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Matematica e cultura 2007 = Mathematics and culture 2007
We talk about theater even if the page cannot tell about Bustric's unforgettable show. And about art, and applied arts, such as geometric structure and spiritual meaning of the Zen garden of Ryoanji in Kyoto, and of soap bubbles, which are almost never lacking in Venetian encounters, Four-dimensional bubbles and gigantic bubbles that serve as a model for the Olympic swimming pool in Bejing
Matematica e cultura 2006 = Mathematics and Culture 2006
The series Matematica e cultura, through a journey that began ten years ago, in an ever new, surprising and fascinating way, tries to describe the influences and links existing between the world of mathematics and that of aeronautics, medicine, biology, but also art, cinema. , of theater, literature or history: "A tribute to Mario Merz could not be missing, following his Fibonacci numbers towards infinity. And cinema, that of Davide Ferrario who takes up that thread, those numbers that fly over Turin. film on the axiom of parallels, a Venetian film E.
Martingale Methods in Financial Modelling
This book provides a comprehensive, self-contained and up-to-date treatment of the main topics in the theory of option pricing. The first part of the text starts with discrete-time models of financial markets, including the Cox-Ross-Rubinstein binomial model. The passage from discrete- to continuous-time models, done in the Black-Scholes model setting, assumes familiarity with basic ideas and results from stochastic calculus. However, an Appendix containing all the necessary results is included. This model setting is later generalized to cover standard and exotic options involving several assets and/or currencies. An outline of the general theory of arbitrage pricing is presented. The second part of the text is devoted to the term structure modelling and the pricing of interest-rate derivatives. The main emphasis is on models that can be made consistent with market pricing practice.
Markov Processes, Brownian Motion, and Time Symmetry
The book consists of two parts. Part I,This part introduces strong Markov processes and their potential theory. In particular,it studies Brownian motion, and shows how it generates classical potential theory.Part II, focus on the effects of time reversal, duality, and time-symmetry on potential theory. Certain theorems in Part I are re-proved in Part II under slightly weaker hypotheses. The volume is very useful for people who wish to learn Markov processes but it seems to the reviewer that it is also of great interest to specialists in this area who could derive much stimulus from it. One can be convinced that it will receive wide circulation." (Mathematical Reviews)
Markov Decision Processes with Their Applications
Markov decision processes (MDPs), also called stochastic dynamic programming, were first studied in the 1960s. MDPs can be used to model and solve dynamic decision-making problems that are multi-period and occur in stochastic circumstances. There are three basic branches in MDPs: discrete-time MDPs, continuous-time MDPs and semi-Markov decision processes. Starting from these three branches, many generalized MDPs models have been applied to various practical problems. These models include partially observable MDPs, adaptive MDPs, MDPs in stochastic environments, and MDPs with multiple objectives, constraints or imprecise parameters.
Markov Chains : Models, Algorithms and Applications
Markov chains are a particularly powerful and widely used tool for analyzing a variety of stochastic (probabilistic) systems over time. This monograph will present a series of Markov models, starting from the basic models and then building up to higher-order models. Included in the higher-order discussions are multivariate models, higher-order multivariate models, and higher-order hidden models. In each case, the focus is on the important kinds of applications that can be made with the class of models being considered in the current chapter. Special attention is given to numerical algorithms that can efficiently solve the models. Therefore, Markov Chains: Models, Algorithms and Applications outlines recent developments of Markov chain models for modeling queueing sequences, Internet, re-manufacturing systems, reverse logistics, inventory systems, bio-informatics, DNA sequences, genetic networks, data mining, and many other practical systems.
Market-Consistent Actuarial Valuation
It is a challenging task to read the balance sheet of an insurance company. This derives from the fact that different positions are often measured by different yardsticks. Assets, for example, are mostly valued at market prices whereas liabilities are often measured by established actuarial methods. Market-Consistent Actuarial Valuation presents powerful methods to measure liabilities and assets in the same way. The mathematical framework that leads to market-consistent values for insurance liabilities is explained in detail by the authors. Topics covered are Stochastic discounting, Valuation portfolio in life and non-life insurance, Asset and liability management, Financial risks, Insurance technical risks, and Solvency.
Maple and Mathematica : A Problem Solving Approach for Mathematics
the history of mathematics there are many situations in which cal- lations were performed incorrectly for important practical applications. the history of computing the number began in Egypt and Babylon about 2000 years BC, since then many mathematicians have calculated (e. g. , Archimedes, Ptolemy, Vi` ete, etc. ). In modern mathematics there exist computers that can perform various mathematical operations for which humans are incapable. Therefore the computers can be used to verify the results obtained by humans, to discovery new results, to - prove the result sthatahumancanobtain without anytechnology
Malliavin Calculus for Lévy Processes with Applications to Finance
While the original works on Malliavin calculus aimed to study the smoothness of densities of solutions to stochastic differential equations, this book has another goal. It portrays the most important and innovative applications in stochastic control and finance, such as hedging in complete and incomplete markets, optimisation in the presence of asymmetric information and also pricing and sensitivity analysis. In a self-contained fashion, both the Malliavin calculus with respect to Brownian motion and general Lévy type of noise are treated. Besides, forward integration is included and indeed extended to general Lévy processes. The forward integration is a recent development within anticipative stochastic calculus that, together with the Malliavin calculus, provides new methods for the study of insider trading problems.
Maîtriser laléatoire : Exercices résolus de probabilités et statistique = Mastering Randomness : Solved Exercises in Probability and Statistics
Consists of 245 solved exercises that cover all the basic concepts of probability and statistics. The work is structured in nine chapters, each containing a brief introduction, bibliographic references to more specialized works, as well as a series of exercises and their detailed solutions. Ranked in increasing order of difficulty, these will allow the reader to appreciate the extent of his progress. This book can be used as a supplement to any theory manual on statistics and probability. Due to the great diversity of the examples offered, it will suit a diverse readership: students of economics, psychology, social sciences, mathematics, physics, chemistry, medicine or biology.
MacLaurins Physical Dissertations
The Scottish mathematician Colin MacLaurin (1698-1746) is best known for developing and extending Newton’s work in calculus, geometry and gravitation; his 2-volume work "Treatise of Fluxions" (1742) was the first systematic exposition of Newton’s methods. It is well known that MacLaurin was awarded prizes by the Royal Academy of Sciences, Paris, for his earlier work on the collision of bodies (1724) and the tides (1740); however, the contents of these essays are less familiar – although some of the material is discussed in the Treatise of Fluxions - and the essays themselves often hard to obtain.
Macchine matematiche : Dalla storia alla scuola = Mathematical Machines: From History to School
Presents the main mathematical machines for drawing curves, for applying geometrical transformations or for making classical perspectives.The publication constitutes an example of how history of mathematics may be useful for teaching today’s mathematics.
Loop Spaces, Characteristic Classes and Geometric Quantization
This book deals with the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Various developments in mathematical physics (e.g., in knot theory, gauge theory, and topological quantum field theory) have led mathematicians and physicists to search for new geometric structures on manifolds and to seek a synthesis of ideas from geometry, topology and category theory. In this spirit, this book develops the differential geometry associated to the topology and obstruction theory of certain fiber bundles (more precisely, associated to grebes). The theory is a 3-dimensional analog of the familiar Kostant--Weil theory of line bundles. In particular the curvature now becomes a 3-form.
Logica Universalis : Towards a General Theory of Logic
Modern logic has been intimately connected with algebra since its origins in figures such as Boole, De Morgan, and Peirce. But while universal algebra is a long recognized field, universal logic has only recently been named as such. This is perhaps because classical logic was until relatively recently taken by many as the "one true logic". But with the proliferation of special purpose non-classical logics in recent years, universal logic is clearly a field whose time has come. This book contains many excellent papers demonstrating the value of this approach.
Logica Universalis : Towards a General Theory of Logic
Signifies the arrival of a new renaissance in logic, a new revival not only of logic, but of the vision of logic as a unifying tool for science as a whole, including mathematics, physics, cosmology, computer science and AI. The book and the vision behind it give logic, conceived as a scientific study of rationality, new unifying power, new perspectives, and new horizons.Universal Logic is not a new logic, but a general theory of logics, considered as mathematical structures. The name was introduced about ten years ago, but the subject is as old as the beginning of modern logic: Alfred Tarski and other Polish logicians such as Adolf Lindenbaum developed a general theory of logics at the end of the 1920s based on consequence operations and logical matrices. The subject was revived after the flowering of thousands of new logics during the last thirty years: there was a need for a systematic theory of logics to put some order in this chaotic multiplicity.
Local Newforms for GSp(4)
Local Newforms for GSp(4) describes a theory of new- and oldforms for representations of GSp(4) over a non-archimedean local field. This theory considers vectors fixed by the paramodular groups, and singles out certain vectors that encode canonical information, such as L-factors and epsilon-factors, through their Hecke and Atkin-Lehner eigenvalues. While there are analogies to the GL(2) case, this theory is novel and unanticipated by the existing framework of conjectures. An appendix includes extensive tables about the results and the representation theory of GSp(4).
Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems : Results and Examples
Once again KAM theory is committed in the context of nearly integrable Hamiltonian systems. While elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n-parameter families. Hence, without the need for untypical conditions or external parameters, torus bifurcations of high co-dimension may be found in a single given Hamiltonian system. The text moves gradually from the integrable case, in which symmetries allow for reduction to bifurcating equilibria, to non-integrability, where smooth parametrisations have to be replaced by Cantor sets. Planar singularities and their versal unfoldings are an important ingredient that helps to explain the underlying dynamics in a transparent way.
Linking and Aligning Scores and Scales
In this book, experts in statistics and psychometrics describe classes of linkages, the history of score linkings, data collection designs, and methods used to achieve sound score linkages. They describe and critically discuss applications to a variety of domains including equating of achievement exams, linkages between computer-delivered exams and paper-and-pencil exams, concordances between the current version of the SAT® and its predecessor, concordances between the ACT® and the SAT®, vertical linkages of exams that span grade levels, and linkages of scales from high-stakes state assessments to the scales of the National Assessment of Educational Progress (NAEP).
Linear Systems
Linear systems theory plays a broad and fundamental role in electrical, mechanical, chemical and aerospace engineering, communications, and signal processing. A thorough introduction to systems theory with emphasis on control is presented in this self-contained textbook. The book examines the fundamental properties that govern the behavior of systems by developing their mathematical descriptions. Linear time-invariant, time-varying, continuous-time, and discrete-time systems are covered. Rigorous development of classic and contemporary topics in linear systems, as well as extensive coverage of stability and polynomial matrix/fractional representation, provide the necessary foundation for further study of systems and control.
Linear Programming : Foundations and Extensions
Linear Programming: Foundations and Extensions is an introduction to the field of optimization. The book emphasizes constrained optimization, beginning with a substantial treatment of linear programming, and proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. The book is carefully written. Specific examples and concrete algorithms precede more abstract topics. Topics are clearly developed with a large number of numerical examples worked out in detail.
