الصفحة 7
الصفحة 7
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.
Evidence-based Clinical Orthodontics
Takes an unbiased approach to orthodontics by systematically reviewing the relevant clinical literature and analyzing the scientific evidence to help practitioners select the most effective and efficient modes of treatment. Each chapter addresses a specific topic by summarizing the literature, critically reviewing the evidence, and offering impartial recommendations that can be adopted by clinical practitioners.
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).
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.
Epiphyseal Growth Plate Fractures
This comprehensive reference work covers all aspects of growth plate fractures and their complications. Following general reviews of growth plate fractures, 21 chapters deal with each epiphyseal growth plate in the body. All of these chapters are constructed similarly for easy and quick retrieval of the required information. The main emphasis is on evaluation (diagnosis) and management (treatment). A separate section is devoted to premature partial physeal arrest, as this is by far the most common and feared complication of a growth plate fracture and its treatment is involved and controversial. The case studies included are often based on 20- to 30-year follow-ups, revealing cases that originally appeared to be quite satisfactory at the conclusion of growth but were found to have turned out quite poorly years later.
Epilepsy
Epilepsy has remained a significant social concern and financial burden globally. It is the most common neurological disease of the brain. Around 1% of the people worldwide have epilepsy and this disease affects people of all ages, Although the different types of epilepsy vary greatly, medication appropriate can control seizures in about 70% of patients, Medications are mainstays in controlling epileptic seizures, Partial seizures, which are the most common seizure type in adults, can be effectively controlled by virtually all the standard and newer antiepileptic drugs (AEDs). For the generalized epilepsies, valproate remains the drug of choice.
Environment Learning for Indoor Mobile Robots : A Stochastic State Estimation Approach to Simultaneous Localization and Map Building
This monograph covers theoretical aspects of simultaneous localization and map building for mobile robots, such as estimation stability, nonlinear models for the propagation of uncertainties, temporal landmark compatibility, as well as issues pertaining the coupling of control and SLAM. One of the most relevant topics covered in this monograph is the theoretical formalism of partial observability in SLAM. The authors show that the typical approach to SLAM using a Kalman filter results in marginal filter stability, making the final reconstruction estimates dependant on the initial vehicle estimates. However, by anchoring the map to a fixed landmark in the scene, they are able to attain full observability in SLAM, with reduced covariance estimates.
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.
Energy and Environment
Energy and Environment is a volume on energy and environmental modeling that describes a broad variety of modeling methodologies, embodied in models of varying scopes and philosophies, ranging from top-down integrated assessment models to bottom-up partial equilibrium models, to hybrid models.
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
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.
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."
Domain Decomposition Methods in Science and Engineering XVII
This volume contains a selection of papers presented at the 17th International Conference on Domain Decomposition Methods in Science and Engineering held at St. Wolfgang / Strobl, Austria, July 3 - 7, 2006. Domain decomposition is an active, interdisciplinary research area concerned with the development, analysis, and implementation of coupling and decoupling strategies in mathematical and computational models. Domain decomposition techniques provide efficient tools for treating problems in all Computational Sciences. The reader will become familiar with the newest domain decomposition technologies and their use for modeling and simulating of complex problems from different fields of applications.
Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations
Domain decomposition methods are divide and conquer methods for the parallel and computational solution of partial differential equations of elliptic or parabolic type. They include iterative algorithms for solving the discretized equations, techniques for non-matching grid discretizations and techniques for heterogeneous approximations. This book serves as an introduction to this subject, with emphasis on matrix formulations. The topics studied include Schwarz, substructuring, Lagrange multiplier and least squares-control hybrid formulations, multilevel methods, non-self adjoint problems, parabolic equations, saddle point problems (Stokes, porous media and optimal control), non-matching grid discretizations, heterogeneous models, fictitious domain methods, variational inequalities, maximum norm theory, eigenvalue problems, optimization problems and the Helmholtz scattering problem. Selected convergence theory is included.
Domain Decomposition Methods - Algorithms and Theory
This book offers a comprehensive presentation of some of the most successful and popular domain decomposition preconditioners for finite and spectral element approximations of partial differential equations. It places strong emphasis on both algorithmic and mathematical aspects. It covers in detail important methods such as FETI and balancing Neumann-Neumann methods and algorithms for spectral element methods.
Direct Methods in the Calculus of Variations
Studies vectorial problems in the calculus of variations and quasiconvex analysis. It is a new edition of the earlier book published in 1989 and has been updated with some new material and examples added. This monograph will appeal to researchers and graduate students in mathematics and engineering.
Digital Simulation in Electrochemistry
The book shows how to numerically solve the parabolic partial differential equations (pdes) encountered in electroanalytical chemistry. It does this in a didactic manner, by first introducing the basic equations to be solved and some model systems as text cases, for which solutions exist. Then it treats basic numerical approximation for derivatives and techniques for the numerical solution of ordinary differential equations, from which the more complicated methods for pdes can be derived. The major implicit methods are described in detail, and the handling of homogeneous chemical reactions, including coupled and nonlinear cases, is detailed. More advanced techniques are presented briefly, as well as some commercially available program packages.
Digital Restorative Dentistry : A Guide to Materials, Equipment, and Clinical Procedures
Offers up-to-date, readily understandable guidance on the materials and equipment employed in digital restorative dentistry and on the specific clinical procedures that may be performed using the new technologies. The key components of digital restorative dentistry – image acquisition, prosthetic/restorative design, and fabrication – are fully addressed. Readers will find helpful information on scanners, the software for prosthetic design, and the materials and technologies for prosthesis fabrication, including laser sintering, 3D printing, CAD/CAM, and laser ablation. The section on clinical procedures explains all aspects of the use of digital technologies in the treatment of patients requiring removable partial dentures, complete dentures, fixed partial prostheses, crowns, endodontics, and implant surgery and prosthodontics. The field of restorative and prosthetic dentistry is undergoing rapid transition as these new technologies come to play an increasingly central role in everyday dental practice. In bridging the knowledge gap that this technological revolution has created in the field of dentistry, the book will satisfy the needs of both dentists and dental students.
Digital Removable Partial Denture Technology : From Design Analysis to Practical Skills
Introduces esthetic clasp as an innovative method that improves the appearance of clasps by changing the clasp design. It details the concept of esthetic clasp, the classification of esthetic clasp design methods, the clinical pathway of esthetic clasp techniques, many selected cases, and the logos of different kinds of esthetic clasps.
