The book deals with the numerical simulation of noise in semiconductor devices operating in linear (small-signal) and nonlinear (large-signal) conditions. The main topics of the book are: An overview of the physical basis of noise in semiconductor devices, a detailed treatment of numerical noise simulation in small-signal conditions, and a presentation of innovative developments in the noise simulation of semiconductor devices operating in large-signal quasi-periodic conditions. The main benefit that the reader will derive from the book is the ability to understand, and, if needed, replicate the development of numerical, physics-based noise simulation of semiconductor devices in small-signal and large-signal conditions.

This and the previous volume of the OT series contain the proceedings of the Workshop on Operator Theory and its Applications, IWOTA 95, which was held at the University of Regensburg, Germany, July 31 to August 4, 1995. It was the eigth workshop of this kind. Following is a list of the seven previous workshops with reference to their proceedings: 1981 Operator Theory (Santa Monica, California, USA) 1983 Applications of Linear Operator Theory to Systems and Networks (Rehovot, Israel), OT 12 1985 Operator Theory and its Applications (Amsterdam, The Netherlands), OT 19 1987 Operator Theory and Functional Analysis (Mesa, Arizona, USA), OT 35 1989 Matrix and Operator Theory (Rotterdam, The Netherlands), OT 50 1991 Operator Theory and Complex Analysis (Sapporo, Japan), OT 59 1993 Operator Theory and Boundary Eigenvalue Problems (Vienna, Austria), OT 80 IWOTA 95 offered a rich programme on a wide range of latest developments in operator theory and its applications. The programme consisted of 6 invited plenary lectures, 54 invited special topic lectures and more than 100 invited session talks. About 180 participants from 25 countries attended the workshop, more than a third came from Eastern Europe. The conference covered different aspects of linear and nonlinear spectral prob lems, starting with problems for abstract operators up to spectral theory of ordi nary and partial differential operators, pseudodifferential operators, and integral operators. The workshop was also focussed on operator theory in spaces with indefinite metric, operator functions, interpolation and extension problems."

The "Turbulence and Interactions 2006" (TI2006) conference was held on the island of Porquerolles, France, May 29-June 2, 2006. The scientific sponsors of the conference were * Association Francaise de Mecanique, * CD-adapco, * DGA * Ecole Polytechnique Federale de Lausanne (EPFL), * ERCOFTAC : European Research Community on Flow, Turbulence and Combustion, * FLUENT, * The French Ministery of Foreign Affairs, * Laboratoire de Modelisation en Mecanique, Paris 6, * ONERA. The conference was a unique event. Never before have so many organisations concerned with turbulence works come together in one conference. As the title "Turbulence and Interactions" anticipated, the workshop was not run with parallel sessions but instead of one united gathering where people had strong interactions and discussions. Many of the 85 or so attendants were veterans of previous ERCOFTAC conferences. Some young researchers attended their very first int- national meeting. The organisers were fortunate in obtaining the presence of the following - vited speakers: N. Adams (TUM, Germany), C. Cambon (ECL, France), J.-P. Dussauge (Polytech Marseille, France), D.A. Gosman (Imperial College, UK), Y. Kaneda (Nagoya University, Japan), O. Simonin (IMFT, France), G. Tryggvason (WPI, USA), D. Veynante (ECP, France), F. Waleffe (University of Wisconsin, USA), Y.K. Zhou (University of California, USA). The topics covered by the 59 papers ranged from experimental results through theory to computations. The papers of the conference went through the usual - viewing process for two special issues of international journals : Computers and Fluids, and Flow, Turbulence and Combustion.

In this book, the author considers separable programming and, in particular, one of its important cases - convex separable programming. Some general results are presented, techniques of approximating the separable problem by linear programming and dynamic programming are considered. Convex separable programs subject to inequality/ equality constraint(s) and bounds on variables are also studied and iterative algorithms of polynomial complexity are proposed. As an application, these algorithms are used in the implementation of stochastic quasigradient methods to some separable stochastic programs. Numerical approximation with respect to I1 and I4 norms, as a convex separable nonsmooth unconstrained minimization problem, is considered as well. Audience: Advanced undergraduate and graduate students, mathematical programming/ operations research specialists.

In his 1974 seminal paper 'Elliptic modules', V G Drinfeld introduced objects into the arithmetic geometry of global function fields which are nowadays known as 'Drinfeld Modules'. They have many beautiful analogies with elliptic curves and abelian varieties. They study of their moduli spaces leads amongst others to explicit class field theory, Jacquet-Langlands theory, and a proof of the Shimura-Taniyama-Weil conjecture for global function fields.This book constitutes a carefully written instructional course of 12 lectures on these subjects, including many recent novel insights and examples. The instructional part is complemented by research papers centering around class field theory, modular forms and Heegner points in the theory of global function fields.The book will be indispensable for everyone who wants a clear view of Drinfeld's original work, and wants to be informed about the present state of research in the theory of arithmetic geometry over function fields.

This book is aimed to be both a textbook for graduate students and a starting point for applicationsscientists. It is designedto show how to implementspectral methods to approximate the solutions of partial differential equations. It presents a syst- atic development of the fundamental algorithms needed to write spectral methods codes to solve basic problems of mathematical physics, including steady potentials, transport, and wave propagation. As such, it is meant to supplement, not replace, more general monographs on spectral methods like the recently updated "Spectral Methods: Fundamentals in Single Domains" and "Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics" by Canuto, Hussaini, Quarteroni and Zang, which provide detailed surveys of the variety of methods, their performance and theory. I was motivated by comments that I have heard over the years that spectral me- ods are "too hard to implement." I hope to dispel this view-or at least to remove the "too." Although it is true that a spectral code is harder to hack together than a s- ple ?nite difference code (at least a low order ?nite difference method on a square domain), I show that only a few fundamental algorithms for interpolation, differen- ation, FFT and quadrature-the subjects of basic numerical methods courses-form the building blocks of any spectral code, even for problems in complex geometries. Ipresentthealgorithmsnotonlytosolveproblemsin1D, but2Daswell, toshowthe ?exibility of spectral methods and to make as straightforward as possible the tr- sition from simple, exploratory programs that illustrate the behavior of the methods to application programs.

Table of Contents: D. Duffie: Martingales, Arbitrage, and Portfolio Choice * J. Frohlich: Mathematical Aspects of the Quantum Hall Effect * M. Giaquinta: Analytic and Geometric Aspects of Variational Problems for Vector Valued Mappings * U. Hamenstadt: Harmonic Measures for Leafwise Elliptic Operators Along Foliations * M. Kontsevich: Feynman Diagrams and Low-Dimensional Topology * S.B. Kuksin: KAM-Theory for Partial Differential Equations * M. Laczkovich: Paradoxical Decompositions: A Survey of Recent Results * J.-F. Le Gall: A Path-Valued Markov Process and its Connections with Partial Differential Equations * I. Madsen: The Cyclotomic Trace in Algebraic K-Theory * A.S. Merkurjev: Algebraic K-Theory and Galois Cohomology * J. Nekovar: Values of L-Functions and p-Adic Cohomology * Y.A. Neretin: Mantles, Trains and Representations of Infinite Dimensional Groups * M.A. Nowak: The Evolutionary Dynamics of HIV Infections * R. Piene: On the Enumeration of Algebraic Curves - from Circles to Instantons * A. Quarteroni: Mathematical Aspects of Domain Decomposition Methods * A. Schrijver: Paths in Graphs and Curves on Surfaces * B. Silverman: Function Estimation and Functional Data Analysis * V. Strassen: Algebra and Complexity * P. Tukia: Generalizations of Fuchsian and Kleinian Groups * C. Viterbo: Properties of Embedded Lagrange Manifolds * D. Voiculescu: Alternative Entropies in Operator Algebras * M. Wodzicki : Algebraic K-Theory and Functional Analysis * D. Zagier: Values of Zeta Functions and Their Applications

This book presents an operator theoretic approach to robust control analysis for linear time-varying systems. It emphasizes the conceptual similarity with the H control theory for time-invariant systems and at the same time clarifies the major difficulties confronted in the time varying case. The necessary operator theory is developed from first principles and the book is as self-contained as possible. After presenting the necessary results from the theories of Toeplitz operators and nest algebras, linear systems are defined as input- output operators and the relationship between stabilization and the existance of co-prime factorizations is described. Uniform optimal control problems are formulated as model-matching problems and are reduced to four block problems. Robustness is considered both from the point of view of fractional representations and the "time varying gap" metric, and the relationship between these types of uncertainties is clarified. The book closes with the solution of the orthogonal embedding problem for time varying contractive systems. This book will be useful to both mathematicians interested in the potential applications of operator theory in control and control engineers who wish to deal with some of the more mathematically sophisticated extension of their work.

This introduction to applied nonlinear dynamics and chaos places emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior. The new edition has been updated and extended throughout, and contains a detailed glossary of terms.

From the reviews:

"Will serve as one of the most eminent introductions to the geometric theory of dynamical systems." --Monatshefte f r Mathematik

This and the next volume of the OT series contain the proceedings of the Work shop on Operator Theory and its Applications, IWOTA 95, which was held at the University of Regensburg, Germany, July 31 to August 4, 1995. It was the eigth workshop of this kind. Following is a list of the seven previous workshops with reference to their proceedings: 1981 Operator Theory (Santa Monica, California, USA) 1983 Applications of Linear Operator Theory to Systems and Networks (Rehovot, Israel), OT 12 1985 Operator Theory and its Applications (Amsterdam, The Netherlands), OT 19 1987 Operator Theory and Functional Analysis (Mesa, Arizona, USA), OT 35 1989 Matrix and Operator Theory (Rotterdam, The Netherlands), OT 50 1991 Operator Theory and Complex Analysis (Sapporo, Japan), OT 59 1993 Operator Theory and Boundary Eigenvalue Problems (Vienna, Austria), OT 80 IWOTA 95 offered a rich programme on a wide range of latest developments in operator theory and its applications. The programme consisted of 6 invited plenary lectures, 54 invited special topic lectures and more than 100 invited session talks. About 180 participants from 25 countries attended the workshop, more than a third came from Eastern Europe. The conference covered different aspects of linear and nonlinear spectral prob lems, starting with problems for abstract operators up to spectral theory of ordi nary and partial differential operators, pseudodifferential operators, and integral operators. The workshop was also focussed on operator theory in spaces with indefinite metric, operator functions, interpolation and extension problems.

This book offers an essential compendium of astronomical high-resolution techniques. Recent years have seen considerable developments in such techniques, which are critical to advances in many areas of astronomy. As reflected in the book, these techniques can be divided into direct methods, interferometry, and reconstruction methods, and can be applied to a huge variety of astrophysical systems, ranging from planets, single stars and binaries to active galactic nuclei, providing angular resolution in the micro- to tens of milliarcsecond scales. Written by experts in their fields, the chapters cover adaptive optics, aperture masking imaging, spectra disentangling, interferometry, lucky imaging, Roche tomography, imaging with interferometry, interferometry of AGN, AGN reverberation mapping, Doppler- and magnetic imaging of stellar surfaces, Doppler tomography, eclipse mapping, Stokes imaging, and stellar tomography. This book is intended to enable a next generation of astronomers to apply high-resolution techniques. It informs readers on how to achieve the best angular resolution in the visible and near-infrared regimes from diffraction-limited to micro-arcsecond scales.

The theory of practical rationality does not belong to one academic discipline alone. There are quite divergent philosophical, economical, sociological, psychological and politological contributions. Sometimes the disciplinary boundaries impede theoretical progress. On the other hand it is an indication for the high complexity of the subject that so many divergent paradigms compete with one another, or - what is worse - live separately in a kind of splendid isolation. Decision theory in the broader sense, embracing the theory of games and collective choice theory, can help to understand practical reason in philosophical analysis. But there are interesting aspects which cannot be dealt with adequately within a decision-theoretic conceptual framework. To have both of these convictions justifies to neglect dis ciplinary boundaries and poses a problem for the orthodoxies of either sides. All the essays of this volume focus on the relation between economic rationality and practical reason and discuss different aspects of the same problem, i. e. a basic deficiency in the standard economic theory of practical rationality. But philosophical analysis would not be of much help if it just rejected the economic paradigm. It must rather help to integrate economic aspects into a broader view on practical reason."

The Schur complement plays an important role in matrix analysis, statistics, numerical analysis, and many other areas of mathematics and its applications. This book describes the Schur complement as a rich and basic tool in mathematical research and applications and discusses many significant results that illustrate its power and fertility. The eight chapters of the book cover themes and variations on the Schur complement, including its historical development, basic properties, eigenvalue and singular value inequalities, matrix inequalities in both finite and infinite dimensional settings, closure properties, and applications in statistics, probability, and numerical analysis. Although the book is primarily intended to serve as a research reference, it will also be useful for graduate and advanced undergraduate courses in mathematics, applied mathematics, and statistics. The contributing authors' exposition makes most of the material accessible to readers with a sound foundation in linear algebra.

This book discusses the latest advances in algorithms for symbolic summation, factorization, symbolic-numeric linear algebra and linear functional equations. It presents a collection of papers on original research topics from the Waterloo Workshop on Computer Algebra (WWCA-2016), a satellite workshop of the International Symposium on Symbolic and Algebraic Computation (ISSAC'2016), which was held at Wilfrid Laurier University (Waterloo, Ontario, Canada) on July 23-24, 2016. This workshop and the resulting book celebrate the 70th birthday of Sergei Abramov (Dorodnicyn Computing Centre of the Russian Academy of Sciences, Moscow), whose highly regarded and inspirational contributions to symbolic methods have become a crucial benchmark of computer algebra and have been broadly adopted by many Computer Algebra systems.

This book deals with the theory and applications of the Reformulation- Linearization/Convexification Technique (RL T) for solving nonconvex optimization problems. A unified treatment of discrete and continuous nonconvex programming problems is presented using this approach. In essence, the bridge between these two types of nonconvexities is made via a polynomial representation of discrete constraints. For example, the binariness on a 0-1 variable x . can be equivalently J expressed as the polynomial constraint x . (1-x . ) = 0. The motivation for this book is J J the role of tight linear/convex programming representations or relaxations in solving such discrete and continuous nonconvex programming problems. The principal thrust is to commence with a model that affords a useful representation and structure, and then to further strengthen this representation through automatic reformulation and constraint generation techniques. As mentioned above, the focal point of this book is the development and application of RL T for use as an automatic reformulation procedure, and also, to generate strong valid inequalities. The RLT operates in two phases. In the Reformulation Phase, certain types of additional implied polynomial constraints, that include the aforementioned constraints in the case of binary variables, are appended to the problem. The resulting problem is subsequently linearized, except that certain convex constraints are sometimes retained in XV particular special cases, in the Linearization/Convexijication Phase. This is done via the definition of suitable new variables to replace each distinct variable-product term. The higher dimensional representation yields a linear (or convex) programming relaxation.

Table of contents: Plenary Lectures * V.I. Arnold: The Vassiliev Theory of Discriminants and Knots * L. Babai: Transparent Proofs and Limits to Approximation * C. De Concini: Poisson Algebraic Groups and Representations of Quantum Groups at Roots of 1 * S.K. Donaldson: Gauge Theory and Four-Manifold Topology * W. Muller: Spectral Theory and Geometry * D. Mumford: Pattern Theory: A Unifying Perspective * A.-S. Sznitman: Brownian Motion and Obstacles * M. Vergne: Geometric Quantization and Equivariant Cohomology * Parallel Lectures * Z. Adamowicz: The Power of Exponentiation in Arithmetic * A. Bjorner: Subspace Arrangements * B. Bojanov: Optimal Recovery of Functions and Integrals * J.-M. Bony: Existence globale et diffusion pour les modeles discrets * R.E. Borcherds: Sporadic Groups and String Theory * J. Bourgain: A Harmonic Analysis Approach to Problems in Nonlinear Partial Differatial Equations * F. Catanese: (Some) Old and New Results on Algebraic Surfaces * Ch. Deninger: Evidence for a Cohomological Approach to Analytic Number Theory * S. Dostoglou and D.A. Salamon: Cauchy-Riemann Operators, Self-Duality, and the Spectral Flow

This book presents the contributions of the 20th century to economic theory in a mathematical language and in historical sequence. General equilibrium is the focal point of the book; but also a number of macroeconomic models, especially with respect to the first half of the century, are considered. Dynamic models are extensively studied per se, and not merely as extensions of their static counterparts. The book with its extensive bibliography gives a broad view over the developments in mathematical economics and is therefore an invaluable source of information for researchers and students working in this field.

A function is convex if its epigraph is convex. This geometrical structure has very strong implications in terms of continuity and differentiability. Separation theorems lead to optimality conditions and duality for convex problems. A function is quasiconvex if its lower level sets are convex. Here again, the geo metrical structure of the level sets implies some continuity and differentiability properties for quasiconvex functions. Optimality conditions and duality can be derived for optimization problems involving such functions as well. Over a period of about fifty years, quasiconvex and other generalized convex functions have been considered in a variety of fields including economies, man agement science, engineering, probability and applied sciences in accordance with the need of particular applications. During the last twenty-five years, an increase of research activities in this field has been witnessed. More recently generalized monotonicity of maps has been studied. It relates to generalized convexity off unctions as monotonicity relates to convexity. Generalized monotonicity plays a role in variational inequality problems, complementarity problems and more generally, in equilibrium prob lems."

Nonsmooth energy functions govern phenomena which occur frequently in nature and in all areas of life. They constitute a fascinating subject in mathematics and permit the rational understanding of yet unsolved or partially solved questions in mechanics, engineering and economics. This is the first book to provide a complete and rigorous presentation of the quasidifferentiability approach to nonconvex, possibly nonsmooth, energy functions, of the derivation and study of the corresponding variational expressions in mechanics, engineering and economics, and of their numerical treatment. The new variational formulations derived are illustrated by many interesting numerical problems. The techniques presented will permit the reader to check any solution obtained by other heuristic techniques for nonconvex, nonsmooth energy problems. A civil, mechanical or aeronautical engineer can find in the book the only existing mathematically sound technique for the formulation and study of nonconvex, nonsmooth energy problems. Audience: The book will be of interest to pure and applied mathematicians, physicists, researchers in mechanics, civil, mechanical and aeronautical engineers, structural analysts and software developers. It is also suitable for graduate courses in nonlinear mechanics, nonsmooth analysis, applied optimization, control, calculus of variations and computational mechanics.

This superb new book is one of the first publications in recent years to provide a broad overview of this interdisciplinary field. Most of the book is written in a self contained manner, assuming only a general knowledge of statistical mechanics and basic probabilty theory . It provides the reader with a sound introduction to the field and to the analytical techniques necessary to follow its most recent developments

A Mathematical Approach to Special Relativity introduces the mathematical formalisms of special and general relativity. Developed from the author's experience teaching physics to students across all levels, the valuable resource introduces key concepts, building in complexity and using increasingly advanced mathematical tools as it progresses. Without assuming a background in calculus, the text begins with symmetry, before delving more deeply into Galilean relativity. Throughout, the book provides examples and useful "Guides to the Literature." This unique text emphasizes the experimental consequences and verifications of the underpinning theory in order to provide students with a solid foundation in this key area.

The research presented here includes important contributions on the commissioning of the ATLAS experiment and the discovery of the Higgs boson. The thesis describes essential work on the alignment of the inner tracker during the commissioning of the experiment and development of the electron identification algorithm. The subsequent analysis focuses on the search for the Higgs boson in the WW channel, including the development of a method to model the critical W+jet background. In addition, the thesis provides excellent introductions, suitable for non-specialists, to Higgs physics, to the LHC, and to the ATLAS experiment.

Introduction to Dynamical Systems and Geometric Mechanics provides a comprehensive tour of two fields that are intimately entwined: dynamical systems is the study of the behavior of physical systems that may be described by a set of nonlinear first-order ordinary differential equations in Euclidean space, whereas geometric mechanics explore similar systems that instead evolve on differentiable manifolds. The first part discusses the linearization and stability of trajectories and fixed points, invariant manifold theory, periodic orbits, Poincare maps, Floquet theory, the Poincare-Bendixson theorem, bifurcations, and chaos. The second part of the book begins with a self-contained chapter on differential geometry that introduces notions of manifolds, mappings, vector fields, the Jacobi-Lie bracket, and differential forms.

Mathematical Methods for Signal and Image Analysis and Representation presents the mathematical methodology for generic image analysis tasks. In the context of this book an image may be any m-dimensional empirical signal living on an n-dimensional smooth manifold (typically, but not necessarily, a subset of spacetime). The existing literature on image methodology is rather scattered and often limited to either a deterministic or a statistical point of view. In contrast, this book brings together these seemingly different points of view in order to stress their conceptual relations and formal analogies. Furthermore, it does not focus on specific applications, although some are detailed for the sake of illustration, but on the methodological frameworks on which such applications are built, making it an ideal companion for those seeking a rigorous methodological basis for specific algorithms as well as for those interested in the fundamental methodology per se. Covering many topics at the forefront of current research, including anisotropic diffusion filtering of tensor fields, this book will be of particular interest to graduate and postgraduate students and researchers in the fields of computer vision, medical imaging and visual perception.