This book deals in a concise format with the methods used to develop mathematical models for water and wastewater treatment. It provides a systematic approach to mass balances, transport and transformation processes, kinetics, stoichiometry, reactor hydraulics, residence time distribution, heterogeneous systems, and dynamic behaviour of reactors. In addition it includes an introduction into parameter identification, error analysis, error propagation, process control, time series analysis, stochastic modelling and probabilistic design. Written as a textbook, it contains many solved practical applications.

This is a thoroughly revised and enlarged second edition that presents the main results of descriptive complexity theory, that is, the connections between axiomatizability of classes of finite structures and their complexity with respect to time and space bounds. The logics that are important in this context include fixed-point logics, transitive closure logics, and also certain infinitary languages; their model theory is studied in full detail. The book is written in such a way that the respective parts on model theory and descriptive complexity theory may be read independently.

This book focuses on a development for assessing mental changes using eye pupil reactions, namely extracting emotional change from the response to evaluate the viewer's interest in visual information. The pupil of the eye reacts to both brightness and emotional state, including interest, enjoyment, and mental workload. Because pupillary change is a biological signal, various artifacts influence measurements of eye images. Technical procedures are required to extract mental activities from pupillary changes, and they are summarized here step by step, although some procedures contain earlier techniques such as analog video processing. This study examines the possibility of estimating the viewer's interest and enjoyment of viewing movies by measuring the dynamic pupillary changes, blinking, and subjective interest responses. In evaluation of pupil size, there was a significant difference in pupil size between the higher and the lower shot for the degree of subject interest response in each kind of movies. The first part of the book shows a pupil reaction model for brightness changes to extract mental activities. Pupil reactions were observed for various visual stimuli in brightness changes. With regard to the characteristics of pupillary changes, a model with a three-layer neural network was developed and the performance was evaluated. Characteristics of pupil reactions during model development are summarized here. The second part examines the possibility of estimating the viewer's interest and enjoyment of television programs by measuring dynamic pupillary changes, blinking, and subjective interest responses. The final part describes a development of estimation model of pupil size for blink artifact. The model development was able to estimate pupillary changes and pupil size while the viewer was blinking and was applied to pupillary changes in viewing television programs.

Progress in today's high-technology industries is strongly associated with the development of new mathematical tools. A typical illustration of this partnership is the mathematical modelling and numerical simulation of electric circuits and semiconductor devices. At the second Oberwolfach conference devoted to this important and timely field, scientists from around the world, mainly applied mathematicians and electrical engineers from industry and universities, presented their new results. Their contributions, forming the body of this work, cover electric circuit simulation, device simulation and process simulation. Discussions on experiences with standard software packages and improvements of such packages are included. In the semiconductor area special lectures were given on new modelling approaches, numerical techniques and existence and uniqueness results. In this connection, mention is made, for example, of mixed finite element methods, an extension of the Baliga-Patankar technique for a three dimensional simulation, and the connection between semiconductor equations and the Boltzmann equations.

The main objective of Credit Risk: Modeling, Valuation and Hedging is to present a comprehensive survey of the past developments in the area of credit risk research, as well as to put forth the most recent advancements in this field. An important aspect of this text is that it attempts to bridge the gap between the mathematical theory of credit risk and the financial practice, which serves as the motivation for the mathematical modeling studied in the book. Mathematical developments are presented in a thorough manner and cover the structural (value-of-the-firm) and the reduced (intensity-based) approaches to credit risk modeling, applied both to single and to multiple defaults. In particular, the book offers a detailed study of various arbitrage-free models of defaultable term structures with several rating grades.

The Mathematical Elasticity set contains three self-contained volumes that together provide the only modern treatise on elasticity. They introduce contemporary research on three-dimensional elasticity, the theory of plates, and the theory of shells. Each volume contains proofs, detailed surveys of all mathematical prerequisites, and many problems for teaching and self-study. An extended preface and extensive bibliography have been added to each volume to highlight the progress that has been made since the original publication. The first book, Three-Dimensional Elasticity, covers the modeling and mathematical analysis of nonlinear three-dimensional elasticity. In volume two, Theory of Plates, asymptotic methods provide a rigorous mathematical justification of the classical two-dimensional linear plate and shallow shell theories. The objective of Theory of Shells, the final volume, is to show how asymptotic methods provide a rigorous mathematical justification of the classical two-dimensional linear shell theories: membrane, generalized membrane, and flexural. These classic textbooks are for advanced undergraduates, first-year graduate students, and researchers in pure or applied mathematics or continuum mechanics. They are appropriate for courses in mathematical elasticity, theory of plates and shells, continuum mechanics, computational mechanics, and applied mathematics in general.

Practical Goal Programming is intended to allow academics and practitioners to be able to build effective goal programming models, to detail the current state of the art, and to lay the foundation for its future development and continued application to new and varied fields. Suitable as both a text and reference, its nine chapters first provide a brief history, fundamental definitions, and underlying philosophies, and then detail the goal programming variants and define them algebraically. Chapter 3 details the step-by-step formulation of the basic goal programming model, and Chapter 4 explores more advanced modeling issues and highlights some recently proposed extensions.

Chapter 5 then details the solution methodologies of goal programming, concentrating on computerized solution by the Excel Solver and LINGO packages for each of the three main variants, and includes a discussion of the viability of the use of specialized goal programming packages. Chapter 6 discusses the linkages between Pareto Efficiency and goal programming. Chapters 3 to 6 are supported by a set of ten exercises, and an Excel spreadsheet giving the basic solution of each example is available at an accompanying website.

Chapter 7 details the current state of the art in terms of the integration of goal programming with other techniques, and the text concludes with two case studies which were chosen to demonstrate the application of goal programming in practice and to illustrate the principles developed in Chapters 1 to 7. Chapter 8 details an application in healthcare, and Chapter 9 describes applications in portfolio selection.

The Mathematical Elasticity set contains three self-contained volumes that together provide the only modern treatise on elasticity. They introduce contemporary research on three-dimensional elasticity, the theory of plates, and the theory of shells. Each volume contains proofs, detailed surveys of all mathematical prerequisites, and many problems for teaching and self-study. An extended preface and extensive bibliography have been added to each volume to highlight the progress that has been made since the original publication. The first book, Three-Dimensional Elasticity, covers the modeling and mathematical analysis of nonlinear three-dimensional elasticity. In volume two, Theory of Plates, asymptotic methods provide a rigorous mathematical justification of the classical two-dimensional linear plate and shallow shell theories. The objective of Theory of Shells, the final volume, is to show how asymptotic methods provide a rigorous mathematical justification of the classical two-dimensional linear shell theories: membrane, generalized membrane, and flexural. These classic textbooks are for advanced undergraduates, first-year graduate students, and researchers in pure or applied mathematics or continuum mechanics. They are appropriate for courses in mathematical elasticity, theory of plates and shells, continuum mechanics, computational mechanics, and applied mathematics in general.

This thesis has two parts, each based on an application of the renormalization-group (RG). The first part is an analysis of the d-dimensional Coulomb gas. The goal was to determine if the Wilson RG could provide input into particle-in-cell simulations in plasma physics, which are the main family of simulation methods used in this field. The role of the RG was to identify the effect of coarse-graining on the coupling constants as a function of the cut-offs. The RG calculation reproduced established results, but in a more concise form, and showed the effect of the cut-offs on the Debye screening length.
The main part of the thesis is the application of the dynamic RG to turbulence in magnetohydrodynamics. After transformation to Elsasser variables, which is a symmetrisation of the original equations, the solution is presented as a functional integral, which includes stirring forces, their conjugates and functional Jacobian. The coarse-graining of the functional integral is represented as a diagrammatic expansion, followed by rescaling, and casting the results into differential equations for the analysis of RG trajectories. Detailed comparisons are made with the Navier-Stokes limit and with previous calculations for MHD.

This book collects papers presented at the International Conference on Mathematical Modelling and Computational Intelligence Techniques (ICMMCIT) 2021, held at the Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram, Tamil Nadu, India, from 10-12 February 2021. Significant contributions from renowned researchers from fields of applied analysis, mathematical modelling and computing techniques have been received for this conference. Chapters emphasize on the research of computational nature focusing on new algorithms, their analysis and numerical results, as well as applications in physical, biological, social, and behavioural sciences. The accepted papers are organized in topical sections as mathematical modelling, image processing, control theory, graphs and networks, and inventory control.

The topology optimization method solves the basic engineering problem of distributing a limited amount of material in a design space. The first edition of this book has become the standard text on optimal design, which is concerned with the optimization of structural topology, shape and material. This edition has been substantially revised and updated to reflect progress made in modelling and computational procedures. It also encompasses a comprehensive and unified description of the state of the art of the so-called material distribution method, based on the use of mathematical programming and finite elements. Applications treated include not only structures but also MEMS and materials.

Over the past decade there has been an increasing demand for suitable material in the area of mathematical modelling as applied to science, engineering, business and management. Recent developments in computer technology and related software have provided the necessary tools of increasing power and sophistication which have significant implications for the use and role of mathematical modelling in the above disciplines. In the past, traditional methods have relied heavily on expensive experimentation and the building of scaled models, but now a more flexible and cost effective approach is available through greater use of mathematical modelling and computer simulation. In particular, developments in computer algebra, symbolic manipulation packages and user friendly software packages for large scale problems, all have important implications in both the teaching of mathematical modelling and, more importantly, its use in the solution of real world problems. Many textbooks have been published which cover the art and techniques of modelling as well as specific mathematical modelling techniques in specialist areas within science and business. In most of these books the mathematical material tends to be rather tailor made to fit in with a one or two semester course for teaching students at the undergraduate or postgraduate level, usually the former. This textbook is quite different in that it is intended to build on and enhance students' modelling skills using a combination of case studies and projects.

This book uses numerical analysis as the main tool to investigate methods in machine learning and neural networks. The efficiency of neural network representations for general functions and for polynomial functions is studied in detail, together with an original description of the Latin hypercube method and of the ADAM algorithm for training. Furthermore, unique features include the use of Tensorflow for implementation session, and the description of on going research about the construction of new optimized numerical schemes.

The Model-Free Prediction Principle expounded upon in this monograph is based on the simple notion of transforming a complex dataset to one that is easier to work with, e.g., i.i.d. or Gaussian. As such, it restores the emphasis on observable quantities, i.e., current and future data, as opposed to unobservable model parameters and estimates thereof, and yields optimal predictors in diverse settings such as regression and time series. Furthermore, the Model-Free Bootstrap takes us beyond point prediction in order to construct frequentist prediction intervals without resort to unrealistic assumptions such as normality. Prediction has been traditionally approached via a model-based paradigm, i.e., (a) fit a model to the data at hand, and (b) use the fitted model to extrapolate/predict future data. Due to both mathematical and computational constraints, 20th century statistical practice focused mostly on parametric models. Fortunately, with the advent of widely accessible powerful computing in the late 1970s, computer-intensive methods such as the bootstrap and cross-validation freed practitioners from the limitations of parametric models, and paved the way towards the `big data' era of the 21st century. Nonetheless, there is a further step one may take, i.e., going beyond even nonparametric models; this is where the Model-Free Prediction Principle is useful. Interestingly, being able to predict a response variable Y associated with a regressor variable X taking on any possible value seems to inadvertently also achieve the main goal of modeling, i.e., trying to describe how Y depends on X. Hence, as prediction can be treated as a by-product of model-fitting, key estimation problems can be addressed as a by-product of being able to perform prediction. In other words, a practitioner can use Model-Free Prediction ideas in order to additionally obtain point estimates and confidence intervals for relevant parameters leading to an alternative, transformation-based approach to statistical inference.

This textbook provides a comprehensive and instructive coverage of vehicular traffic flow dynamics and modeling. It makes this fascinating interdisciplinary topic, which to date was only documented in parts by specialized monographs, accessible to a broad readership. Numerous figures and problems with solutions help the reader to quickly understand and practice the presented concepts. This book is targeted at students of physics and traffic engineering and, more generally, also at students and professionals in computer science, mathematics, and interdisciplinary topics. It also offers material for project work in programming and simulation at college and university level. The main part, after presenting different categories of traffic data, is devoted to a mathematical description of the dynamics of traffic flow, covering macroscopic models which describe traffic in terms of density, as well as microscopic many-particle models in which each particle corresponds to a vehicle and its driver. Focus chapters on traffic instabilities and model calibration/validation present these topics in a novel and systematic way. Finally, the theoretical framework is shown at work in selected applications such as traffic-state and travel-time estimation, intelligent transportation systems, traffic operations management, and a detailed physics-based model for fuel consumption and emissions.

This thesis describes a new connection between algebraic geometry, topology, number theory and quantum field theory. It offers a pedagogical introduction to algebraic topology, allowing readers to rapidly develop basic skills, and it also presents original ideas to inspire new research in the quest for dualities. Its ambitious goal is to construct a method based on the universal coefficient theorem for identifying new dualities connecting different domains of quantum field theory. This thesis opens a new area of research in the domain of non-perturbative physics-one in which the use of different coefficient structures in (co)homology may lead to previously unknown connections between different regimes of quantum field theories. The origin of dualities is an issue in fundamental physics that continues to puzzle the research community with unexpected results like the AdS/CFT duality or the ER-EPR conjecture. This thesis analyzes these observations from a novel and original point of view, mainly based on a fundamental connection between number theory and topology. Beyond its scientific qualities, it also offers a pedagogical introduction to advanced mathematics and its connection with physics. This makes it a valuable resource for students in mathematical physics and researchers wanting to gain insights into (co)homology theories with coefficients or the way in which Grothendieck's work may be connected with physics.

This book provides an overview of power electronic converters for numerical simulations based on DIgSILENT PowerFactory. It covers the working principles, key assumptions and implementation of models of different types of these power systems. The book is divided into three main parts: the first discusses high-voltage direct currents, while the second part examines distribution systems and micro-grids. Lastly, the third addresses the equipment and technologies used in modelling and simulation. Each chapter includes practical examples and exercises, and the accompanying software illustrates essential models, principles and performance using DIgSILENT PowerFactory. Exploring various current topics in the field of modelling power systems, this book will appeal to a variety of readers, ranging from students to practitioners.

With the use of ecological models, managers and decision makers can make sure that the ecological systems affected by their decisions are accurately represented. Unfortunately, the most relevant ecological science and modeling techniques are often not used because managers are not familiar with them or find them inappropriate for their circumstances. The authors of this volume hope to close the gap between the state of the art in ecological modeling and the state of the practice in the use of models as decision-making tools. It will serve as a readable introduction to modeling for people involved in resource management and will also review specific applications of interest to more experienced modelers. The first chapters detail several successful uses of ecological models in resource management. There are then five pairs of chapters addressing important issues in ecological modeling, including barriers to the use of modeling in decision making, evolving approaches in the field, effective use of data, the toolkit approach to management, and the various scientific and technological investments required for productive modeling. Ecologists and other scientists will learn how best to focus their research for practical, real-world applications, and resource managers and other practitioners will learn the most appropriate methods of understanding dynamic processes and making projections about the implications of their decisions.

This book provides a sound theoretical basis for the the different gravity field recovery methods and the numerics of satellite-to-satellite tracking data. It represents lectures given at the 'Wilhelm and Else Heraeus Autumn School' in Bad Honnef, Germany, October 4-9, 2015. The emphasis of the school was on providing a sound theoretical basis for the different gravity field recovery methods and the numerics of data analysis. The approaches covered here are the variational equations (classical approach), the acceleration approach and the energy balance approach, all of which are used for global gravity field recovery on the basis of satellite observations. The theory of parameter estimation in satellite gravimetry and concepts for orbit determination are also included. The book guides readers through a broad range of topics in satellite gravimetry, supplemented by the necessary theoretical background and numerical examples. While it provides a comprehensive overview for those readers who are already familiar with satellite gravity data processing, it also offers an essential reference guide for graduate and undergraduate students interested in this field.

Sustainable development within urban and rural areas, transportation systems, logistics, supply chain management, urban health, social services, and architectural design are taken into consideration in the cohesive network models provided in this book. The ideas, methods, and models presented consider city landscapes and quality of life conditions based on mathematical network models and optimization. Interdisciplinary Works from prominent researchers in mathematical modeling, optimization, architecture, engineering, and physics are featured in this volume to promote health and well-being through design. Specific topics include: - Current technology that form the basis of future living in smart cities - Interdisciplinary design and networking of large-scale urban systems - Network communication and route traffic optimization - Carbon dioxide emission reduction - Closed-loop logistics chain management and operation - Modeling the effect urban environments on aging - Health care infrastructure - Urban water system management - Architectural design optimization Graduate students and researchers actively involved in architecture, engineering, building physics, logistics, supply chain management, and mathematical optimization will find the interdisciplinary work presented both informative and inspiring for further research.

Adaptivity and learning have in recent decades become a common concern of scientific disciplines. These issues have arisen in mathematics, physics, biology, informatics, economics, and other fields more or less simultaneously. The aim of this publication is the interdisciplinary discourse on the phenomenon of learning and adaptivity. Different perspectives are presented and compared to find fruitful concepts for the disciplines involved. The authors select problems showing representative traits concerning the frame up, the methods and the achievements rather than to present extended overviews.

This book discusses recent developments and contemporary research in mathematics, statistics and their applications in computing. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world. The conference has emerged as a powerful forum, offering researchers a venue to discuss, interact and collaborate and stimulating the advancement of mathematics and its applications in computer science. The book will allow aspiring researchers to update their knowledge of cryptography, algebra, frame theory, optimizations, stochastic processes, compressive sensing, functional analysis, complex variables, etc. Educating future consumers, users, producers, developers and researchers in mathematics and computing is a challenging task and essential to the development of modern society. Hence, mathematics and its applications in computer science are of vital importance to a broad range of communities, including mathematicians and computing professionals across different educational levels and disciplines.

Column Generation is an insightful overview of the state-of-the-art in integer programming column generation and its many applications. The volume begins with "A Primer in Column Generation" which outlines the theory and ideas necessary to solve large-scale practical problems, illustrated with a variety of examples. Other chapters follow this introduction on "Shortest Path Problems with Resource Constraints," "Vehicle Routing Problem with Time Window," "Branch-and-Price Heuristics," "Cutting Stock Problems," each dealing with methodological aspects of the field. Three chapters deal with transportation applications: "Large-scale Models in the Airline Industry," "Robust Inventory Ship Routing by Column Generation," and "Ship Scheduling with Recurring Visits and Visit Separation Requirements." Production is the focus of another three chapters: "Combining Column Generation and Lagrangian Relaxation," "Dantzig-Wolfe Decomposition for Job Shop Scheduling," and "Applying Column Generation to Machine Scheduling." The final chapter by FranAois Vanderbeck, "Implementing Mixed Integer Column Generation," reviews how to set-up the Dantzig-Wolfe reformulation, adapt standard MIP techniques to the column generation context (branching, preprocessing, primal heuristics), and deal with specific column generation issues (initialization, stabilization, column management strategies).

The book is the first systematic treatment of column generation methodologies. It will provide students, researchers, and experienced column generation users with a much-needed state-of-the-art survey of the field.

Hydraulic Servo-systems details the basic concepts of many recent developments of nonlinear identification and nonlinear control and their application to hydraulic servo-systems: developments such as feedback linearisation and fuzzy control. It also reviews the principles, benefits and limitations associated with standard control design approaches such as linear state feedback control, feedforward control and compensation for static nonlinearities, because of their continued practical importance. Featuring: theoretical (physically based) modelling of hydraulic servo-systems; experimental modelling (system identification); control strategies for hydraulic servo-systems; case studies and experimental results. Appendices outline the most important fundamentals of (nonlinear) differential geometry and fuzzy control. The book is very application-oriented and provides the reader with detailed working procedures and hints for implementation routines and software tools. It will interest scientists and qualified engineers involved in the analysis and design of hydraulic control systems, especially in advanced hydraulic industries, the aeronautical and space and automotive industries.

This volume presents state of the art theories, new developments, and important applications of Partial Least Square (PLS) methods. The text begins with the invited communications of current leaders in the field who cover the history of PLS, an overview of methodological issues, and recent advances in regression and multi-block approaches. The rest of the volume comprises selected, reviewed contributions from the 8th International Conference on Partial Least Squares and Related Methods held in Paris, France, on 26-28 May, 2014. They are organized in four coherent sections: 1) new developments in genomics and brain imaging, 2) new and alternative methods for multi-table and path analysis, 3) advances in partial least square regression (PLSR), and 4) partial least square path modeling (PLS-PM) breakthroughs and applications. PLS methods are very versatile methods that are now used in areas as diverse as engineering, life science, sociology, psychology, brain imaging, genomics, and business among both academics and practitioners. The selected chapters here highlight this diversity with applied examples as well as the most recent advances.