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Linear Systems Control : Deterministic and Stochastic Methods
Modern control theory and in particular state space or state variable methods can be adapted to the description of many different systems because it depends strongly on physical modeling and physical intuition. The laws of physics are in the form of differential equations and for this reason, this book concentrates on system descriptions in this form. This means coupled systems of linear or nonlinear differential equations. The physical approach is emphasized in this book because it is most natural for complex systems. It also makes what would ordinarily be a difficult mathematical subject into one which can straightforwardly be understood intuitively and which deals with concepts which engineering and science students are already familiar.
Linear Partial Differential Equations for Scientists and Engineers
This significantly expanded fourth edition is designed as an introduction to the theory and applications of linear PDEs. The authors provide fundamental concepts, underlying principles, a wide range of applications, and various methods of solutions to PDEs. In addition to essential standard material on the subject, the book contains new material that is not usually covered in similar texts and reference books, including conservation laws, the spherical wave equation, the cylindrical wave equation, higher-dimensional boundary-value problems, the finite element method, fractional partial differential equations, and nonlinear partial differential equations with applications.
Linear Functional Analysis
This introduction to the ideas and methods of linear functional analysis shows how familiar and useful concepts from finite-dimensional linear algebra can be extended or generalized to infinite-dimensional spaces. Aimed at advanced undergraduates in mathematics and physics, the book assumes a standard background of linear algebra, real analysis (including the theory of metric spaces), and Lebesgue integration, although an introductory chapter summarizes the requisite material. The initial chapters develop the theory of infinite-dimensional normed spaces, in particular Hilbert spaces, after which the emphasis shifts to studying operators between such spaces. Functional analysis has applications to a vast range of areas of mathematics; the final chapters discuss the particularly important areas of integral and differential equations.
Linear Estimation and Detection in Krylov Subspaces
Focuses on the foundations of linear estimation theory which is essential for effective signal processing. In its first part, it gives a comprehensive overview of several key methods like reduced-rank signal processing and Krylov subspace methods of numerical mathematics. Based on the derivation of the multistage Wiener filter in its most general form, the relationship between statistical signal processing and numerical mathematics is presented. In the second part, the theory is applied to iterative multiuser detection receivers (Turbo equalization) which are typically desired in wireless communication systems.
Linear Differential Equations and Group Theory from Riemann to Poincaré
A study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. The central focus is on the convergence of three mathematical topics: the hypergeometric and related linear differential equations, group theory, and on-Euclidean geometry. The text for this second edition has been greatly expanded and revised, and the existing appendices enriched with historical accounts of the Riemann–Hilbert problem, the uniformization theorem, Picard–Vessiot theory, and the hypergeometric equation in higher dimensions. The exercises have been retained, making it possible to use the book as a companion to mathematics courses at the graduate level.
Linear Algebra Thoroughly Explained
Linear Algebra Thoroughly Explained provides a comprehensive introduction to the subject suitable for adoption as a self-contained text for courses at undergraduate and postgraduate level. The clear and comprehensive presentation of the basic theory is illustrated throughout with an abundance of worked examples. The book is written for teachers and students of linear algebra at all levels and across mathematics and the applied sciences, particularly physics and engineering.
Limit Cycles of Differential Equations
Contains the lecture series originally delivered at the "Advanced Course on Limit Cycles of Differential Equations" in the Centre de Recerca Matemàtica Barcelona in 2006.The topics covered are the center-focus problem for polynomial vector fields, and the application of abelian integrals to limit cycle bifurcations. Both topics are related to Hilbert's sixteenth problem. In particular, the book will be of interest to students and researchers working in the qualitative theory of dynamical systems.
Light Scattering Reviews 3 : Light Scattering and Reflection
Ddevoted to modern knowledge and milestones in both experimental and theoretical techniques related to light scattering and radiative transport problems. It will consist of 3 parts comprising 11 contributions written by world leading experts in their respective fields. The general focus of the book will be on remote sensing of geophysical media. The first part will be devoted exclusively to studies of single light scattering by particles of different shapes and chemical compositions. The first chapter will review in situ measurements of cloud optical characteristics like cloud extinction and phase function, with the emphasis on ice clouds. Chapter 2 will cover opitcally soft particles common in marine environments and bio-suspensions while Chapter 3 will describe numerical techniques applicable not only to isotropic but also to chiral and anisotropic mdia. The final chapter in this part will deal with spatial symmetries in light scattering problems.
Light Scattering Reviews 2
Part of the ""Light Scattering Reviews"" series that is devoted to modern knowledge and milestones in both experimental and theoretical techniques related to light scattering and radiative transport problems. This work gives a picture of developments in the area of remote sensing and radiative transfer.
Light Scattering Reviews
Light Scattering Reviews is the first book in a series devoted to bringing together the state-of-the-art and milestones in our knowledge of light scattering media optics (LSMO). Contributions from leading researchers focus on both the theoretical and experimental results in the area. The book provides a valuable picture of recent developments in light scattering. It facilitates studies in LSMO and will be of great importance for researchers in a variety of disciplines. Divided into three parts, this volume first discusses single light scattering, followed by multiple light scattering and finally looks at the possible applications in combustion and marine research.
Light Scattering from Polymer Solutions and Nanoparticle Dispersions
Light scattering is a very powerful method to characterize the structure of polymers and nanoparticles in solution. Recent technical developments have strongly enhanced the possible applications of this technique, overcoming previous limitations like sample turbidity or insufficient experimental time scales. However, despite their importance, these new developments have not yet been presented in a comprehensive form. In addition, and maybe even more important to the broad audience, there lacks a simple-to-read textbook for students and non-experts interested in the basic principles and fundamental techniques of light scattering. As part of the Springer Laboratory series, this book tries not only to provide such a simple-to-read and illustrative textbook about the seemingly very complicated topic of light scattering from polymers and nanoparticles in dilute solution, but also intends to cover some of the newest technical developments in experimental light scattering.
Light scattering by systems of particles : Null-field method with discrete sources : Theory and programs
Light Scattering by Systems of Particles comprehensively develops the theory of the null-field method, while covering almost all aspects and current applications. The "Null-field Method with Discrete Sources" is an extension of the Null-field Method (also called T-Matrix Method) to compute light scattering by arbitrarily shaped dielectric particles. This book incorporates FORTRAN programs and exemplary simulation results that demonstrate all aspects of the latest developments of the method. Worked examples of the application of the FORTRAN programs show readers how to adapt or modify the programs for their specific application.
Light Scattering by Optically Soft Particles: Theory and Applications
Deals with a particular class of approximation methods in the context of light scattering by small particles. This class of approximations has been termed as eikonal or soft particle approximations. The eikonal approximation was studied extensively in the potential scattering and then adopted in optical scattering problems. In this context, the eikonal and other soft particle approximations pertain to scatterers whose relative refractive index compared to surrounding medium is close to unity. The study of these approximations is very important because soft particles occur abundantly in nature. For example, the particles that occur in ocean optics, biomedical optics, atmospheric optics and in many industrial applications can be classified as soft particles. This book was written in recognition of the long-standing and current interest in the field of scattering approximations for soft particles. It should prove to be a useful addition for researchers in the field of light scattering.
Light and Light Sources : High-Intensity Discharge Lamps
Light and Light Sources gives an introduction to the working principles of high-intensity discharge (HID) lamps and points out challenges and problems associated with the development and operation of HID lamps. The state-of-the-art in electrode and plasma diagnostics as well as numerical methods used for the understanding of HID lamps are described. This volume addresses students as well as scientists and researchers at universities and in industry.
Light Absorption in Sea Water
Takes a fresh, holistic approach to the problems of light absorption and absorbers in seawaters, discussing the fundamentals of light absorption at various depths in seawaters of different trophicity by absorbers of diverse origin. The authors have drawn their information from a substantial body of contemporary research results published in the subject literature (over 700 references) as well as their own work during the last 30 years. No other book presently available examines the issues of light absorption and absorbers in seawaters in such a manner. The physical and chemical properties, as well as the optical constants, of organic and inorganic suspended particulate matter (SPM), are discussed in the context of their relationship to the light absorption properties of SPM. Special emphasis is placed on the role of the phytoplankton and the pigments it contains which are particularly strong and important absorbers of visible light in the sea.
Lifting Modules : Supplements and Projectivity in Module Theory
Extending modules are generalizations of injective modules and, dually, lifting modules generalize projective supplemented modules. There is a certain asymmetry in this duality. While the theory of extending modules is well documented in monographs and text books, the purpose of our monograph is to provide a thorough study of supplements and projectivity conditions needed to investigate classes of modules related to lifting modules. The text begins with an introduction to small submodules, the radical, variations on projectivity, and hollow dimension. The subsequent chapters consider preradicals and torsion theories (in particular related to small modules), decompositions of modules (including the exchange property and local semi-T-nilpotency), supplements in modules (with specific emphasis on semilocal endomorphism rings), finishing with a long chapter on lifting modules, leading up their use in the theory of perfect rings, Harada rings, and quasi-Frobenius rings.
Lifelong Learning, Participation and Equity
In many countries, schools, universities and other traditional learning institutions are not providing for the educational needs of all members of the community. In many communities, particularly in regional, rural and disadvantaged areas, there are only limited options for people to undertake learning. Limited participation in learning has the danger of reinforcing people’s alienation from mainstream education and from participation and inclusion in social institutions and economic and community life more generally. This book addresses the challenge of identifying effective ways of accommodating the learning needs of all people and in so doing achieving the goals of lifelong learning for all.
Lifelong Learning - Signs, Discourses, Practices
This text explores the different ways in which the various social practices in which people participate becomes signed as learning, how and why that occurs and with what consequences. It takes seriously the linguistic turn in social theory to draw upon semiotics and poststructuralism through which to explore the significance of lifelong learning as an emerging discourse in education. The text explores the different ways in which learning conveys meaning and is given meaning. Given this, lifelong learning therefore is a way, and a significant way, in which learning is fashioned. The text then explores the notion that, if learning is lifelong and lifewide, what precisely is learning as distinct from other social practices and how those practices are given meaning as learning.
Life in the Universe : Expectations and Constraints
Energy, chemistry, solvents, and habitats -- the basic elements of living systems - define the opportunities and limitations for life on other worlds. This class-tested text examines each of these parameters in crucial depth and makes the argument that life forms we would recognize may be more common in our solar system than many assume. It also considers, however, exotic forms of life that would not have to rely on carbon as basic chemical element, solar energy as a main energy source, or water as primary solvent. Finally the question of detecting bio- and geosignature of such life forms is discussed, ranging from Earth environments to deep space. While speculative considerations in this emerging field of science cannot be avoided, the authors have tried to present their study with the breadth and seriousness that a scientific approach to this issue requires. They seek an operational definition of life and investigate the realm of possibilities that nature offers to realize this very special state of matter and avoid scientific jargon wherever possible to make this intrinsically interdisciplinary subject understandable to a broad range of readers.
Life - As a Matter of Fat : The Emerging Science of Lipidomics
Lipids are as important for life as proteins, sugars, and genes. The present book gives a multi-disciplinary perspective on the physics of life and the particular role played by lipids and the lipid-bilayer component of cell membranes. The book is aimed at undergraduate students and young research workers within physics, chemistry, biochemistry, molecular biology, nutrition, as well as pharmaceutical and biomedical sciences. The emphasis is on the physical properties of lipid membranes seen as soft and molecularly structured interfaces. By combining and synthesizing insights obtained from a variety of recent studies, an attempt is made to clarify what membrane structure is and how it can be quantitatively described. Furthermore, it is shown how biological function mediated by membranes is controlled by lipid membrane structure and organization on length scales ranging from the size of the individual molecule, across molecular assemblies of proteins and lipid domains in the range of nanometers, to the size of whole cells. Applications of lipids in nano-technology and biomedicine are also described.
