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The Functional Analysis of Quantum Information Theory: A Collection of Notes Based on Lectures by Gilles Pisier, K. R. Parthasarathy, Vern Paulsen and Andreas Winter (Lecture Notes in Physics #902)

This book provides readers with a concise introduction to current studies on operator-algebras and their generalizations, operator spaces and operator systems, with a special focus on their application in quantum information science. This basic framework for the mathematical formulation of quantum information can be traced back to the mathematical work of John von Neumann, one of the pioneers of operator algebras, which forms the underpinning of most current mathematical treatments of the quantum theory, besides being one of the most dynamic areas of twentieth century functional analysis. Today, von Neumann’s foresight finds expression in the rapidly growing field of quantum information theory. These notes gather the content of lectures given by a very distinguished group of mathematicians and quantum information theorists, held at the IMSc in Chennai some years ago, and great care has been taken to present the material as a primer on the subject matter. Starting from the basic definitions of operator spaces and operator systems, this text proceeds to discuss several important theorems including Stinespring’s dilation theorem for completely positive maps and Kirchberg’s theorem on tensor products of C*-algebras. It also takes a closer look at the abstract characterization of operator systems and, motivated by the requirements of different tensor products in quantum information theory, the theory of tensor products in operator systems is discussed in detail. On the quantum information side, the book offers a rigorous treatment of quantifying entanglement in bipartite quantum systems, and moves on to review four different areas in which ideas from the theory of operator systems and operator algebras play a natural role: the issue of zero-error communication over quantum channels, the strong subadditivity property of quantum entropy, the different norms on quantum states and the corresponding induced norms on quantum channels, and, lastly, the applications of matrix-valued random variables in the quantum information setting.

Functional Approach to Nonlinear Models of Water Flow in Soils (Mathematical Modelling: Theory and Applications #21)

This work of applied mathematics focuses on the functional study of the nonlinear boundary value problems relating to water flow in porous media, a topic which has not up to now been explored in book form. The author shows that abstract theory may be sometimes easier and richer in consequences for applications than standard classical approaches are. The volume deals with diffusion type models, emphasizing the mathematical treatment of their nonlinear aspects.

Functional Differential Equations and Bifurcation: Proceedings of a Conference, Held at Sao Carlos, Brazil, July 2-7, 1979 (Lecture Notes in Mathematics #799)

Functional Fractional Calculus for System Identification and Controls

In this book, not only are mathematical abstractions discussed in a lucid manner, but also several practical applications are given particularly for system identification, description and then efficient controls. The reader gets a feeling of the wide applicability of fractional calculus in the field of science and engineering. With this book, a starter can understand the concepts of this emerging field with a minimal effort and basic mathematics.

Functional Integration: Basics and Applications (Nato Science Series B: #361)

The program of the Institute covered several aspects of functional integration -from a robust mathematical foundation to many applications, heuristic and rigorous, in mathematics, physics, and chemistry. It included analytic and numerical computational techniques. One of the goals was to encourage cross-fertilization between these various aspects and disciplines. The first week was focused on quantum and classical systems with a finite number of degrees of freedom; the second week on field theories. During the first week the basic course, given by P. Cartier, was a presentation of a recent rigorous approach to functional integration which does not resort to discretization, nor to analytic continuation. It provides a definition of functional integrals simpler and more powerful than the original ones. Could this approach accommodate the works presented by the other lecturers? Although much remains to be done before answering "Yes," there seems to be no major obstacle along the road. The other courses taught during the first week presented: a) a solid introduction to functional numerical techniques (A. Sokal) and their applications to functional integrals encountered in chemistry (N. Makri). b) integrals based on Poisson processes and their applications to wave propagation (S. K. Foong), in particular a wave-restorer or wave-designer algorithm yielding the initial wave profile when one can only observe its distortion through a dissipative medium. c) the formulation of a quantum equivalence principle (H. Kleinert) which. given the flat space theory, yields a well-defined quantum theory in spaces with curvature and torsion.

Functional Magnetic Resonance Imaging Processing

With strong numerical and computational focus, this book serves as an essential resource on the methods for functional neuroimaging analysis, diffusion weighted image analysis, and longitudinal VBM analysis. It includes four MRI image modalities analysis methods. The first covers the PWI methods, which is the basis for understanding cerebral flow in human brain. The second part, the book’s core, covers fMRI methods in three specific domains: first level analysis, second level analysis, and effective connectivity study. The third part covers the analysis of Diffusion weighted image, i.e. DTI, QBI and DSI image analysis. Finally, the book covers (longitudinal) VBM methods and its application to Alzheimer’s disease study.

Functional Metal Oxide Nanostructures (Springer Series in Materials Science #149)

Metal oxides and particularly their nanostructures have emerged as animportant class of materials with a rich spectrum of properties and greatpotential for device applications. In this book, contributions from leadingexperts emphasize basic physical properties, synthesis and processing, and thelatest applications in such areas as energy, catalysis and data storage. Functional Metal Oxide Nanostructuresis an essential reference for any materials scientist or engineer with aninterest in metal oxides, and particularly in recent progress in defectphysics, strain effects, solution-based synthesis, ionic conduction, and theirapplications.

Functional Networks with Applications: A Neural-Based Paradigm (The Springer International Series in Engineering and Computer Science #473)

Artificial neural networks have been recognized as a powerful tool to learn and reproduce systems in various fields of applications. Neural net­ works are inspired by the brain behavior and consist of one or several layers of neurons, or computing units, connected by links. Each artificial neuron receives an input value from the input layer or the neurons in the previ­ ous layer. Then it computes a scalar output from a linear combination of the received inputs using a given scalar function (the activation function), which is assumed the same for all neurons. One of the main properties of neural networks is their ability to learn from data. There are two types of learning: structural and parametric. Structural learning consists of learning the topology of the network, that is, the number of layers, the number of neurons in each layer, and what neurons are connected. This process is done by trial and error until a good fit to the data is obtained. Parametric learning consists of learning the weight values for a given topology of the network. Since the neural functions are given, this learning process is achieved by estimating the connection weights based on the given information. To this aim, an error function is minimized using several well known learning methods, such as the backpropagation algorithm. Unfortunately, for these methods: (a) The function resulting from the learning process has no physical or engineering interpretation. Thus, neural networks are seen as black boxes.

Functional Polymer Nanocomposites for Wastewater Treatment (Springer Series in Materials Science #323)

This book provides an overview of the latest advances in applications of nanocomposites in wastewater treatment. This book is dedicated to recent developments in the application of polymer nanocomposites to wastewater treatment. Based on their morphology and tailored compositions, polymer nanocomposites provide powerful tools for environmental remediation via selective adsorption of contaminants in complex environmental matrices. The book reviews recent progress in this field, covering various nanocomposite fabrication routes and novel applications for pollutant sensing and detection. It includes discussion of different types of nanocomposites based on metal–organic frameworks and hydrogels, while also covering related topics such as nanocomposite membranes, photocatalysts, and bio-nanocomposites for pollution abatement. Ideal for researchers and engineers in the field, this collection of contributed chapters offers a timely review of current research in nanomaterials for cost-effective pollution control technologies.

Functional Renormalization and Ultracold Quantum Gases (Springer Theses)

Modern techniques from quantum field theory are applied in this work to the description of ultracold quantum gases. This leads to a unified description of many phenomena including superfluidity for bosons and fermions, classical and quantum phase transitions, different dimensions, thermodynamic properties and few-body phenomena as bound state formation or the Efimov effect. The non-perturbative treatment with renormalization group flow equations can account for all known limiting cases by solving one single equation. It improves previous results quantitatively and brings qualitatively new insights. As an example, new quantum phase transitions are found for fermions with three spin states. Ultracold atomic gases can be seen as an interesting model for features of high energy physics and for condensed matter theory. The research reported in this thesis helps to solve the difficult complexity problem in modern theoretical physics.

Functions of Natural Organic Matter in Changing Environment

Functions of Natural Organic Matter in Changing Environment presents contributions from the 16th Meeting of the International Humic Substances Society (IHSS 16) held in Hangzhou, China on September 9-14, 2012. It provides a comprehensive and updated research advance in the field of characterization, function, application of humic substances (HS) and natural organic matter (NOM) in environment, agriculture, and industry. A broad range of topics are covered: i) formation, structure and characteristics of HS and NOM; ii) HS/NOM and carbon sequestration; iii) HS/NOM and biogeochemical cycling of nutrients; iv) HS/NOM and the environmental processes of toxic elements and anthropogenic organics; v) HS/NOM, naturally occurring and engineered nanoparticles; vi) HS/NOM, biodiversity and ecosystem health; vii) HS/NOM in water and water treatment; viii) characterization and function of biochar in the environment; and ix) industrial products and application of HS. The book will be an invaluable reference for chemists, biologists, environmental scientists, ecologists, soil scientists, water scientists, agronomists, global change researchers and policy makers. Jianming Xu is Professor and Director at the Institute of Soil and Water Resources and Environmental Science, Zhejiang University, Hangzhou, China. Jianjun Wu is Professor at the Institute of Soil and Water Resources and Environmental Science, Zhejiang University, Hangzhou, China. Yan He is Associate Professor at the Institute of Soil and Water Resources and Environmental Science, Zhejiang University, Hangzhou, China.

Functions, Spaces, and Expansions: Mathematical Tools in Physics and Engineering (Applied and Numerical Harmonic Analysis)

This graduate-level textbook is a detailed exposition of key mathematical tools in analysis aimed at students, researchers, and practitioners across science and engineering. Every topic covered has been specifically chosen because it plays a key role outside the field of pure mathematics. Although the treatment of each topic is mathematical in nature, and concrete applications are not delineated, the principles and tools presented are fundamental to exploring the computational aspects of physics and engineering. Readers are expected to have a solid understanding of linear algebra, in Rn and in general vector spaces. Familiarity with the basic concepts of calculus and real analysis, including Riemann integrals and infinite series of real or complex numbers, is also required.

Fundamental Algorithms in Computational Fluid Dynamics (Scientific Computation)

Intended as a textbook for courses in computational fluid dynamics at the senior undergraduate or graduate level, this book is a follow-up to the book Fundamentals of Computational Fluid Dynamics by the same authors, which was published in the series Scientific Computation in 2001. Whereas the earlier book concentrated on the analysis of numerical methods applied to model equations, this new book concentrates on algorithms for the numerical solution of the Euler and Navier-Stokes equations. It focuses on some classical algorithms as well as the underlying ideas based on the latest methods. A key feature of the book is the inclusion of programming exercises at the end of each chapter based on the numerical solution of the quasi-one-dimensional Euler equations and the shock-tube problem. These exercises can be included in the context of a typical course and sample solutions are provided in each chapter, so readers can confirm that they have coded the algorithms correctly.

Fundamental Aspects of Plasma Chemical Physics: Transport (Springer Series on Atomic, Optical, and Plasma Physics #74)

Fundamental Aspects of Plasma Chemical Physics: Transport develops basic and advanced concepts of plasma transport to the modern treatment of the Chapman-Enskog method for the solution of the Boltzmann transport equation. The book invites the reader to consider actual problems of the transport of thermal plasmas with particular attention to the derivation of diffusion- and viscosity-type transport cross sections, stressing the role of resonant charge-exchange processes in affecting the diffusion-type collision calculation of viscosity-type collision integrals.A wide range of topics is then discussed including (1) the effect of non-equilibrium vibrational distributions on the transport of vibrational energy, (2) the role of electronically excited states in the transport properties of thermal plasmas, (3) the dependence of transport properties on the multitude of Saha equations for multi-temperature plasmas, and (4) the effect of the magnetic field on transport properties. Throughout the book, worked examples are provided to clarify concepts and mathematical approaches. This book is the second of a series of three published by the Bari group on fundamental aspects of plasma chemical physics. The first book, Fundamental Aspects of Plasma Chemical Physics: Thermodynamics, is dedicated to plasma thermodynamics; and the third, Fundamental Aspects of Plasma Chemical Physics: Kinetics, deals with plasma kinetics.

Fundamental Aspects of Plasma Chemical Physics: Kinetics (Springer Series on Atomic, Optical, and Plasma Physics #85)

Describing non-equilibrium "cold" plasmas through a chemical physics approach, this book uses the state-to-state plasma kinetics, which considers each internal state as a new species with its own cross sections. Extended atomic and molecular master equations are coupled with Boltzmann and Monte Carlo methods to solve the electron energy distribution function. Selected examples in different applied fields, such as microelectronics, fusion, and aerospace, are presented and discussed including the self-consistent kinetics in RF parallel plate reactors, the optimization of negative ion sources and the expansion of high enthalpy flows through nozzles of different geometries.The book will cover the main aspects of the state-to-state kinetic approach for the description of nonequilibrium cold plasmas, illustrating the more recent achievements in the development of kinetic models including the self-consistent coupling of master equations and Boltzmann equation for electron dynamics. To give a complete portrayal, the book will assess fundamental concepts and theoretical formulations, based on a unified methodological approach, and explore the insight in related scientific problems still opened for the research community.

Fundamental Aspects of Plasma Chemical Physics: Thermodynamics (Springer Series on Atomic, Optical, and Plasma Physics #66)

Fundamental Aspects of Plasma Chemical Physics - Thermodynamics develops basic and advanced concepts of plasma thermodynamics from both classical and statistical points of view.After a refreshment of classical thermodynamics applied to the dissociation and ionization regimes, the book invites the reader to discover the role of electronic excitation in affecting the properties of plasmas, a topic often overlooked by the thermal plasma community.Particular attention is devoted to the problem of the divergence of the partition function of atomic species and the state-to-state approach for calculating the partition function of diatomic and polyatomic molecules. The limit of ideal gas approximation is also discussed, by introducing Debye-Huckel and virial corrections.Throughout the book, worked examples are given in order to clarify concepts and mathematical approaches.This book is a first of a series of three books to be published by the authors on fundamental aspects of plasma chemical physics. The next books will discuss transport and kinetics.

Fundamental Aspects of Turbulent Flows in Climate Dynamics: Lecture Notes of the Les Houches Summer School: Volume 109, August 2017 (Lecture Notes of the Les Houches Summer School #109)

This volume, number 109 of the Les Houches Summer School series, presents the lectures held in August 2017 on the subject of turbulent flows in climate dynamics. Leading scientists in the fields of climate dynamics, atmosphere and ocean dynamics, geophysical fluid dynamics, physics and non-linear sciences present their views on this fast growing and interdisciplinary field of research, by venturing upon fundamental problems of atmospheric convection, clouds, large scale circulation, and predictability. Climate is controlled by turbulent flows. Turbulent motions are responsible for the bulk of the transport of energy, momentum, and water vapor in the atmosphere, which determine the distribution of temperature, winds, and precipitation on Earth. The aim of this book is to survey what is known about how turbulent flows control climate, what role they may play in climate change, and to outline where progress in this important area can be expected, given today's computational and observational capabilities. This book reviews the state-of-the-art developments in this field and provides an essential background to future studies. All chapters are written from a pedagogical perspective, making the book accessible to masters and PhD students and all researchers wishing to enter this field.

Fundamental Astronomy

Fundamental Astronomy gives a well-balanced and comprehensive introduction to the various fields of classical and modern astronomy. While emphasizing both the astronomical concepts and the underlying physical principles, the text provides a sound basis for more profound studies in the astronomical sciences. The present corrected printing of the revised and enlarged third edition of this successful textbook includes a host of new knowledge acquired in recent years. In particular the chapters on observations and on the physics of the Sun have been thoroughly revised.

Fundamental Astronomy

The much enlarged second edition of this successful textbook includes a host of new knowledge acquired in recent years. The book provides a well-balanced and comprehensive introduction to the various fields of classical and modern astronomy. With its emphasis on both the astronomical concepts and the underlying physical principles, the text serves as a sound basis for more profound studies in the astronomical sciences.

Fundamental Astronomy (Springer Study Edition Ser.)

Fundamental Astronomy is a well-balanced, comprehensive introduction to classical and modern astronomy. While emphasizing both the astronomical concepts and the underlying physical principles, the text provides a sound basis for more profound studies in the astronomical sciences. This is the fifth edition of the successful undergraduate textbook and reference work. It has been extensively modernized and extended in the parts dealing with extragalactic astronomy and cosmology. You will also find augmented sections on the solar system and extrasolar planets as well as a new chapter on astrobiology. Long considered a standard text for physical science majors, Fundamental Astronomy is also an excellent reference work for dedicated amateur astronomers.

Fundamental Astronomy

Fundamental Astronomy is a well-balanced, comprehensive introduction to classical and modern astronomy. While emphasizing both the astronomical concepts and the underlying physical principles, the text provides a sound basis for more profound studies in the astronomical sciences. This is the fifth edition of the successful undergraduate textbook and reference work. It has been extensively modernized and extended in the parts dealing with extragalactic astronomy and cosmology. You will also find augmented sections on the solar system, extrasolar planets and astrobiology. Long considered a standard text for physical science majors, Fundamental Astronomy is also an excellent reference work for dedicated amateur astronomers.

Fundamental Astronomy

Fundamental Astronomy is a well-balanced, comprehensive introduction to classical and modern astronomy. While emphasizing both the astronomical concepts and the underlying physical principles, the text provides a sound basis for more profound studies in the astronomical sciences. This is the fifth edition of the successful undergraduate textbook and reference work. It has been extensively modernized and extended in the parts dealing with extragalactic astronomy and cosmology. You will also find augmented sections on the solar system and extrasolar planets as well as a new chapter on astrobiology. Long considered a standard text for physical science majors, Fundamental Astronomy is also an excellent reference work for dedicated amateur astronomers.

Fundamental Behavior of Unsaturated Widely-Graded Soil: The Hydraulic and Mechanic Behavior of Coarse-fine Mixed Soil and its Influence on Slope Stability

This book focuses on the engineering properties of unsaturated widely graded soils and their influence on slope stability. This book characterizes the natural widely graded colluvial soils from macroscale, mesoscale, and microscale viewpoints, introduces the techniques for measuring hydro-mechanical properties for unsaturated widely graded colluvial soils, and clarifies the hydro-mechanical behavior and the failure mechanism of widely graded colluvial soils subjected to environmental loads. This book improves the understanding of rainfall-induced landslides on natural slopes. Researchers and engineers in the field of civil engineering can benefit from the book.

Fundamental Contributions to the Continuum Theory of Evolving Phase Interfaces in Solids: A Collection of Reprints of 14 Seminal Papers

A traditional way to honor distinguished scientists is to combine collections of papers solicited from friendly colleagues into dedicatory volumes. To honor our friend and colleague Mort Gurtin on the occasion of his sixty-fifth birthday, we followed a surer path to produce a work of intrinsic and lasting scientific value: We collected pa­ pers that we deemed seminal in the field of evolving phase interfaces in solids, a field to which Mort Gurtin himself has made fundamental contributions. Our failure for lack of space to include in this volume every paper of major significance is mitigated by the ma­ gisterial introduction prepared by Eliot Fried, which assesses the contributions of nu­ merous works. We hope that this collection will prove useful and stimulating to both researchers and students in this exciting field. August 1998 JohnM. Ball David Kinderlehrer Paulo Podio-Guidugli Marshall Slemrod Contents Introduction: Fifty Years of Research on Evolving Phase Interfaces By Eliot Fried. 0 •••••••••••••••••••••••••••••••••••••••••••••••• 0 ••••• 1 I. Papers on Materials Science Surface Tension as a Motivation for Sintering By C. Herring 33 Two-Dimensional Motion of Idealized Grain Boundaries By W. W. Mullins 0 ••••••••••• 0 ••••••••••••••••••• 70 Morphological. Stability of a Particle Growing by Diffusion or Heat Flow By w. w. Mullins and R. F. Sekerka 75 Energy Relations and the Energy-Momentum Tensor in Continuum Mechanics By J. D. Eshelby 82 The Interactions of Composition and Stress in Crystalline Solids By F. e. Larche and 1. W. Cahn 120 II.

Fundamental Directions in Mathematical Fluid Mechanics (Advances in Mathematical Fluid Mechanics)

This volume consists of six articles, each treating an important topic in the theory ofthe Navier-Stokes equations, at the research level. Some of the articles are mainly expository, putting together, in a unified setting, the results of recent research papers and conference lectures. Several other articles are devoted mainly to new results, but present them within a wider context and with a fuller exposition than is usual for journals. The plan to publish these articles as a book began with the lecture notes for the short courses of G.P. Galdi and R. Rannacher, given at the beginning of the International Workshop on Theoretical and Numerical Fluid Dynamics, held in Vancouver, Canada, July 27 to August 2, 1996. A renewed energy for this project came with the founding of the Journal of Mathematical Fluid Mechanics, by G.P. Galdi, J. Heywood, and R. Rannacher, in 1998. At that time it was decided that this volume should be published in association with the journal, and expanded to include articles by J. Heywood and W. Nagata, J. Heywood and M. Padula, and P. Gervasio, A. Quarteroni and F. Saleri. The original lecture notes were also revised and updated.