduced in this book are proven to be highly effective compared with the well-known codes in the scientific literature. This book also addresses challenging problems at the forefront of modern numerical analysis and presents a wide range of modern tools and techniques.

This book commemorates the 75th birthday of Prof. George Jaiani - Georgia's leading expert on shell theory. He is also well known outside Georgia for his individual approach to shell theory research and as an organizer of meetings, conferences and schools in the field. The collection of papers presented includes articles by scientists from various countries discussing the state of the art and new trends in the theory of shells, plates, and beams. Chapter 20 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

This book provides up-to-date developments in the stability analysis and (anti-)synchronization control area for complex-valued neural networks systems with time delay. It brings out the characteristic systematism in them and points out further insight to solve relevant problems. It presents a comprehensive, up-to-date, and detailed treatment of dynamical behaviors including stability analysis and (anti-)synchronization control. The materials included in the book are mainly based on the recent research work carried on by the authors in this domain. The book is a useful reference for all those from senior undergraduates, graduate students, to senior researchers interested in or working with control theory, applied mathematics, system analysis and integration, automation, nonlinear science, computer and other related fields, especially those relevant scientific and technical workers in the research of complex-valued neural network systems, dynamic systems, and intelligent control theory.

This book presents time synchronization and its essential role as a conduit of optimized networks and as one of the key imperatives of ubiquitous connectivity. The author discusses how, without proper time synchronization, many mission critical infrastructures such as 5G mobile networks, smart grids, data centres CATV, and industrial networks would render in serious performance issues and may be subject to catastrophic failure. The book provides a thorough understanding of time synchronization from fundamental concepts to the application of time synchronization in NextGen mission critical infrastructure. Readers will find information not only on designing the optimized products for mission critical infrastructure but also on building NextGen mission critical infrastructure.

* Written in a fluid and accessible style, replete with exercises; ideal for undergraduate courses * Suitable for students of land surveying and natural science, as well as professionals, but also for map amateurs

The Fifth European Conference on Industrial Mathematics (ECMI 90) took place at Lahti, Finland on June 6-9, 1990. The conference was organised by the Rolf Nevanlinna Institute together with the Lahti Research and Training Centre of the University of Helsinki. Like its predecessors the Lahti meeting was devoted to the exchange of experience, ideas and methods from various fields of industrial mathematics. The series of ECMI conferences have clearly established an important forum of interaction between the advancing front of technology and one of its crucial development resources, modern applications-oriented mathematics. The precise title of the conferences has been the subject of some discussion and it has been argued that there is no such area which can be labelled as "industrial mathematics." This is certainly true if one thinks only in terms of the range of ideas, theorems, methods and algorithms constituting mathematics all of which may be applied. However with another viewpoint industrial mathematics is not a collection of topics but refers to the interactive process in which mathematics, the science, meets the real world of applications. Ideally this interaction involves both good mathematics and technological advance. The computer revolution has created a new era in technology with the increased computational capability to simulate complex industrial processes, devices, and other technolog- making it possible ical systems. This simulation depends on mathematical modelling and analysis and these techniques, sometimes ingenious but often quite routine, have provided a powerful tool for industrial scientists and creative research management.

The mathematical theory of Krylov subspace methods with a focus on solving systems of linear algebraic equations is given a detailed treatment in this principles-based book. Starting from the idea of projections, Krylov subspace methods are characterised by their orthogonality and minimisation properties. Projections onto highly nonlinear Krylov subspaces can be linked with the underlying problem of moments, and therefore Krylov subspace methods can be viewed as matching moments model reduction. This allows enlightening reformulations of questions from matrix computations into the language of orthogonal polynomials, Gauss-Christoffel quadrature, continued fractions, and, more generally, of Vorobyev's method of moments. Using the concept of cyclic invariant subspaces, conditions are studied that allow the generation of orthogonal Krylov subspace bases via short recurrences. The results motivate the important practical distinction between Hermitian and non-Hermitian problems. Finally, the book thoroughly addresses the computational cost while using Krylov subspace methods. The investigation includes effects of finite precision arithmetic and focuses on the method of conjugate gradients (CG) and generalised minimal residuals (GMRES) as major examples. There is an emphasis on the way algebraic computations must always be considered in the context of solving real-world problems, where the mathematical modelling, discretisation and computation cannot be separated from each other. The book also underlines the importance of the historical context and demonstrates that knowledge of early developments can play an important role in understanding and resolving very recent computational problems. Many extensive historical notes are included as an inherent part of the text as well as the formulation of some omitted issues and challenges which need to be addressed in future work. This book is applicable to a wide variety of graduate courses on Krylov subspace methods and related subjects, as well as benefiting those interested in the history of mathematics.

The Workshop on Hyperbolic Conservation Laws and Related Analysis with Applications at the International Centre for Mathematical Sciences (Edinburgh, UK) held in Edinburgh, September 2011, produced this fine collection of original research and survey articles. Many leading mathematicians attended the event and submitted their contributions for this volume.This book presents thirteen papers, representing the most significant advances and current trends in nonlinear hyperbolic conservation laws, related analysisand applications. Topics covered include a survey on multidimensional systems of conservation laws as well as novel results on liquid crystals, conservation laws with discontinuous flux functions, and applications to sedimentation. Also included are articles on recent advances in the Euler equations and the Navier Stokes Fourier Poisson system, in addition to new results on collective phenomena described by the Cucker Smale model.

The present volume is addressed toresearchers and graduate students interested in partial differential equations and related analysis with applications.

The present monograph is dedicated to a new branch of the theory of climate, which is titled by the authors, "Mathematical Theory of Climate. " The foundation of this branch is the investigation of climate models by the methods of the qUalitative theory of differential equa tions. In the Russian edition the book was named "Fundamentals of the Mathematical Theory of Climate. " Respecting the recommenda tions of Wayne Yuhasz (we are truly grateful to him for this advice), we named the English edition of the book "Mathematics of Climate Modelling. " This title appears to be more appropriate, since the con structive results of the theory are at present preliminary and have not been fully tested with experiments in climate modelling. This branch of science is yet developing and its practical results will be obtained only in the near future. Nevertheless, we want to keep the terminology which we have used in the introduction to the Russian edition of the book, since the authors hope that this term will be accepted by the scientific community for identification of a given branch of climate theory. On preparing the English edition, new ideas were established con necting some significant new research results obtained by the author. We are deeply grateful to G. Marchuk for continual encourage ment of this scientific enterprise and fruitful discussions, to our young colleagues A. Gorelov, E. Kazantsev, A. Gritsun, and A."

This book presents revised versions of the best papers selected from the symposium Mathematical Progress in Expressive Image Synthesis (MEIS2013) held in Fukuoka, Japan, in 2013. The topics cover various areas of computer graphics (CG), such as surface deformation/editing, character animation, visual simulation of fluids, texture and sound synthesis and photorealistic rendering. From a mathematical point of view, the book also presents papers addressing discrete differential geometry, Lie theory, computational fluid dynamics, function interpolation and learning theory. This book showcases the latest joint efforts between mathematicians, CG researchers and practitioners exploring important issues in graphics and visual perception.The book provides a valuable resource for all computer graphics researchers seeking open problem areas, especially those now entering the field who have not yet selected a research direction."

This book develops new mathematical methods and tools to model living systems. The material it presents can be used in such real-world applications as immunology, transportation engineering, and economics. The first part of the book deals with deriving general evolution equations that can be customized to particular systems of interest in the applied sciences. The second part of the book deals with various models and applications. The book will be a valuable resource to all involved in modeling complex social systems and living matter in general.

The polymer industry raises a large number of relevant mathematical problems with respect to the quality of manufactured polymer parts. These include in particular questions about: - the production of the polymeric material from a monomer (based on the Ziegler-Natta catalytic process) - the crystallization kinetic of the polymer melt - the coupling of the crystallization process with the fluid dynamics of the manufacturing process such as extrusion, injection moulding of film blowing, etc.This book provides the first unified presentation of the mathematical modelling of polymerization, crystallization and extrusion of polymer melts, by means of advanced methods, presented in an accessible way for applied scientists and engineers. The present volume is the result of a long-term cooperation between different research teams in Europe within the ECMI Special Interest Group on "Polymers".

This book collects some recent works on the application of dynamic game and control theory to the analysis of environmental problems. This collec tion of papers is not the outcome of a conference or of a workshop. It is rather the result of a careful screening from among a number of contribu tions that we have solicited across the world. In particular, we have been able to attract the work of some of the most prominent scholars in the field of dynamic analyses of the environment. Engineers, mathematicians and economists provide their views and analytical tools to better interpret the interactions between economic and environmental phenomena, thus achiev ing, through this interdisciplinary effort, new and interesting results. The goal of the book is more normative than descriptive. All papers include careful modelling of the dynamics of the main variables involved in the game between nature and economic agents and among economic agents themselves, as well-described in Vrieze's introductory chapter. Fur thermore, all papers use this careful modelling framework to provide policy prescriptions to the public agencies authorized to regulate emission dy namics. Several diverse problems are addressed: from global issues, such as the greenhouse effect or deforestation, to international ones, such as the management of fisheries, to local ones, for example, the control of effluent discharges. Moreover, pollution problems are not the only concern of this book."

This open access book presents a structural model and an associated test instrument designed to provide a detailed analysis of professional competences for teaching mathematical modelling. The conceptualisation is based on the COACTIV model, which describes aspects, areas and facets of professional competences of teachers. The manual provides an overview of the essential teaching skills in application-related contexts and offers the tools needed to capture these aspects. It discusses the objectives and application areas of the instrument, as well as the development of the test. In addition, it describes the implementation and evaluates the quality and results of the structural equation analysis of the model. Teaching mathematical modelling is a cognitively challenging activity for (prospective) teachers. Thus, teacher education requires a detailed analysis of professional competence for teaching mathematical modelling. Measuring this competence requires theoretical models that accurately describe requirements placed upon teachers, as well as appropriate evaluation tools that adequately capture skills and abilities in this field. This book presents an instrument that measures the professional competences in a sample of 349 prospective teachers.

This book is the first comprehensive tutorial on matheuristics. Matheuristics are based on mathematical extensions of previously known heuristics, mainly metaheuristics, and on original, area-specific approaches. This tutorial provides a detailed discussion of both contributions, presenting the pseudocodes of over 40 algorithms, abundant literature references, and for each case a step-by-step description of a sample run on a common Generalized Assignment Problem example. C++ source codes of all algorithms are available in an associated SW repository.

This book provides an overview of state-of-the-art implementations of quantum random number generators (QRNGs), and especially examines their relation to classical statistical randomness models and numerical techniques for computing random numbers. The reader - who ideally has a background in classical statistics, computer science, or cryptography - is introduced to the world of quantum bits step by step, and explicit relations between QRNGs and their classical counterparts are identified along the way. Random number generation is a major pillar of cryptography. Capitalizing on the randomness inherent in quantum phenomena is a rapidly evolving branch of quantum cryptography with countless applications for the future. The value of quantum randomness for cryptographic purposes is empirically demonstrated in statistical evaluations of QRNGs' performance compared to classical techniques for true and pseudorandom number generation. The book then provides an overview of technical implementations of QRNGs, before a concluding discussion of major achievements and remaining obstacles in the field rounds out the coverage, while also opening the door for future research directions.

This book introduces advanced mathematical methods and techniques for analysis and simulation of models in mathematical epidemiology. Chronological age and class-age play an important role in the description of infectious diseases and this text provides the tools for the analysis of this type of partial differential equation models. This book presents general theoretical tools as well as large number of specific examples to guide the reader to develop their own tools that they may then apply to study structured models in mathematical epidemiology. The book will be a valuable addition to the arsenal of all researchers interested in developing theory or studying specific models with age structure.