This edited volume is a collection of selected research articles discussing the analysis of infectious diseases by using mathematical modelling in recent times. Divided into two parts, the book gives a general and country-wise analysis of Covid-19. Analytical and numerical techniques for virus models are presented along with the application of mathematical modelling in the analysis of their spreading rates and treatments. The book also includes applications of fractional differential equations as well as ordinary, partial and integrodifferential equations with optimization methods. Probability distribution and their bio-mathematical applications have also been studied. This book is a valuable resource for researchers, scholars, biomathematicians and medical experts.

This edited volume provides an essential resource for urban morphology, the study of urban forms and structures, offering a much-needed mathematical perspective. Experts on a variety of mathematical modeling techniques provide new insights into specific aspects of the field, such as street networks, sustainability, and urban growth. The chapters collected here make a clear case for the importance of tools and methods to understand, model, and simulate the formation and evolution of cities. The chapters cover a wide variety of topics in urban morphology, and are conveniently organized by their mathematical principles. The first part covers fractals and focuses on how self-similar structures sort themselves out through competition. This is followed by a section on cellular automata, and includes chapters exploring how they generate fractal forms. Networks are the focus of the third part, which includes street networks and other forms as well. Chapters that examine complexity and its relation to urban structures are in part four.The fifth part introduces a variety of other quantitative models that can be used to study urban morphology. In the book's final section, a series of multidisciplinary commentaries offers readers new ways of looking at the relationship between mathematics and urban forms. Being the first book on this topic, Mathematics of Urban Morphology will be an invaluable resource for applied mathematicians and anyone studying urban morphology. Additionally, anyone who is interested in cities from the angle of economics, sociology, architecture, or geography will also find it useful. "This book provides a useful perspective on the state of the art with respect to urban morphology in general and mathematics as tools and frames to disentangle the ideas that pervade arguments about form and function in particular. There is much to absorb in the pages that follow and there are many pointers to ways in which these ideas can be linked to related theories of cities, urban design and urban policy analysis as well as new movements such as the role of computation in cities and the idea of the smart city. Much food for thought. Read on, digest, enjoy." From the foreword by Michael Batty

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.

Starting with an introduction to the numerous features of Mathematica (R), this book continues with more complex material. It provides the reader with lots of examples and illustrations of how the benefits of Mathematica (R) can be used. Composed of eleven chapters, it includes the following: A chapter on several sorting algorithms Functions (planar and solid) with many interesting examples Ordinary differential equations Advantages of Mathematica (R) dealing with the Pi number The power of Mathematica (R) working with optimal control problems Introduction to Mathematica (R) with Applications will appeal to researchers, professors and students requiring a computational tool.

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.

Mathematical methods and theories with interdisciplinary applications are presented in this book. The eighteen contributions presented in this Work have been written by eminent scientists; a few papers are based on talks which took place at the International Conference at the Hellenic Artillery School in May 2015. Each paper evaluates possible solutions to long-standing problems such as the solvability of the direct electromagnetic scattering problem, geometric approaches to cyber security, ellipsoid targeting with overlap, non-equilibrium solutions of dynamic networks, measuring ballistic dispersion, elliptic regularity theory for the numerical solution of variational problems, approximation theory for polynomials on the real line and the unit circle, complementarity and variational inequalities in electronics, new two-slope parameterized achievement scalarizing functions for nonlinear multiobjective optimization, and strong and weak convexity of closed sets in a Hilbert space. Graduate students, scientists, engineers and researchers in pure and applied mathematical sciences, operations research, engineering, and cyber security will find the interdisciplinary scientific perspectives useful to their overall understanding and further research.

Mathematical Models and Algorithms for Power System Optimization helps readers build a thorough understanding of new technologies and world-class practices developed by the State Grid Corporation of China, the organization responsible for the world's largest power distribution network. This reference covers three areas: power operation planning, electric grid investment and operational planning and power system control. It introduces economic dispatching, generator maintenance scheduling, power flow, optimal load flow, reactive power planning, load frequency control and transient stability, using mathematic models including optimization, dynamic, differential and difference equations.

Introduction to Modeling in Physiology and Medicine, Second Edition, develops a clear understanding of the fundamental principles of good modeling methodology. Sections show how to create valid mathematical models that are fit for a range of purposes. These models are supported by detailed explanation, extensive case studies, examples and applications. This updated edition includes clearer guidance on the mathematical prerequisites needed to achieve the maximum benefit from the material, a greater detail regarding basic approaches to modeling, and discussions on non-linear and stochastic modeling. The range of case study material has been substantially extended, with examples drawn from recent research experience. Key examples include a cellular model of insulin secretion and its extension to the whole-body level, a model of insulin action during a meal/oral glucose tolerance test, a large-scale simulation model of type 1 diabetes and its use in in silico clinical trials and drug trials.

The book addresses the development of the basic knowledge of the subsurface solute transfer with a particular emphasis on field data collection and analysis coupled with modeling (analytical and numerical) tool application. The relevant theoretical developments are concerned mainly with the formulation and solution of deterministic mass-transport equations for a wide range of engineering issues in groundwater quality assessment and forecasting.

The book gives many computational examples and case studies drawn from the conducted field investigations. The analyzed problems are as follows: investigation and prediction of groundwater contamination by industrial contaminants and solutions (radionuclides, chloride and nitrate brine) with special focus on the effect of (a) aquifer heterogeneity, anisotropy, and dual porosity, (b) density contrast existing between industrial waste and groundwater, or in density-stratified artesian and coastal groundwater systems; (c) physicochemical interactions that play a major role in retarding (e.g. adsorption) or enhancing (e.g. interactions between dissolved species and mobile colloids) contaminant transport;prediction of the effects of pumping on groundwater quality at wellfields;groundwater dating using stable and radioactive isotopes for prediction and assessment of contamination potential;field and laboratory tests' design and analysis, and monitoring data interpretation;partitioning of surface and subsurface flows using isotope techniques.

One of the most essential topics addressed in the book is the migration and fate of radionuclides. Model development is motivated by field data analysis from a number of radioactively contaminated sites in the Russian Federation: near-surface radioactive waste disposal sites and deep-well radioactive waste injection sites. They play a unique role in the advancement of knowledge of the subsurface behavior and fate of many hazardous radionuclides and can be considered as field-scale laboratories.

Thus, the book, along with theoretical findings, contains field information, which will facilitate the understanding of subsurface solute transport and the development of a methodology for practical applications to groundwater hydrology.

Mathematical Modelling in Motor Neuroscience: State of the Art and Translation to the Clinic, Gaze Orienting Mechanisms and Disease, Volume 249, the latest release in the Progress in Brain Research series, highlights new advances in the field, with this new volume presenting interesting chapters on a variety of topics, including Sequential Bayesian updating, Maps and Sensorimotor Transformations for Eye-Head Gaze Shifts: Role of the Midbrain Superior Colliculus, Modeling Gaze Position-Dependent Opsoclonus, Eye Position-Dependent Opsoclonus in Mild Traumatic Brain Injury, Saccades in Parkinson's disease -- hypometric, slow, and maladaptive, Brainstem Neural Circuits for Fixation and Generation of Saccadic Eye Movements, and much more.

Continuamentenasconoifatti 1 aconfusionedelleteorie 2 Carlo Dossi Electromagnetism is withoutany doubt a fascinating area of physics, engineering and mathematics. Since the early pioneeringworks ofAmpere, Faraday, and Maxwell, the scienti?cliteratureon this subject has become immense, and books devoted to almost all of its aspects have been published in the meantime. However, webelievethatthereisstillsomeplacefornew booksdealingwithel- tromagnetism, particularly if they are focused on more speci?c models, or try to mix different levels of analysis: rigorous mathematical results, sound numerical appro- mation schemes, real-life examples from physics and engineering. The complete mathematical description of electromagnetic problems is provided by the celebrated Maxwell equations, a system of partial differential equations - pressed interms ofphysical quantitiesliketheelectric?eld, themagnetic?eld and the currentdensity.Maxwell'scontributiontotheformulationofthese equationsisrelated to the introductionof a speci?c term, called displacement current, that he proposed to add to the set of equations generally assumed to hold at that time, in order to ensure the conservation of the electric charge. The presence of the displacement current permits to describe one of the most - portant phenomenon in electromagnetism, namely, wave propagation; however, in many interesting applications the propagation speed of the wave is very high with respect to the ratio of some typical length and time scale of the considered device, and therefore the dominant aspect becomes the diffusionof the electromagnetic ?elds. When the focus is on diffusioninstead of propagation, from the modelingpointof view this corresponds to neglecting the time derivative of the electric induction (i.e., thedisplacement current introducedby Maxwell)or, alternatively,neglectingthe time derivative of the magnetic induction.

This book covers computational statistics-based approaches for Artificial Intelligence. The aim of this book is to provide comprehensive coverage of the fundamentals through the applications of the different kinds of mathematical modelling and statistical techniques and describing their applications in different Artificial Intelligence systems. The primary users of this book will include researchers, academicians, postgraduate students, and specialists in the areas of data science, mathematical modelling, and Artificial Intelligence. It will also serve as a valuable resource for many others in the fields of electrical, computer, and optical engineering. The key features of this book are: Presents development of several real-world problem applications and experimental research in the field of computational statistics and mathematical modelling for Artificial Intelligence Examines the evolution of fundamental research into industrialized research and the transformation of applied investigation into real-time applications Examines the applications involving analytical and statistical solutions, and provides foundational and advanced concepts for beginners and industry professionals Provides a dynamic perspective to the concept of computational statistics for analysis of data and applications in intelligent systems with an objective of ensuring sustainability issues for ease of different stakeholders in various fields Integrates recent methodologies and challenges by employing mathematical modeling and statistical techniques for Artificial Intelligence

This comprehensive textbook/reference provides an in-depth overview of the key aspects of transportation analysis, with an emphasis on modeling real transportation systems and executing the models. Topics and features: presents comprehensive review questions at the end of each chapter, together with detailed case studies, useful links, references and suggestions for further reading; supplies a variety of teaching support materials at the book's webpage on Springer.com, including a complete set of lecture slides; examines the classification of models used for multimodal transportation systems, and reviews the models and evaluation methods used in transportation planning; explains traffic assignment to road networks, and describes computer simulation integration platforms and their use in the transportation systems sector; provides an overview of transportation simulation tools, and discusses the critical issues in the design, development and use of the simulation models.

Isogeometric analysis (IGA) consists of using the same higher-order and smooth spline functions for the representation of geometry in Computer Aided Design as for the approximation of solution fields in Finite Element Analysis. Now, about fifteen years after its creation, substantial works are being reported in IGA, which make it very competitive in scientific computing. This book provides a contemporary vision of IGA by first discussing the current challenges in achieving a true bridge between design and analysis, then proposing original solutions that answer the issues from an analytical point of view, and, eventually, studying the shape optimization of structures, which is one of the greatest applications of IGA. To handle complex structures, a full analysis-to-optimization framework is developed, based on non-invasive coupling, parallel domain decomposition and immersed geometrical modeling. This seems to be very robust, taking on all of the attractive features of IGA (the design-analysis link, numerical efficiency and natural regularization), giving us the opportunity to explore new types of design.

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

Features recent trends and advances in the theory and techniques used to accurately measure and model growth Growth Curve Modeling: Theory and Applications features an accessible introduction to growth curve modeling and addresses how to monitor the change in variables over time since there is no one size fits all approach to growth measurement. A review of the requisite mathematics for growth modeling and the statistical techniques needed for estimating growth models are provided, and an overview of popular growth curves, such as linear, logarithmic, reciprocal, logistic, Gompertz, Weibull, negative exponential, and log-logistic, among others, is included. In addition, the book discusses key application areas including economic, plant, population, forest, and firm growth and is suitable as a resource for assessing recent growth modeling trends in the medical field. SAS(R) is utilized throughout to analyze and model growth curves, aiding readers in estimating specialized growth rates and curves. Including derivations of virtually all of the major growth curves and models, Growth Curve Modeling: Theory and Applications also features: Statistical distribution analysis as it pertains to growth modeling Trend estimations Dynamic site equations obtained from growth models Nonlinear regression Yield-density curves Nonlinear mixed effects models for repeated measurements data Growth Curve Modeling: Theory and Applications is an excellent resource for statisticians, public health analysts, biologists, botanists, economists, and demographers who require a modern review of statistical methods for modeling growth curves and analyzing longitudinal data. The book is also useful for upper-undergraduate and graduate courses on growth modeling.

This monograph is dedicated to the derivation and analysis of fluid models occurring in plasma physics. It focuses on models involving quasi-neutrality approximation, problems related to laser propagation in a plasma, and coupling plasma waves and electromagnetic waves. Applied mathematicians will find a stimulating introduction to the world of plasma physics and a few open problems that are mathematically rich. Physicists who may be overwhelmed by the abundance of models and uncertain of their underlying assumptions will find basic mathematical properties of the related systems of partial differential equations. A planned second volume will be devoted to kinetic models.

First and foremost, this book mathematically derives certain common fluid models from more general models. Although some of these derivations may be well known to physicists, it is important to highlight the assumptions underlying the derivations and to realize that some seemingly simple approximations turn out to be more complicated than they look. Such approximations are justified using asymptotic analysis wherever possible. Furthermore, efficient simulations of multi-dimensional models require precise statements of the related systems of partial differential equations along with appropriate boundary conditions. Some mathematical properties of these systems are presented which offer hints to those using numerical methods, although numerics is not the primary focus of the book.

Dye-Sensitized Solar Cells: Mathematical Modelling and Materials Design and Optimization presents the latest information as edited from leaders in the field. It covers advances in DSSC design, fabrication and mathematical modelling and optimization, providing a comprehensive coverage of various DSSC advances that includes different system scales, from electronic to macroscopic level, and a consolidation of the results with fundamentals. The book is extremely useful as a monograph for graduate students and researchers, but is also a comprehensive, general reference on state-of-the-art techniques in modelling, optimization and design of DSSCs.

The text covers a wide range of topics such as mathematical modeling of crop pest control management, water resources management, impact of anthropogenic activities on atmospheric carbon dioxide concentrations, impact of climate changes on melting of glaciers and polar bear populations, dynamics of slow-fast predator-prey system and spread and control of HIV epidemic. It emphasizes the use of mathematical modeling to investigate the fluid flow problems including the breaking of viscoelastic jet, instability arising in nanofiber, flow in an annulus channel, and thermal instability in nano-fluids in a comprehensive manner. This book will be a readily accessible source of information for the students, researchers and policymakers interested in the application of mathematical and computational modeling techniques to investigate various biological and engineering phenomena. Features Focuses on the current modeling and computational trends to investigate various ecological, epidemiological, and engineering systems. Presents the mathematical modeling of a wide range of ecological and environmental issues including crop pest control management, water resources management, the effect of anthropogenic activities on atmospheric carbon dioxide concentrations, and impact of climate changes on melting of glaciers and polar bear population. Covers a wide range of topics including the breaking of viscoelastic jet, instability arising in nanofiber, flow in an annulus channel, and thermal instability in nano-fluids. Examines evolutionary models i.e., models of time-varying processes. Highlights the recent developments in the analytical methods to investigate the nonlinear dynamical systems. Showcases diversified applications of computational techniques to solve practical biological and engineering problems. The book focuses on the recent research developments in the mathematical modeling and scientific computing of biological and engineering systems. It will serve as an ideal reference text for senior undergraduate, graduate students, and researchers in diverse fields including ecological engineering, environmental engineering, computer engineering, mechanical engineering, mathematics, and fluid dynamics.

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.

As the role of the modern engineer is markedly different from that of even a decade ago, the theme of engineering mathematics educa tion (EME) is an important one. The need for mathematical model ling (MM) courses and consideration of the educational impact of computer-based technology environments merit special attention. This book contains the proceeding of the NATO Advanced Research Workshop held on this theme in July 1993. We have left the industrial age behind and have entered the in formation age. Computers and other emerging technologies are penetrating society in depth and gaining a strong influence in de termining how in future society will be organised, while the rapid change of information requires a more qualified work force. This work force is vital to high technology and economic competitive ness in many industrialised countries throughout the world. Within this framework, the quality of EME has become an issue. It is expected that the content of mathematics courses taught in schools of engineering today have to be re-evaluated continuously with regard to computer-based technology and the needs of mod ern information society. The main aim of the workshop was to pro vide a forum for discussion between mathematicians, engineering scientists, mathematics educationalists, and courseware develop ers in the higher education sector and to focus on the issues and problems of the design of more relevant and appropriate MM courses for engineering education."

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.

The state of the art in Biopharmaceutics, Pharmacokinetics, and Pharmacodynamics Modeling is presented in this new second edition book. It shows how advanced physical and mathematical methods can expand classical models in order to cover heterogeneous drug-biological processes and therapeutic effects in the body. The book is divided into four parts; the first deals with the fundamental principles of fractals, diffusion and nonlinear dynamics; the second with drug dissolution, release, and absorption; the third with epirical, compartmental, and stochastic pharmacokinetic models, with two new chapters, one on fractional pharmacokinetics and one on bioequivalence; and the fourth mainly with classical and nonclassical aspects of pharmacodynamics. The classical models that have relevance and application to these sciences are also considered throughout. This second edition has new information on reaction limited models of dissolution, non binary biopharmaceutic classification system, time varying models, and interface models. Many examples are used to illustrate the intrinsic complexity of drug administration related phenomena in the human, justifying the use of advanced modeling methods. This book will appeal to graduate students and researchers in pharmacology, pharmaceutical sciences, bioengineering, and physiology. Reviews of the first edition: "This book presents a novel modelling approach to biopharmaceutics, pharmacokinetics and pharmacodynamic phenomena. This state-of-the-art volume will be helpful to students and researchers in pharmacology, bioengineering, and physiology. This book is a must for pharmaceutical researchers to keep up with recent developments in this field." (P. R. Parthasarathy, Zentralblatt MATH, Vol. 1103 (5), 2007) "These authors are the unique (or sole) contributors in this area that are working on these questions and bring a special expertise to the field that is now being recognized as essential to understanding biological system and kinetic/dynamic characteristics in drug development...This text is an essential primer for those who would envision the incorporation of heterogeneous approaches to systems where homogeneous approaches are not sufficient to describe the system." (Robert R. Bies, Journal of Clinical Pharmacology, Vol. 46, 2006)

Advanced Problem Solving Using Maple (TM): Applied Mathematics, Operations Research, Business Analytics, and Decision Analysis applies the mathematical modeling process by formulating, building, solving, analyzing, and criticizing mathematical models. Scenarios are developed within the scope of the problem-solving process. The text focuses on discrete dynamical systems, optimization techniques, single-variable unconstrained optimization and applied problems, and numerical search methods. Additional coverage includes multivariable unconstrained and constrained techniques. Linear algebra techniques to model and solve problems such as the Leontief model, and advanced regression techniques including nonlinear, logistics, and Poisson are covered. Game theory, the Nash equilibrium, and Nash arbitration are also included. Features: The text's case studies and student projects involve students with real-world problem solving Focuses on numerical solution techniques in dynamical systems, optimization, and numerical analysis The numerical procedures discussed in the text are algorithmic and iterative Maple is utilized throughout the text as a tool for computation and analysis All algorithms are provided with step-by-step formats About the Authors: William P. Fox is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School. Currently, he is an adjunct professor, Department of Mathematics, the College of William and Mary. He received his PhD at Clemson University and has many publications and scholarly activities including twenty books and over one hundred and fifty journal articles. William C. Bauldry, Prof. Emeritus and Adjunct Research Prof. of Mathematics at Appalachian State University, received his PhD in Approximation Theory from Ohio State. He has published many papers on pedagogy and technology, often using Maple, and has been the PI of several NSF-funded projects incorporating technology and modeling into math courses. He currently serves as Associate Director of COMAP's Math Contest in Modeling (MCM).

In contrast to mainstream economics, complexity theory conceives the economy as a complex system of heterogeneous interacting agents characterised by limited information and bounded rationality. Agent Based Models (ABMs) are the analytical and computational tools developed by the proponents of this emerging methodology. Aimed at students and scholars of contemporary economics, this book includes a comprehensive toolkit for agent-based computational economics, now quickly becoming the new way to study evolving economic systems. Leading scholars in the field explain how ABMs can be applied fruitfully to many real-world economic examples and represent a great advancement over mainstream approaches. The essays discuss the methodological bases of agent-based approaches and demonstrate step-by-step how to build, simulate and analyse ABMs and how to validate their outputs empirically using the data. They also present a wide set of applications of these models to key economic topics, including the business cycle, labour markets, and economic growth.