الصفحة 13
الصفحة 13
Mathematical Problems from Applied Logic II : Logics for the XXIst Century
Mathematical Problems from Applied Logic II presents chapters from selected, world renowned, logicians. Important topics of logic are discussed from the point of view of their further development in light of requirements arising from their successful application in areas such as Computer Science and AI language. Fields covered include: logic of provability, applications of computability theory to biology, psychology, physics, chemistry, economics, and other basic sciences; computability theory and computable models; logic and space-time geometry; hybrid systems; logic and region-based theory of space.
Mathematical Problems from Applied Logic I : Logics for the XXIst Century
Mathematical Problems from Applied Logic I presents chapters from selected, world renowned, logicians. Important topics of logic are discussed from the point of view of their further development in light of requirements arising from their successful application in areas such as Computer Science and AI language. An overview of the current state as well as open problems and perspectives are clarified in such fields as non-standard inferences in description logics, logic of provability, logical dynamics and computability theory. The book contains interesting contributions concerning the role of logic today, including some unexpected aspects of contemporary logic and the application of logic. This should be of interest to logicians and mathematicians in general.
Mathematical Physics of Quantum Mechanics : Selected and Refereed Lectures from QMath9
At the QMath9 meeting, young scientists learn about the state of the art in the mathematical physics of quantum systems. Based on that event, this book offers a selection of outstanding articles written in pedagogical style comprising six sections which cover new techniques and recent results on spectral theory, statistical mechanics, Bose-Einstein condensation, random operators, magnetic Schrödinger operators and much more. For postgraduate students, Mathematical Physics of Quantum Systems serves as a useful introduction to the research literature. For more expert researchers, this book will be a concise and modern source of reference.
Mathematical Models of Granular Matter
Granular matter displays a variety of peculiarities that distinguish it from other appearances studied in condensed matter physics and renders its overall mathematical modelling somewhat arduous. Prominent directions in the modelling granular flows are analyzed from various points of view. Foundational issues, numerical schemes and experimental results are discussed. The volume furnishes a rather complete overview of the current research trends in the mechanics of granular matter. Various chapters introduce the reader to different points of view and related techniques. New models describing granular bodies as complex bodies are presented. Results on the analysis of the inelastic Boltzmann equations are collected in different chapters. Gallavotti-Cohen symmetry is also discussed.
Mathematical Models of Financial Derivatives
Mathematical Models of Financial Derivatives is a textbook on the theory behind modeling derivatives using the financial engineering approach, focussing on the martingale pricing principles that are common to most derivative securities. A wide range of financial derivatives commonly traded in the equity and fixed income markets are analyzed, emphasizing on the aspects of pricing, hedging and their risk management. Starting from the renowned Black-Scholes-Merton formulation of option pricing model, readers are guided through the text on the new advances on the state-of-the-art derivative pricing models and interest rate models. Both analytic techniques and numerical methods for solving various types of derivative pricing models are emphasized.
Isomorphisms Between H¹ Spaces
Presents a thorough and self-contained presentation of H¹ and its known isomorphic invariants, such as the uniform approximation property, the dimension conjecture, and dichotomies for the complemented subspaces. The necessary background is developed from scratch. This includes a detailed discussion of the Haar system, together with the operators that can be built from it (averaging projections, rearrangement operators, paraproducts, Calderon-Zygmund singular integrals). Complete proofs are given for the classical martingale inequalities of C. Fefferman, Burkholder, and Khinchine-Kahane, and for large deviation inequalities. Complex interpolation, analytic families of operators, and the Calderon product of Banach lattices are treated in the context of H^p spaces. Througout the book, special attention is given to the combinatorial methods developed in the field, particularly J. Bourgain's proof of the dimension conjecture, L. Carleson's biorthogonal system in H¹, T. Figiel's integral representation, W.B. Johnson's factorization of operators, B. Maurey's isomorphism, and P. Jones' proof of the uniform approximation property. An entire chapter is devoted to the study of combinatorics of colored dyadic intervals."
Isomonodromic Deformations and Frobenius Manifolds : An Introduction
The notion of a Frobenius structure on a complex analytic manifold appeared at the end of the seventies in the theory of singularities of holomorphic functions. Motivated by physical considerations, further development of the theory has opened new perspectives on, and revealed new links between, many apparently unrelated areas of mathematics and physics. Based on a series of graduate lectures, this book provides an introduction to algebraic geometric methods in the theory of complex linear differential equations. Starting from basic notions in complex algebraic geometry, it develops some of the classical problems of linear differential equations and ends with applications to recent research questions related to mirror symmetry.
IP Traffic Theory and Performance
This book presents different approaches in IP traffic theory and classifies them, especially towards applications in the Internet. It comprises the state of the art in this area, which is currently presented only by numerous research papers and overview articles. The book provides an ideal starting point for detailed studies of traffic analysis in IP networks. It gives the reader the possibility to judge on different models and to select the appropriate for his individual needs in applications.
Invexity and Optimization
Invexity and Optimization presents results on invex function and their properties in smooth and nonsmooth cases, pseudolinearity and eta-pseudolinearity. Results on optimality and duality for a nonlinear scalar programming problem are presented, second and higher order duality results are given for a nonlinear scalar programming problem, and saddle point results are also presented. Invexity in multiobjective programming problems and Kuhn-Tucker optimality conditions are given for a multiobjecive programming problem, Wolfe and Mond-Weir type dual models are given for a multiobjective programming problem and usual duality results are presented in presence of invex functions. Continuous-time multiobjective problems are also discussed. Quadratic and fractional programming problems are given for invex functions. Symmetric duality results are also given for scalar and vector cases.
Investment valuation and asset pricing : Models and methods
Offers an overview of original works on foundational asset pricing studies that follows their historical publication chronologically throughout the text. Each chapter stays close to the original works of these major authors, including quotations, examples, graphical exhibits, and empirical results. Additionally, it includes statistical concepts and methods as applied to finance. These statistical materials are crucial to learning asset pricing, which often applies statistical tests to evaluate different asset pricing models.
Inverse Problems for Partial Differential Equations
The topic of the inverse problems is of substantial and rapidly growing interest for many scientists and engineers. The second edition covers most important recent developments in the field of inverse problems, describing theoretical and computational methods, and emphasizing new ideas and techniques. It also reflects new changes since the first edition, including some corrections. This edition is considerably expanded, with some concepts such as pseudo-convexity, and proofs simplified. New material is added to reflect recent progress in theory of inverse problems.This book is intended for mathematicians working with partial differential equations and their applications, and physicists, geophysicists and engineers involved with experiments in nondestructive evaluation, seismic exploration, remote sensing and tomography.
Inverse Problems and Imaging : Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy September 15–21, 2002
Nowadays we are facing numerous and important imaging problems: nondestructive testing of materials, monitoring of industrial processes, enhancement of oil production by efficient reservoir characterization, emerging developments in noninvasive imaging techniques for medical purposes - computerized tomography (CT), magnetic resonance imaging (MRI), positron emission tomography (PET), X-ray and ultrasound tomography, etc. In the CIME Summer School on Imaging (Martina Franca, Italy 2002), leading experts in mathematical techniques and applications presented broad and useful introductions for non-experts and practitioners alike to many aspects of this exciting field. The volume contains part of the above lectures completed and updated by additional contributions on other related topics: a general presentation and introduction (Moscoso), X-ray tomography (Natterer), Electromagnetic imaging (Dorn, Bertete-Aguirre, Papanicolaou), coherent imaging in telecommunications in a multiple input-multiple output setup (Dorn), polarization based optical imaging (Moscoso), topological derivatives used in shape reconstruction related to inverse scattering problems (Carpio, Rapún), Point interactions (Dell’Antonio, Figari, Teta).
Invariant Probabilities of Markov-Feller Operators and Their Supports
In this book invariant probabilities for a large class of discrete-time homogeneous Markov processes known as Feller processes are discussed. These Feller processes appear in the study of iterated function systems with probabilities, convolution operators, certain time series, etc. Rather than dealing with the processes, the transition probabilities and the operators associated with these processes are studied.
Invariant Manifolds for Physical and Chemical Kinetics
By bringing together various ideas and methods for extracting the slow manifolds the authors show that it is possible to establish a more macroscopic description in nonequilibrium systems. The book treats slowness as stability. A unifying geometrical viewpoint of the thermodynamics of slow and fast motion enables the development of reduction techniques, both analytical and numerical. Examples considered in the book range from the Boltzmann kinetic equation and hydrodynamics to the Fokker-Planck equations of polymer dynamics and models of chemical kinetics describing oxidation reactions. Special chapters are devoted to model reduction in classical statistical dynamics, natural selection, and exact solutions for slow hydrodynamic manifolds. The book will be a major reference source for both theoretical and applied model reduction. Intended primarily as a postgraduate-level text in nonequilibrium kinetics and model reduction, it will also be valuable to PhD students and researchers in applied mathematics, physics and various fields of engineering.
Introduzione alla teoria della misura e all’analisi funzionale = Introduction to measurement theory and functional analysis
Presents a treatment of the theory of measure from an abstract point of view, with particular emphasis on some aspects of interest in probability. The typical arguments of the theory of integration are developed in a rather in-depth way, trying where possible to deduce classical results from the modern setting of the theory as well. The text has a modular structure, with interconnections between the parts: some chapters deal with theoretical aspects, others are dedicated to more applied topics. Alongside the numerous examples, a wide range of exercises is proposed.
Introduzione al Calcolo Scientifico : Esercizi e problemi risolti con MATLAB = Introduction to scientific computing : Exercises and problem solved with MATLAB
Introduces the fundamental concepts for the numerical modeling of partial differential problems. We consider the classic linear elliptic, parabolic and hyperbolic equations, but also other equations, such as those of diffusion and transport, of Navier-Stokes, and the conservation laws. Numerous physical examples underlying these equations are provided, their main mathematical properties are studied, then numerical resolution methods based on finite elements, finite differences, finite volumes and spectral methods are proposed and analyzed. In particular, the algorithmic and computer implementation aspects are discussed and some easy-to-use programs in C ++ language are provided. The text does not presuppose an advanced mathematical knowledge of partial differential equations: the strictly indispensable concepts in this regard are reported in the Appendix. THE VOLUME is therefore suitable for students of scientific degree courses (Engineering, Mathematics, Physics, Chemistry, Information Sciences) and recommended for researchers from the academic and extra-academic world who want to approach this interesting branch of applied mathematics.
Introductory Statistics with R
R is an Open Source implementation of the S language. It works on multiple computing platforms and can be freely downloaded. R is now in widespread use for teaching at many levels as well as for practical data analysis and methodological development. This book provides an elementary-level introduction to R, targeting both non-statistician scientists in various fields and students of statistics. The main mode of presentation is via code examples with liberal commenting of the code and the output, from the computational as well as the statistical viewpoint. A supplementary R package can be downloaded and contains the data sets.
Introductory Lectures on Fluctuations of Lévy Processes with Applications
Lévy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their mathematical significance is justified by their application in many areas of classical and modern stochastic models including storage models, renewal processes, insurance risk models, optimal stopping problems, mathematical finance and continuous-state branching processes.The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Lévy processes with jumps in only one direction.
Introduction to Variance Estimation
The book provides instruction on the methods that are vital to data-driven decision making in business, government, and academe. It will appeal to survey statisticians and other scientists engaged in the planning and conduct of survey research, and to those analyzing survey data and charged with extracting compelling information from such data. It will appeal to graduate students and university faculty who are focused on the development of new theory and methods and on the evaluation of alternative methods. Software developers concerned with creating the computer tools necessary to enable sound decision-making will find it essential.
Introduction to the basic concepts of modern physics : Special relativity, quantum and statistical physics
These notes are designed as a text book for a course on the Modern Physics Theory for undergraduate students. The purpose is providing a rigorous and self-contained presentation of the simplest theoretical framework using elementary mathematical tools.
