This book concerns issues related to biomathematics, medicine, or cybernetics as practiced by engineers. Considered population dynamics models are still in the interest of researchers, and even this interest is increasing, especially now in the time of SARS-CoV-2 coronavirus pandemic, when models are intensively studied in order to help predict its behaviour within human population. The structures of population dynamics models and practical methods of finding their solutions are discussed. Finally, the hypothesis of the existence of non-trivial ergodic properties of the model of erythropoietic response dynamics formulated by A. Lasota in the form of delay differential equation with unimodal feedback is analysed. The research can be compared with actual medical data, as well as shows that the structures of population models can reflect the dynamic structures of reality.

The Poisson process, a core object in modern probability, enjoys a richer theory than is sometimes appreciated. This volume develops the theory in the setting of a general abstract measure space, establishing basic results and properties as well as certain advanced topics in the stochastic analysis of the Poisson process. Also discussed are applications and related topics in stochastic geometry, including stationary point processes, the Boolean model, the Gilbert graph, stable allocations, and hyperplane processes. Comprehensive, rigorous, and self-contained, this text is ideal for graduate courses or for self-study, with a substantial number of exercises for each chapter. Mathematical prerequisites, mainly a sound knowledge of measure-theoretic probability, are kept in the background, but are reviewed comprehensively in the appendix. The authors are well-known researchers in probability theory; especially stochastic geometry. Their approach is informed both by their research and by their extensive experience in teaching at undergraduate and graduate levels.

Modern economic growth is characterized by structural changes based on the introduction of new technologies into economics. The replacement and renova tion of technologies in industrial environments undergoing technical change is clearly one of the key aspects of economic development. The mathematical modeling of evolutionary economics under technical change (TC) has been rigorously considered by many authors during last decades. There is a wide variety of economic approaches and models describing different aspects of technical change. Among these are the models of embodied technical progress [19], [35], [70], [129], endogenous growth models [94], [102], the models of technological innovations [31], [32], [41], and others. The perspective self organization evolutionary approach is developed in [20], [38], [122], [123], [124], [126], which unites the aspects of diffusion of new technologies, technological and behavioral diversity of firms, learning mechanisms, age-dependent effects, and other important features of real-life economics. On the whole, an interest in evolutionary economics has brought considerable progress in the description and conceptualization of the sources, characteristics, direction and effects of technical change [125]. However, the modeling and control of technology lifetime under technical change has received rather little attention in mathematical economics in con trary to other aspects of technical progress. The lifetime of technologies has rarely been formally treated as a part of more general mathematical theory of economic dynamics. A problem which is still to be resolved consists in establishing the rational strategies of technologies' replacement under various assumptions on the behavior of technical change.

This thesis develops a pioneering methodology and a concept for identifying critical loads and load model parameters in large power networks based on their influence on power system stability. The research described in the thesis first develops an automatic load modelling tool (ALMT) that can be used to automatically build load model from actual measured power system data without human intervention and the benefits of the ALMY are explored. Secondly, it develops a pioneering framework based on Morris screening method for ranking power system load model parameters based on their influence on overall power system stability (voltage, frequency, transient and small disturbance stability) considering different load models and loading conditions. Thirdly, a novel probabilistic methodology for determining the accuracy levels of critical load model parameters has been developed. This book will be of interest to students and researchers within the field of electrical engineering, as well as industry professionals.

This volume is concerned with a detailed description of the canonical operator method - one of the asymptotic methods of linear mathematical physics. The book is, in fact, an extension and continuation of the authors' works [59], [60], [65]. The basic ideas are summarized in the Introduction. The book consists of two parts. In the first, the theory of the canonical operator is develop ed, whereas, in the second, many applications of the canonical operator method to concrete problems of mathematical physics are presented. The authors are pleased to express their deep gratitude to S. M. Tsidilin for his valuable comments. THE AUTHORS IX INTRODUCTION 1. Various problems of mathematical and theoretical physics involve partial differential equations with a small parameter at the highest derivative terms. For constructing approximate solutions of these equations, asymptotic methods have long been used. In recent decades there has been a renaissance period of the asymptotic methods of linear mathematical physics. The range of their applicability has expanded: the asymptotic methods have been not only continuously used in traditional branches of mathematical physics but also have had an essential impact on the development of the general theory of partial differential equations. It appeared recently that there is a unified approach to a number of problems which, at first sight, looked rather unrelated.

This book presents the stream-tube method (STM), a method offering computational means of dealing with the two- and three-dimensional properties of numerous incompressible materials in static and dynamic conditions. The authors show that the kinematics and stresses associated with the flow and deformation in such materials can be treated by breaking the system down into simple computational sub-domains in which streamlines are straight and parallel and using one or two mapping functions in steady-state and non-steady-state conditions. The STM is considered for various problems in non-Newtonian fluid mechanics with different geometries. The book makes use of examples and applications to illustrate the use of the STM. It explores the possibilities of computation on simple mapped rectangular domains and three-dimensional parallel-piped domains under different conditions. Complex materials with memory are considered simply without particle tracking problems. Readers, including researchers, engineers and graduate students, with a foundational knowledge of calculus, linear algebra, differential equations and fluid mechanics will benefit most greatly from this book.

As technology progresses, we are able to handle larger and larger datasets. At the same time, monitoring devices such as electronic equipment and sensors (for registering images, temperature, etc.) have become more and more sophisticated. This high-tech revolution offers the opportunity to observe phenomena in an increasingly accurate way by producing statistical units sampled over a finer and finer grid, with the measurement points so close that the data can be considered as observations varying over a continuum. Such continuous (or functional) data may occur in biomechanics (e.g. human movements), chemometrics (e.g. spectrometric curves), econometrics (e.g. the stock market index), geophysics (e.g. spatio-temporal events such as El Nino or time series of satellite images), or medicine (electro-cardiograms/electro-encephalograms). It is well known that standard multivariate statistical analyses fail with functional data. However, the great potential for applications has encouraged new methodologies able to extract relevant information from functional datasets. This Handbook aims to present a state of the art exploration of this high-tech field, by gathering together most of major advances in this area. Leading international experts have contributed to this volume with each chapter giving the key original ideas and comprehensive bibliographical information. The main statistical topics (classification, inference, factor-based analysis, regression modelling, resampling methods, time series, random processes) are covered in the setting of functional data. The twin challenges of the subject are the practical issues of implementing new methodologies and the theoretical techniques needed to expand the mathematical foundations and toolbox. The volume therefore mixes practical, methodological and theoretical aspects of the subject, sometimes within the same chapter. As a consequence, this book should appeal to a wide audience of engineers, practitioners and graduate students, as well as academic researchers, not only in statistics and probability but also in the numerous related application areas.

This monograph focuses on the mathematical and numerical analysis of simplicial partitions and the finite element method. This active area of research has become an essential part of physics and engineering, for example in the study of problems involving heat conduction, linear elasticity, semiconductors, Maxwell's equations, Einstein's equations and magnetic and gravitational fields. These problems require the simulation of various phenomena and physical fields over complicated structures in three (and higher) dimensions. Since not all structures can be decomposed into simpler objects like d-dimensional rectangular blocks, simplicial partitions are important. In this book an emphasis is placed on angle conditions guaranteeing the convergence of the finite element method for elliptic PDEs with given boundary conditions. It is aimed at a general mathematical audience who is assumed to be familiar with only a few basic results from linear algebra, geometry, and mathematical and numerical analysis.

This book presents new results on applications of geometric algebra. The time when researchers and engineers were starting to realize the potential of quaternions for - plications in electrical, mechanic, and control engineering passed a long time ago. Since the publication of Space-Time Algebra by David Hestenes (1966) and Clifford Algebra to Geometric Calculus: A Uni?ed Language for Mathematics and Physics by David Hestenes and Garret Sobczyk (1984), consistent progress in the app- cations of geometric algebra has taken place. Particularly due to the great dev- opments in computer technology and the Internet, researchers have proposed new ideas and algorithms to tackle a variety of problems in the areas of computer science and engineering using the powerful language of geometric algebra. In this process, pioneer groups started the conference series entitled "Applications of Geometric Algebra in Computer Science and Engineering" (AGACSE) in order to promote the research activity in the domain of the application of geometric algebra. The ?rst conference, AGACSE'1999, organized by Eduardo Bayro-Corrochano and Garret Sobczyk, took place in Ixtapa-Zihuatanejo, Mexico, in July 1999. The contri- tions were published in Geometric Algebra with Applications in Science and En- neering, Birkhauser, 2001. The second conference, ACACSE'2001, was held in the Engineering Department of the Cambridge University on 9-13 July 2001 and was organizedbyLeoDorst,ChrisDoran,andJoanLasenby. Thebestconferencecont- butions appeared as a book entitled Applications of Geometric Algebra in Computer Science and Engineering, Birkhauser, 2002. The third conference, AGACSE'2008, took place in August 2008 in Grimma, Leipzig, Germany.

Cognition-driven decision support system (DSS) has been recognized as a paradigm in the research and development of business intelligence (BI). Cognitive decision support aims to help managers in their decision making from human cognitive aspects, such as thinking, sensing, understanding and predicting, and fully reuse their experience. Among these cognitive aspects, decision makers situation awareness (SA) and mental models are considered to be two important prerequisites for decision making, particularly in ill-structured and dynamic decision situations with uncertainties, time pressure and high personal stake. In today s business domain, decision making is becoming increasingly complex. To make a successful decision, managers SA about their business environments becomes a critical factor.

This book presents theoretical models as well practical techniques of cognitiondriven DSS. It first introduces some important concepts of cognition orientation in decision making process and some techniques in related research areas including DSS, data warehouse and BI, offering readers a preliminary for moving forward in this book. It then proposes a cognition-driven decision process (CDDP) model which incorporates SA and experience (mental models) as its central components. The goal of the CDDP model is to facilitate cognitive decision support to managers on the basis of BI systems. It also presents relevant techniques developed to support the implementation of the CDDP model in a BI environment. Key issues addressed of a typical business decision cycle in the CDDP model include: natural language interface for a manager s SA input, extraction of SA semantics, construction of data warehouse queries based on the manger s SA and experience, situation information retrieval from data warehouse, how the manager perceives situation information and update SA, how the manager s SA leads to a final decision. Finally, a cognition-driven DSS, FACETS, and two illustrative applications of this system are discussed."

Nonlinear elliptic problems play an increasingly important role in mathematics, science and engineering, creating an exciting interplay between the subjects. This is the first and only book to prove in a systematic and unifying way, stability, convergence and computing results for the different numerical methods for nonlinear elliptic problems. The proofs use linearization, compact perturbation of the coercive principal parts, or monotone operator techniques, and approximation theory. Examples are given for linear to fully nonlinear problems (highest derivatives occur nonlinearly) and for the most important space discretization methods: conforming and nonconforming finite element, discontinuous Galerkin, finite difference, wavelet (and, in a volume to follow, spectral and meshfree) methods. A number of specific long open problems are solved here: numerical methods for fully nonlinear elliptic problems, wavelet and meshfree methods for nonlinear problems, and more general nonlinear boundary conditions. We apply it to all these problems and methods, in particular to eigenvalues, monotone operators, quadrature approximations, and Newton methods. Adaptivity is discussed for finite element and wavelet methods.
The book has been written for graduate students and scientists who want to study and to numerically analyze nonlinear elliptic differential equations in Mathematics, Science and Engineering. It can be used as material for graduate courses or advanced seminars.

Recent advances in scientific computing have caused the field of aerodynamics to change at a rapid pace, simplifying the design cycle of aerospace vehicles enormously - this book takes the readers from core concepts of aerodynamics to recent research, using studies and real-life scenarios to explain problems and their solutions. This book presents in detail the important concepts in computational aerodynamics and aeroacoustics taking readers from the fundamentals of fluid flow and aerodynamics to a more in-depth analysis of acoustic waves, aeroacoustics, computational modelling and processing. This book will be of use to students in multiple branches of engineering, physics and applied mathematics. Additionally, the book can also be used as a text in professional development courses for industry engineers and as a self-help reference for active researchers in both academia and the industry.

This book is aimed to provide comprehensive and systematic knowledge of kinematic synthesis as developed up to date. Modern mechanical systems require advance kinematics knowledge to support mechanism design with sound theories and methods. The book includes not only the classical foundations of kinematic synthesis, but also the latest advances developed by the authors. Moreover, many examples are included to illustrate both methods and their supporting theory. The focus is on systems of rigid bodies forming closed loops. The four-bar linkage, representing the foundations of mechanical systems, is given due attention, in its three domains: planar, spherical, and spatial. The book contains six chapters, the first two covering fundamentals for kinematic synthesis, including qualitative synthesis. Chapters 3-5 describe, in full detail, the function, motion, and path syntheses of single-dof linkages. In the last chapter, the synthesis of single-dof complex linkages, including six-bar and ten-bar linkages, is introduced. The book is suitable for graduate students of mechanical engineering, researchers of mechanism and robot design, and machine design engineers.

This book presents the state of the art in High Performance Computing on modern supercomputer architectures. It addresses trends in hardware and software development in general, as well as the future of High Performance Computing systems and heterogeneous architectures. The contributions cover a broad range of topics, from improved system management to Computational Fluid Dynamics, High Performance Data Analytics, and novel mathematical approaches for large-scale systems. In addition, they explore innovative fields like coupled multi-physics and multi-scale simulations. All contributions are based on selected papers presented at the 26th and 28th Workshops on Sustained Simulation Performance, held at the High Performance Computing Center, University of Stuttgart, Germany, in October 2017 and 2018, and the 27th and 29th Workshops on Sustained Simulation Performance, held at the Cyberscience Center, Tohoku University, Japan, in March 2018 and 2019.

Structural health monitoring (SHM) has emerged as a prominent research area in recent years owing to increasing concerns about structural safety, and the need to monitor and extend the lives of existing structures. Structural Health Monitoring Using Genetic Fuzzy Systems elaborates the process of intelligent SHM development and implementation using the evolutionary system. The use of a genetic algorithm automates the development of the fuzzy system, and makes the method easy to use for problems involving a large number of measurements, damage locations and sizes; such problems being typical of SHM. The ideas behind fuzzy logic, genetic algorithms and genetic fuzzy systems are also explained. The functionality of the genetic fuzzy system architecture is elucidated within a case-study framework, covering: * SHM of beams; * SHM of composite tubes; and * SHM of helicopter rotor blades. Structural Health Monitoring Using Genetic Fuzzy Systems will be useful for aerospace, civil and mechanical engineers working with structures and structured components. It will also be useful for computer scientists and applied mathematicians interested in the application of genetic fuzzy systems to engineering problems.

This research monograph offers an introduction to advanced quantum field theoretical techniques for many-particle systems beyond perturbation theory. Several schemes for resummation of the Feynman diagrams are described. The resulting approximations are especially well suited for strongly correlated fermion and boson systems. Also considered is the crossover from BCS superconductivity to Bose--Einstein condensation in fermion systems with strong attractive interaction. In particular, a field theoretic formulation of "bosonization" is presented; it is published here for the first time. This method is applied to the fractional quantum Hall effect, to the Coulomb plasma, and to several exactly solvable models.

This thesis addresses a novel application of network modelling methodologies to power transformers. It develops a novel thermal model and compares its performance against that of a commercial computational fluid dynamics (CFD) code, as well as in experiments conducted in a dedicated setup built exclusively for this purpose. Hence, the thesis cross-links three of the most important aspects in high-quality research: model development, simulation and experimental validation. Network modelling is used to develop a tool to simulate the thermal performance of power transformers, widely acknowledged to be critical assets in electrical networks. After the strong de-regulation of electricity markets and de-carbonization of worldwide economies, electrical networks have been changing fast. Both asset owners and equipment manufacturers are being driven to develop increasingly accurate modelling capabilities in order to optimize either their operation or their design. Temperature is a critical parameter in every electric machine and power transformers are no exception. As such, the thesis is relevant for a wide range of stakeholders, from utilities to power transformer manufacturers, as well as researchers interested in the energy industry. It is written in straightforward language and employs a highly pedagogic approach, making it also suitable for non-experts.

This book highlights new methods and parametric algorithms for the digital coherent processing of signals in airborne radar systems located on air vehicles. Using the autoregressive (AR) model, it delivers more accurate danger assessments for flight in wind shear and atmospheric turbulence, while also suggesting how they could be implemented. Given its scope, the book is intended for technical experts whose work involves the development, production and operation of airborne radio-electronic systems.

This proceedings volume contains a selection of papers presented at the Fourth International Conference on High Performance Scientific Computing held at the Hanoi Institute of Mathematics, Vietnamese Academy of Science and Technology (VAST), March 2-6, 2009. The conference was organized by the Hanoi Institute of Mathematics, the Interdisciplinary Center for Scientific Computing (IWR), Heidelberg, and its Heidelberg Graduate School of Mathematical and Computational Methods for the Sciences, and Ho Chi Minh City University of Technology. The contributions cover the broad interdisciplinary spectrum of scientific computing and present recent advances in theory, development of methods, and applications in practice. Subjects covered are mathematical modelling, numerical simulation, methods for optimization and control, parallel computing, software development, applications of scientific computing in physics, mechanics, biology and medicine, engineering, hydrology problems, transport, communication networks, production scheduling, industrial and commercial problems.

This book gathers a selection of invited and contributed lectures from the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) held in Lausanne, Switzerland, August 26-30, 2013. It provides an overview of recent developments in numerical analysis, computational mathematics and applications from leading experts in the field. New results on finite element methods, multiscale methods, numerical linear algebra and discretization techniques for fluid mechanics and optics are presented. As such, the book offers a valuable resource for a wide range of readers looking for a state-of-the-art overview of advanced techniques, algorithms and results in numerical mathematics and scientific computing.

The simulation of complex engineering problems often involves an interaction or coupling of individual phenomena, which are traditionally related by themselves to separate fields of applied mechanics. Typical examples of these so- called multifield problems are the thermo-mechanical analysis of solids with coupling between mechanical stress analysis and thermal heat transfer processes, the simulation of coupled deformation and fluid transport mechanisms in porous media, the prediction of mass transport and phase transition phenomena of mixtures, the analysis of sedimentation proces- ses based on an interaction of particle dynamics and viscous flow, the simulation of multibody systems and fluid-structure interactions based on solid-to-solid and solid-to-fluid contact mechanisms.

A. K. Louis, Universitat des Saarlandes, Germany P. Maass, Universitat Potsdam, Germany A. Rieder, Universitat des Saarlandes, Germany Wavelets have in recent years brought new approaches to the areas of analysis and synthesis of signals, a few examples of which include pattern recognition, data compression, numerical analysis, quantum field theory and acoustics. In this book the authors take the reader through both the theory of wavelets and their applications. Chapter one is devoted to the theoretical background of the wavelet transform and to some of its properties, moving on to the discrete transform. The second chapter addresses the functions of wavelets within mathematics and their construction is introduced. Finally, chapter three presents a selection of the broad variety of applications of wavelets, including examples from signal analysis, quality control, data compression in digital image processing, the regularlization of ill posed problems and numerical analysis of boundary value problems. This book provides an invaluable resource for researchers and professionals in applied mathematics, particularly in numerical analysis and signal processing, as well as for engineers and physicists with a strong mathematical background. Contents Notations Introduction

1. The Continuous Wavelet Transform
2. The Discrete Wavelet Transform
3. Applications of the Wavelet Transform

The new edition includes additional analytical methods in the classical theory of viscoelasticity. This leads to a new theory of finite linear viscoelasticity of incompressible isotropic materials. Anisotropic viscoplasticity is completely reformulated and extended to a general constitutive theory that covers crystal plasticity as a special case.

The book provides fault detection and diagnosis approaches from the perspective of filtering analysis. In order to design fault detection filters, it uses set-membership principles to deal with the unknown but bounded noise term. Some regular geometric spaces are introduced, such as the ellipsoid, polyhedron, interval, to describe the feasible parameter sets of the given system. Both principles and engineering practice have been addressed, with more weight placed on engineering practice. Some typical application cases are studied for fault detection and diagnosis in detail, which are power converter, permanent magnet synchronous motor, pitch system of wind turbine. Given its scope, the book offers a valuable guide for students, teachers, engineers and researchers in the field of fault detection and diagnosis.

With approximately 2500 problems, this book provides a collection of practical problems on the basic and advanced data structures, design, and analysis of algorithms. To make this book suitable for self-instruction, about one-third of the algorithms are supported by solutions, and some others are supported by hints and comments. This book is intended for students wishing to deepen their knowledge of algorithm design in an undergraduate or beginning graduate class on algorithms, for those teaching courses in this area, for use by practicing programmers who wish to hone and expand their skills, and as a self-study text for graduate students who are preparing for the qualifying examination on algorithms for a Ph.D. program in Computer Science or Computer Engineering. About all, it is a good source for exam problems for those who teach algorithms and data structure. The format of each chapter is just a little bit of instruction followed by lots of problems. This book is intended to augment the problem sets found in any standard algorithms textbook. This book * begins with four chapters on background material that most algorithms instructors would like their students to have mastered before setting foot in an algorithms class. The introductory chapters include mathematical induction, complexity notations, recurrence relations, and basic algorithm analysis methods. * provides many problems on basic and advanced data structures including basic data structures (arrays, stack, queue, and linked list), hash, tree, search, and sorting algorithms. * provides many problems on algorithm design techniques: divide and conquer, dynamic programming, greedy algorithms, graph algorithms, and backtracking algorithms. * is rounded out with a chapter on NP-completeness.