الصفحة 10
الصفحة 10
Existence and Regularity Properties of the Integrated Density of States of Random Schrödinger Operators
The theory of random Schrödinger operators is devoted to the mathematical analysis of quantum mechanical Hamiltonians modeling disordered solids. Apart from its importance in physics, it is a multifaceted subject in its own right, drawing on ideas and methods from various mathematical disciplines like functional analysis, selfadjoint operators, PDE, stochastic processes and multiscale methods. The present text describes in detail a quantity encoding spectral features of random operators: the integrated density of states or spectral distribution function. Various approaches to the construction of the integrated density of states and the proof of its regularity properties are presented.
Evolutionary Equations : Picard's Theorem for Partial Differential Equations, and Applications
This book provides a solution theory for time-dependent partial differential equations, which classically have not been accessible by a unified method. Instead of using sophisticated techniques and methods, the approach is elementary in the sense that only Hilbert space methods and some basic theory of complex analysis are required. Nevertheless, key properties of solutions can be recovered in an elegant manner.
Evolution of Thin Film Morphology : Modeling and Simulations
Thin film deposition is the most ubiquitous and critical of the processes used to manufacture high tech devices. Morphology and microstructure of thin films directly controls their optical, magnetic, and electrical properties. This book focuses on modeling and simulations used in research on the morphological evolution during film growth. The authors emphasize the detailed mathematical formulation of the problem both through numerical calculations based on Langevin continuum equations, and through Monte Carlo simulations based on discrete surface growth models when an analytical formulism is not convenient. Evolution of Thin-Film Morphology will be of benefit to university researchers and industrial scientists working in the areas of semiconductor processing, optical coating, plasma etching, patterning, micro-machining, polishing, tribology, and any discipline that requires an understanding of thin film growth processes.
Estimation in Conditionally Heteroscedastic Time Series Models
ARCH (autoregressive conditionally heteroscedastic), is well-suited for the description of economic and financial price. Nowadays ARCH has been replaced by more general and more sophisticated models, such as GARCH (generalized autoregressive heteroscedastic). This monograph concentrates on mathematical statistical problems associated with fitting conditionally heteroscedastic time series models to data. This includes the classical statistical issues of consistency and limiting distribution of estimators. Particular attention is addressed to (quasi) maximum likelihood estimation and misspecified models, along to phenomena due to heavy-tailed innovations. The used methods are based on techniques applied to the analysis of stochastic recurrence equations. Proofs and arguments are given wherever possible in full mathematical rigour. Moreover, the theory is illustrated by examples and simulation studies.
Essays in Constructive Mathematics
This book aims to promote constructive mathematics, not by defining it or formalizing it, but by practicing it, by basing all definitions and proofs on finite algorithms. The topics covered derive from classic works of nineteenth century mathematics---among them Galois' theory of algebraic equations, Gauss's theory of binary quadratic forms and Abel's theorem about integrals of rational differentials on algebraic curves. It is not surprising that the first two topics can be treated constructively---although the constructive treatments shed a surprising amount of light on them---but the last topic, involving integrals and differentials as it does, might seem to call for infinite processes. In this case too, however, finite algorithms suffice to define the genus of an algebraic curve, to prove that birationally equivalent curves have the same genus, and to prove the Riemann-Roch theorem. The main algorithm in this case is Newton's polygon, which is given a full treatment. Other topics covered include the fundamental theorem of algebra, the factorization of polynomials over an algebraic number field, and the spectral theorem for symmetric matrices.
Esercizi di finanza matematica = Mathematical finance exercises
This is a collection of exercises that illustrates some fundamental aspects of Mathematical Finance, in particular the valuation of derivatives. It is aimed at students of master's degree courses, but can also be successfully used in first level degree courses, by students who have adequate mathematical training (degree courses in mathematics, engineering). The resolution of the exercises is addressed with the use of methods of both Probability Theory (stochastic processes) and Mathematical Analysis (Partial Derivative Equations).
Ernst Equation and Riemann Surfaces : Analytical and Numerical Methods
Exact solutions to Einstein`s equations have been useful for the understanding of general relativity in many respects. They have led to physical concepts as black holes and event horizons and helped to visualize interesting features of the theory. In addition they have been used to test the quality of various approximation methods and numerical codes. The most powerful solution generation methods are due to the theory of Integrable Systems. In the case of axisymmetric stationary spacetimes the Einstein equations are equivalent to the completely integrable Ernst equation. In this volume the solutions to the Ernst equation associated to Riemann surfaces are studied in detail and physical and mathematical aspects of this class are discussed both analytically and numerically.
Equity Ownership and Performance : An Empirical Study of German Traded Companies
The empirical studies presented in this book model the endogeneity by applying the simultaneous equations methodology on the relation of ownership and financial performance as well as on different ownership dimensions themselves.
Equazioni a derivate parzial I : Complementi ed esercizi
La presente raccolta di problemi ed esercizi nasce dall'esperienza maturata durante il corso di Equazioni a Derivate Parziali (EDP), tenuto nell'ambito delle lauree di primo e secondo livello presso il Politecnico di Milano. Il volume è diviso in due parti; nei primi quattro capitoli l'obiettivo è l'uso di tecniche classiche, come la separazione delle variabili, il principio di massimo o le trasformate di Laplace e Fourier, per risolvere problemi di diffusione, trasporto e vibrazione. Il quinto capitolo invita a familiarizzare con i risultati di base negli spazi di Hilbert, nella teoria delle distribuzioni (o funzioni generalizzate) di Schwartz e in quella degli spazi di Sobolev più comuni. Il sesto ed ultimo capitolo riguarda la formulazione variazionale o debole dei più importanti problemi iniziali e/o al bordo per equazioni ellittiche e di evoluzione. L'introduzione ad ogni capitolo contiene una sintesi degli strumenti teorici più utilizzati.
Entropy Methods for the Boltzmann Equation : Lectures from a Special Semester at the Centre Émile Borel, Institut H. Poincaré, Paris, 2001
Entropy and entropy production have recently become mathematical tools for kinetic and hydrodynamic limits, when deriving the macroscopic behaviour of systems from the interaction dynamics of their many microscopic elementary constituents at the atomic or molecular level. During a special semester on Hydrodynamic Limits at the Centre Émile Borel in Paris, 2001 two of the research courses were held by C. Villani and F. Rezakhanlou. Both illustrate the major role of entropy and entropy production in a mutual and complementary manner and have been written up and updated for joint publication. Villani describes the mathematical theory of convergence to equilibrium for the Boltzmann equation and its relation to various problems and fields, including information theory, logarithmic Sobolev inequalities and fluid mechanics. Rezakhanlou discusses four conjectures for the kinetic behaviour of the hard sphere models and formulates four stochastic variations of this model, also reviewing known results for these.
Ennio De Giorgi : Selected Papers
The book contains a selection of 43 scientific papers by the great mathematician Ennio De Giorgi (1928-1996), which display the broad range of his achievements and his entire intellectual career as a problem solver and as a proponent of deep and ambitious mathematical theories. All papers are written in English and 17 of them appear also in their original Italian version in order to give an impression of De Giorgi’s original style. The editors also provide a short biography of Ennio De Giorgi and a detailed account of his scientific achievements, ranging from his seminal paper on the solution of Hilbert’s 19th problem to the theory of perimeter and minimal surfaces, the theory of G-convergence and the foundations of mathematics.
Elliptic and Parabolic Problems : A Special Tribute to the Work of Haim Brezis
This volume contains contributions by former students and collaborators of Haim Brezis given in honor of his 60th anniversary at a conference in Gaeta. H. Brezis has made significant contributions in the fields of partial differential equations and functional analysis. He is an inspiring teacher and counselor of many mathematicians in the front ranks. The collection of papers presented here grew out from his deep insight of analysis. In addition it reflects Brezis's elegant way of creative thinking
Elements of Numerical Relativity : From Einstein`s Equations to Black Hole Simulations
Spurred by the current development of numerous large-scale projects for detecting gravitational radiation, with the aim to open a completely new window to the observable Universe, numerical relativity has become a major field of research over the past years. Indeed, numerical relativity is the standard approach when studying potential sources of gravitational waves, where strong fields and relativistic velocities are part of any physical scenario. This book can be considered a primer for both graduate students and non-specialist researchers wishing to enter the field. Starting from the most basic insights and aspects of numerical relativity, Elements of Numerical Relativity develops coherent guidelines for the reliable and convenient selection of each of the following key aspects: evolution formalism, gauge, initial and boundary conditions as well as various numerical algorithms. The tests and applications proposed in this book can be performed on a standard PC.
Elements for Physics : Quantities, Qualities, and Intrinsic Theories
While usual presentations of physical theories emphasize the notion of physical quantity, this book shows that there is much to gain when introducing the notion of physical quality. The usual physical quantities simply appear as coordinates over the manifolds representing the physical qualities. This allows to develop physical theories that have a degree of invariance much deeper than the usual one. It is shown that properly developed physical theories contain logarithms and exponentials of tensors: their conspicuous absence in usual theories suggests, in fact, that the fundamental invariance principle stated in this book is lacking in present-day mathematical physics. The book reviews and extends the theory if Lie groups, develops differential geometry, proposing compact definitions of torsion and of curvature, and adapts the usual notion of linear tangent application to the intrinsic point of view proposed for physics. As an illustration, two simple theories are studied with some detail, the theory of heat conduction and the theory of linear elastic media. The equations found differ quantitatively and qualitatively from those usually presented.
Elektromagnetische feldtheorie : für ingenieure und physiker = Electromagnetic field theory : For engineers and physicists
This well-established, didactically excellent textbook combines clarity with extraordinary accuracy in the formation of terms and in the derivations. The electromagnetic field theory and the mathematical methods required for it are taught. Maxwell's equations are presented and explained. This is followed by explanations about electrostatics, flow problems, magnetostatics, quasi-stationary fields and electromagnetic waves. It gives an outlook on fundamental questions, some of which are still open, from physics to quantum mechanics. A chapter on the special theory of relativity, with the help of which numerous problems of electromagnetic field theory can be solved more easily, rounds off the work.
Electromagnetic Radiation : Variational Methods, Waveguides and Accelerators
This is a graduate level textbook on the theory of electromagnetic radiation and its application to waveguides, transmission lines, accelerator physics and synchrotron radiation. It has grown out of lectures and manuscripts by Julian Schwinger prepared during the war at MIT's Radiation Laboratory, updated with material developed by Schwinger at UCLA in the 1970s and 1980s, and by Milton at the University of Oklahoma since 1994. The book includes a great number of straightforward and challenging exercises and problems. It is addressed to students in physics, electrical engineering, and applied mathematics seeking a thorough introduction to electromagnetism with emphasis on radiation theory and its applications.
Elastic Multibody Dynamics : A Direct Ritz Approach
This textbook is an introduction to and exploration of a number of core topics in the field of applied mechanics: On the basis of Lagrange's Principle, a Central Equation of Dynamics is presented which yields a unified view on existing methods. From these, the Projection Equation is selected for the derivation of the motion equations of holonomic and of non-holonomic systems. The method is applied to rigid multibody systems where the rigid body is defined such that, by relaxation of the rigidity constraints, one can directly proceed to elastic bodies. A decomposition into subsystems leads to a minimal representation and to a recursive representation, respectively, of the equations of motion.
Einsteins General Theory of Relativity : With Modern Applications in Cosmology
Einstein’s General Theory of Relativity: With Modern Applications in Cosmology by Oyvind Gron and Sigbjorn Hervik is about gravity and the concept of gravity as Albert Einstein saw it- curved spaces, four-dimensional manifolds and geodesics. The book starts with the 1st principals of relativity and an introduction to Einstein’s field equations. Next up are the three classical tests of the relativity theory and an introduction to black holes.
Einstein Manifolds
"[...] an efficient reference book for many fundamental techniques of Riemannian geometry. [...] despite its length, the reader will have no difficulty in getting the feel of its contents and discovering excellent examples of all interaction of geometry with partial differential equations, topology, and Lie groups. Above all, the book provides a clear insight into the scope and diversity of problems posed by its title."
Dynamics of Flexible Multibody Systems : Rigid Finite Element Method
A new approach is presented for modelling multi-body systems, which constitutes a substantial enhancement of the Rigid Finite Element method. The new approach is based on homogeneous transformations and joint coordinates, and it yields the advantage that equations of motion are automatically generated for systems consisting of alternate rigid and flexible links. Apart from its simple physical interpretation and easy computer implementation, the method is also valuable for educational purposes since it impressively illustrates the impact of mechanical features on the mathematical model. This novel modelling approach is then applied to systems such as offshore-cranes and telescopic rapiers.
