Turbulent combustion sits at the interface of two important nonlinear, multiscale phenomena: chemistry and turbulence. Its study is extremely timely in view of the need to develop new combustion technologies in order to address challenges associated with climate change, energy source uncertainty, and air pollution. Despite the fact that modeling of turbulent combustion is a subject that has been researched for a number of years, its complexity implies that key issues are still eluding, and a theoretical description that is accurate enough to make turbulent combustion models rigorous and quantitative for industrial use is still lacking. In this book, prominent experts review most of the available approaches in modeling turbulent combustion, with particular focus on the exploding increase in computational resources that has allowed the simulation of increasingly detailed phenomena. The relevant algorithms are presented, the theoretical methods are explained, and various application examples are given. The book is intended for a relatively broad audience, including seasoned researchers and graduate students in engineering, applied mathematics and computational science, engine designers and computational fluid dynamics (CFD) practitioners, scientists at funding agencies, and anyone wishing to understand the state-of-the-art and the future directions of this scientifically challenging and practically important field.

Modeling by Object-Driven Linear Elemental Relations (MODLER) is a computer language for representing linear programming models, completely separate from instances defined by data realizations. It also includes representations of binary variables and logical constraints, which arise naturally in large-scale planning and operational decision support. The basic input to MODLER is a model file, and its basic output is a matrix file that is in a standard (MPS) format for most optimizers and for ANALYZE and RANDMOD. MODLER can also generate a syntax file for ANALYZE to enable automatic translation of activities and constraints into English for intelligent analysis support. The book is accompanied by a DOS version of MODLER on 3.5 inch diskettes and A Laboratory Manual for Teaching Linear Programming is available upon request.

Based on a two-semester course aimed at illustrating various interactions of "pure mathematics" with other sciences, such as hydrodynamics, thermodynamics, statistical physics and information theory, this text unifies three general topics of analysis and physics, which are as follows: the dimensional analysis of physical quantities, which contains various applications including Kolmogorov's model for turbulence; functions of very large number of variables and the principle of concentration along with the non-linear law of large numbers, the geometric meaning of the Gauss and Maxwell distributions, and the Kotelnikov-Shannon theorem; and, finally, classical thermodynamics and contact geometry, which covers two main principles of thermodynamics in the language of differential forms, contact distributions, the Frobenius theorem and the Carnot-Caratheodory metric. It includes problems, historical remarks, and Zorich's popular article, "Mathematics as language and method."

The main focus of this book is a pair of cooperative control problems: consensus and cooperative output regulation. Its emphasis is on complex multi-agent systems characterized by strong nonlinearity, large uncertainty, heterogeneity, external disturbances and jointly connected switching communication topologies. The cooperative output regulation problem is a generalization of the classical output regulation problem to multi-agent systems and it offers a general framework for handling a variety of cooperative control problems such as consensus, formation, tracking and disturbance rejection. The book strikes a balance between rigorous mathematical proof and engineering practicality. Every design method is systematically presented together with illustrative examples and all the designs are validated by computer simulation. The methods presented are applied to several practical problems, among them the leader-following consensus problem of multiple Euler-Lagrange systems, attitude synchronization of multiple rigid-body systems, and power regulation of microgrids. The book gives a detailed exposition of two approaches to the design of distributed control laws for complex multi-agent systems-the distributed-observer and distributed-internal-model approaches. Mastering both will enhance a reader's ability to deal with a variety of complex real-world problems. Cooperative Control of Multi-agent Systems can be used as a textbook for graduate students in engineering, sciences, and mathematics, and can also serve as a reference book for practitioners and theorists in both industry and academia. Some knowledge of the fundamentals of linear algebra, calculus, and linear systems are needed to gain maximum benefit from this book. Advances in Industrial Control reports and encourages the transfer of technology in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. The series offers an opportunity for researchers to present an extended exposition of new work in all aspects of industrial control.

Statistics and hypothesis testing are routinely used in areas (such as linguistics) that are traditionally not mathematically intensive. In such fields, when faced with experimental data, many students and researchers tend to rely on commercial packages to carry out statistical data analysis, often without understanding the logic of the statistical tests they rely on. As a consequence, results are often misinterpreted, and users have difficulty in flexibly applying techniques relevant to their own research they use whatever they happen to have learned. A simple solution is to teach the fundamental ideas of statistical hypothesis testing without using too much mathematics.

This book provides a non-mathematical, simulation-based introduction to basic statistical concepts and encourages readers to try out the simulations themselves using the source code and data provided (the freely available programming language R is used throughout). Since the code presented in the text almost always requires the use of previously introduced programming constructs, diligent students also acquire basic programming abilities in R.

The book is intended for advanced undergraduate and graduate students in any discipline, although the focus is on linguistics, psychology, and cognitive science. It is designed for self-instruction, but it can also be used as a textbook for a first course on statistics. Earlier versions of the book have been used in undergraduate and graduate courses in Europe and the US.

Vasishth and Broe have written an attractive introduction to the foundations of statistics. It is concise, surprisingly comprehensive, self-contained and yet quite accessible. Highly recommended.

Harald Baayen, Professor of Linguistics, University of Alberta, Canada

By using the text students not only learn to do the specific things outlined in the book, they also gain a skill set that empowers them to explore new areas that lie beyond the book s coverage.

Colin Phillips, Professor of Linguistics, University of Maryland, USA

Providing an easy explanation of the fundamentals, methods, and applications of chemometrics

- Acts as a practical guide to multivariate data analysis techniques- Explains the methods used in Chemometrics and teaches the reader to perform all relevant calculations- Presents the basic chemometric methods as worksheet functions in Excel- Includes Chemometrics Add In for download which uses Microsoft Excel(R) for chemometrics training- Online downloads includes workbooks with examples

Little by little we are being provided with an arsenal of operative instruments of a non-numerical nature, in the shape of models and algorithms, capable of providing answers to the "aggressions" which our economics and management systems must withstand, coming from an environment full of turmoil.

In the work which we are presenting, we dare to propose a set of elements from which we hope arise focuses capable of renewing those structures of economic thought which are upheld by the geometrical idea.

The concepts of pretopology and topology, habitually marginalized in economics and management studies, have centred our interest in recent times. We consider that it is not possible to conceive formal structures capable of representing the Darwinism concept of economic behaviour today without recurring to this fundamental generalisation of metric spaces.

In our attempts to find a solid base to the structures proposed for the treatment of economic phenomena, we have frequently resorted to the theory of clans and the theory of affinities with results which we believe to be satisfactory. We would like to go further, establishing, if possible, the connection between their axiomatics at the same time as developing some uncertain pretopologies and topologies capable of linking previously unconnected theories, at the same time easing the creation of other new theories."

Infinite dimensional systems can be used to describe many phenomena in the real world. As is well known, heat conduction, properties of elastic plastic material, fluid dynamics, diffusion-reaction processes, etc., all lie within this area. The object that we are studying (temperature, displace ment, concentration, velocity, etc.) is usually referred to as the state. We are interested in the case where the state satisfies proper differential equa tions that are derived from certain physical laws, such as Newton's law, Fourier's law etc. The space in which the state exists is called the state space, and the equation that the state satisfies is called the state equation. By an infinite dimensional system we mean one whose corresponding state space is infinite dimensional. In particular, we are interested in the case where the state equation is one of the following types: partial differential equation, functional differential equation, integro-differential equation, or abstract evolution equation. The case in which the state equation is being a stochastic differential equation is also an infinite dimensional problem, but we will not discuss such a case in this book."

This book describes a comprehensive approach to applying systems science formally to the deep analysis of a wide variety of complex systems. Detailed 'how-to' examples of the three phases (analysis-modeling-design) of systems science are applied to systems of various types (machines, organic (e.g. ecosystem), and supra-organic (e.g. business organizations and government). The complexity of the global system has reached proportions that seriously challenge our abilities to understand the consequences of our use of technology, modification of natural ecosystems, or even how to govern ourselves. For this reason, complex mathematics is eschewed when simpler structures will suffice, allowing the widest possible audience to apply and benefit from the available tools and concepts of systems science in their own work. The book shows, in detail, how to functionally and structurally deconstruct complex systems using a fundamental language of systems. It shows how to capture the discovered details in a structured knowledge base from which abstract models can be derived for simulation. The knowledge base is also shown to be a basis for generating system design specifications for human-built artifacts, or policy recommendations/policy mechanisms for socio-economic-ecological systems management. The book builds on principles and methods found in the authors' textbook Principles of Systems Science (co-authored with Michael Kalton), but without prerequisites. It will appeal to a broad audience that deals with complex systems every day, from design engineers to economic and ecological systems managers and policymakers.

The efforts in nonlinear control over the last few years have led to the level of generality in which conceptual solutions exist for all systems affine in control and the disturbance, and constructive designs exist for a specific class of nonlinear systems - although broad in terms of physical relevance. This monograph presents the fundamentals of global stabilization and optimal control of nonlinear systems with uncertain models. It offers a unified view of deterministic disturbance attenuation, stochastic control, and adaptive control for nonlinear systems. The book addresses a large audience of researchers, students, engineers and mathematicians in the areas of robust and adaptive nonlinear control, nonlinear H... stochastic nonlinear control (including risk-sensitive), and other related areas of control an d dynamical systems theory.

Institutional and Financial Incentives for Social Insurance provides both an empirical and a theoretical account of the main difficulties presently threatening social insurance systems in most industrialized countries. It analyzes the remedies that have been discussed and sometimes introduced and addresses many questions still left largely unresolved: Are newly implemented or proposed reforms providing the correct incentives to all participants in the system? Is the quality of service improving and, if not, what can be done? How should the budgetary problems be solved considering both intra-generational and inter-generational redistributive policies?

The volume describes a number of studies of social security systems in various countries and assesses the effect of various policies, including welfare or unemployment benefits, training and other active labour market policies, the provision of pension, and competition and budget devolution in health care. It applies empirical tests to individual preferences concerning unemployment compensation, and it analyzes nonfunded and funded social security systems, the transition from one system to the other, and the willingness to pay for pensions.

This book will be of interest to academics, researchers and students in public, labour, health and welfare economics, as well as experts and researchers in social insurance.

These proceedings of the international Conference "Ill-Posed and Non-Classical Problems of Mathematical Physics and Analysis," held at the Samarkand State University, Uzbekistan in September 2000 bring together fundamental research articles in the major areas of the numerated fields of analysis and mathematical physics. The book covers the following topics: theory of ill-posed problems inverse problems for differential equations boundary value problems for equations of mixed type integral geometry mathematical modelling and numerical methods in natural sciences

This volume contains a concise description of important mathematical methods of dynamics and suitable economic models. It covers discrete as well as continuous time systems, linear and nonlinear models. Mixing traditional and modern materials, the study covers dynamics with and without optimization, naive and rational expectations, respectively. In addition to standard models of growth and cycles, the book also contains original studies on control of a multisector economy and expectations driven multicohort economy. Numerous examples, problems (with solutions) and figures complete the book.

The mathematical theory of contact mechanics is a growing field in engineering and scientific computing. This book is intended as a unified and readily accessible source for mathematicians, applied mathematicians, mechanicians, engineers and scientists, as well as advanced students. The first part describes models of the processes involved like friction, heat generation and thermal effects, wear, adhesion and damage. The second part presents many mathematical models of practical interest and demonstrates the close interaction and cross-fertilization between contact mechanics and the theory of variational inequalities. The last part reviews further results, gives many references to current research and discusses open problems and future developments. The book can be read by mechanical engineers interested in applications. In addition, some theorems and their proofs are given as examples for the mathematical tools used in the models.

"Symmetries and Semi-invariants in the Analysis of Nonlinear Systems" details the analysis of continuous- and discrete-time dynamical systems described by differential and difference equations respectively. Differential geometry provides the essential tools for the analysis, tools such as first-integrals or orbital symmetries, together with normal forms of vector fields and of maps. The use of such tools allows the solution of some important problems, studied in detail in the text, which includelinearization by state immersionand the computation of nonlinear superposition formulae for nonlinear systems described by solvable Lie algebras.

The theory is developed for general nonlinear systems and, in view of their importance for modeling physical systems, specialized for the class of Hamiltonian systems. By using the strong geometric structure of Hamiltonian systems, the results proposed are stated in a quite different, less complex and more easily comprehensible manner. Throughout the text the results are illustrated by many examples, some of them being physically motivated systems, so that the reader can appreciate how much insight is gained by means of these techniques. Various control systems applications of the techniques are characterized including:

. computation of the flow of nonlinear systems;

. computation of semi-invariants;

. computation of Lyapunov functions for stability analysis.

"Symmetries and Semi-invariants in the Analysis of Nonlinear Systems" will be of interest to researchers and graduate students studying control theory, particularly with respect to nonlinear systems. All the necessary background and mathematical derivations are related in detail but in a simple writing style that makes the book accessible in depth to readers having a standard knowledge of real analysis, linear algebra and systems theory. "

Welcome to ANALYZE, designed to provide computer assistance for analyzing linear programs and their solutions. Chapter 1 gives an overview of ANALYZE and how to install it. It also describes how to get started and how to obtain further documentation and help on-line. Chapter 2 reviews the forms of linear programming models and describes the syntax of a model. One of the routine, but important, functions of ANALYZE is to enable convenient access to rows and columns in the matrix by conditional delineation. Chapter 3 illustrates simple queries, like DISPLAY, LIST, and PICTURE. This chapter also introduces the SUBMAT command level to define any submatrix by an arbitrary sequence of additions, deletions and reversals. Syntactic explanations and a schema view are also illustrated. Chapter 4 goes through some elementary exercises to demonstrate computer assisted analysis and introduce additional conventions of the ANALYZE language. Besides simple queries, it demonstrates the INTERPRT command, which automates the analysis process and gives English explanations of results. The last 2 exercises are diagnoses of elementary infeasible instances of a particular model. Chapter 5 progresses to some advanced uses of ANALYZE. The first is blocking to obtain macro views of the model and for finding embedded substructures, like a netform. The second is showing rates of substitution described by the basic equations. Then, the use of the REDUCE and BASIS commands are illustrated for a variety of applications, including solution analysis, infeasibility diagnosis, and redundancy detection."

Mechanics and mathematics have been complementary partners since Newton's time and the history of science shows much evidence of the beneficial influence of these disciplines on each other. Driven by increasingly elaborate modern technological applications the symbiotic relationship between mathematics and mechanics is continually growing. However, the increasingly large number of specialist journals has generated a duality gap between the two partners, and this gap is growing wider.
Advances in Mechanics and Mathematics (AMMA) is intended to bridge the gap by providing multi-disciplinary publications. This volume, AMMA 2002, includes two parts with three articles by four subject experts. Part 1 deals with nonsmooth static and dynamic systems. A systematic mathematical theory for multibody dynamics with unilateral and frictional constraints and a brief introduction to hemivariational inequalities together with some new developments in nonsmooth semi-linear elliptic boundary value problems are presented. Part 2 provides a comprehensive introduction and the latest research on dendritic growth in fluid mechanics, one of the most profound and fundamental subjects in the area of interfacial pattern formation, a commonly observed phenomenon in crystal growth and solidification processes.
Audience: Scientists and mathematicians, including advanced students (doctoral and post-doctoral level) at universities and in industry interested in mechanics and applied mathematics.

Our time is characterized by an explosive growth in the use of ever more complicated and sophisticated (computer) models. These models rely on dynamical systems theory for the interpretation of their results and on probability theory for the quantification of their uncertainties. A conscientious and intelligent use of these models requires that both these theories are properly understood. This book is to provide such understanding. It gives a unifying treatment of dynamical systems theory and probability theory. It covers the basic concepts and statements of these theories, their interrelations, and their applications to scientific reasoning and physics. The book stresses the underlying concepts and mathematical structures but is written in a simple and illuminating manner without sacrificing too much mathematical rigor. The book is aimed at students, post-docs, and researchers in the applied sciences who aspire to better understand the conceptual and mathematical underpinnings of the models that they use. Despite the peculiarities of any applied science, dynamics and probability are the common and indispensable tools in any modeling effort. The book is self-contained, with many technical aspects covered in appendices, but does require some basic knowledge in analysis, linear algebra, and physics. Peter Muller, now a professor emeritus at the University of Hawaii, has worked extensively on ocean and climate models and the foundations of complex system theories.

A complete and balanced account of communication theory, providing an understanding of both Fourier analysis (and the concepts associated with linear systems) and the characterization of such systems by mathematical operators. Presents applications of the theories to the diffraction of optical wave-fields and the analysis of image-forming systems. Emphasizes a strong mathematical foundation and includes an in-depth consideration of the phenomena of diffraction. Combines all theories to describe the image-forming process in terms of a linear filtering operation for both coherent and incoherent imaging. Chapters provide carefully designed sets of problems. Also includes extensive tables of properties and pairs of Fourier transforms and Hankle Transforms.

Complex analysis is found in many areas of applied mathematics, from fluid mechanics, thermodynamics, signal processing, control theory, mechanical and electrical engineering to quantum mechanics, among others. And of course, it is a fundamental branch of pure mathematics. The coverage in this text includes advanced topics that are not always considered in more elementary texts. These topics include, a detailed treatment of univalent functions, harmonic functions, subharmonic and superharmonic functions, Nevanlinna theory, normal families, hyperbolic geometry, iteration of rational functions, and analytic number theory. As well, the text includes in depth discussions of the Dirichlet Problem, Green's function, Riemann Hypothesis, and the Laplace transform. Some beautiful color illustrations supplement the text of this most elegant subject.

This book addresses the COVID-19 pandemic from a quantitative perspective based on mathematical models and methods largely used in nonlinear physics. It aims to study COVID-19 epidemics in countries and SARS-CoV-2 infections in individuals from the nonlinear physics perspective and to model explicitly COVID-19 data observed in countries and virus load data observed in COVID-19 patients. The first part of this book provides a short technical introduction into amplitude spaces given by eigenvalues, eigenvectors, and amplitudes.In the second part of the book, mathematical models of epidemiology are introduced such as the SIR and SEIR models and applied to describe COVID-19 epidemics in various countries around the world. In the third part of the book, virus dynamics models are considered and applied to infections in COVID-19 patients. This book is written for researchers, modellers, and graduate students in physics and medicine, epidemiology and virology, biology, applied mathematics, and computer sciences. This book identifies the relevant mechanisms behind past COVID-19 outbreaks and in doing so can help efforts to stop future COVID-19 outbreaks and other epidemic outbreaks. Likewise, this book points out the physics underlying SARS-CoV-2 infections in patients and in doing so supports a physics perspective to address human immune reactions to SARS-CoV-2 infections and similar virus infections.

This book explains how standard micro-founded macroeconomics is misguided and proposes an alternative method based on statistical physics. The Great Recession following the bankruptcy of Lehman Brothers in September 2015 amply demonstrated that mainstream micro-founded macroeconomics was in trouble. The new approach advanced in this book reasonably explains important macro-problems such as employment, business cycles, growth, and inflation/deflation. The key concept is demand failures, which modern micro-founded macroeconomics has ignored. "It (Chapter 3) captures analytically a good part of the intuition that underlies the Keynesian economics of people like Tobin and me." Robert Solow, Emeritus Institute Professor of Economics, Massachusetts Institute of Technology, Nobel Laureate in Economics, 1987 "Professor Hiroshi Yoshikawa provides a unique synthesis of statistical physics and macro-economic theory in order to confront the dismal failure in economics and in finance to understand how an economy or a financial market works, given the heterogeneous decision making of many different individual interacting actors. Economics has failed in this regard with the naive and often misleading concept of "representative agents." The author presents many insights on the historical development, concepts, and errors made by the most illustrious economists in the past. This book should be essential readings for any economics students as well as academic researchers and policy makers, who should learn to bring back good-sense thinking in their impactful decisions." Didier Sornette, Professor on the Chair of Entrepreneurial Risks at the Swiss Federal Institute of Technology Zurich (ETH Zurich)

In addition to expanding and clarifying a number of sections of the first edition, it generalizes the analysis that eliminates the noncausal pre-acceleration so that it applies to removing any pre-deceleration as well. It also introduces a robust power series solution to the equation of motion that produces an extremely accurate solution to problems such as the motion of electrons in uniform magnetic fields.

To protect the Earth, China has launched its target of peaking carbon dioxide emissions by 2030, and achieving carbon neutrality by 2060 , which greatly encourages the use and development of renewable energy. Supercritical CO2 power cycle is a promising technology and the radial inflow turbine is the most important component of it, whose design and optimisation are considered as great challenges. This book introduces simulation tools and methods for supercritical CO2 radial inflow turbine, including a high fidelity quasi-one-dimensional design procedure, a non-ideal compressible fluid dynamics Riemann solver within open-source CFD software OpenFOAM framework, and a multi-objective Nelder-Mead geometry optimiser. Enhanced one-dimensional loss models are presented for providing a new insight towards the preliminary design of the supercritical CO2 radial inflow turbine. Since the flow phenomena within the blade channels are complex, involving fluid flow, shock wave transmission and boundary layer separation, only employing the ideal gas model is inadequate to predict the performance of the turbine. Thus, a non-ideal compressible fluid dynamics Riemann solver based on OpenFOAM library is developed. This book addresses the issues related to the turbine design and blade optimization and provides leading techniques. Hence, this book is of great value for the readers working on the supercritical CO2 radial inflow turbine and understanding the knowledge of CFD and turbomachinery.