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الصفحة 6
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.
Magnetic Monopoles
This monograph addresses the field theoretical aspects of magnetic monopoles. Written for graduate students as well as researchers, the author demonstrates the interplay between mathematics and physics. He delves into details as necessary and develops many techniques that find applications in modern theoretical physics. This introduction to the basic ideas used for the description and construction of monopoles is also the first coherent presentation of the concept of magnetic monopoles. It arises in many different contexts in modern theoretical physics, from classical mechanics and electrodynamics to multidimensional branes. The book summarizes the present status of the theory and gives an extensive but carefully selected bibliography on the subject. The first part deals with the Dirac monopole, followed in part two by the monopole in non-abelian gauge theories. The third part is devoted to monopoles in supersymmetric Yang-Mills theories.
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.
Lost Causes in and beyond Physics
Lost Causes in and Beyond Physics deals with a selection of research topics mostly from theoretical physics that have been shown to be a dead-end or continue at least to be highly controversial. This book is written as both an entertainment and serious study and should be accessible to anyone with a background in theoretical physics and 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).
Lines of Inquiry in Mathematical Modelling Research in Education
The book addresses the “balancing act” between developing students’ modelling skills on the one hand, and using modelling to help them learn mathematics on the other, which arises from the integration of modelling into classrooms. In addition the book highlights professional learning and development for in-service teachers, particularly in systems where the introduction of modelling into curricula means reassessing how mathematics is taught.
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.
Linear Partial Differential Equations for Scientists and Engineers
This significantly expanded fourth edition is designed as an introduction to the theory and applications of linear PDEs. The authors provide fundamental concepts, underlying principles, a wide range of applications, and various methods of solutions to PDEs. In addition to essential standard material on the subject, the book contains new material that is not usually covered in similar texts and reference books, including conservation laws, the spherical wave equation, the cylindrical wave equation, higher-dimensional boundary-value problems, the finite element method, fractional partial differential equations, and nonlinear partial differential equations with applications.
Linear Optimization Problems with Inexact Data
Linear programming attracted the interest of mathematicians during and after World War II when the first computers were constructed and methods for solving large linear programming problems were sought in connection with specific practical problems—for example, providing logistical support for the U.S. Armed Forces or modeling national economies. Early attempts to apply linear programming methods to solve practical problems failed to satisfy expectations. There were various reasons for the failure. One of them, which is the central topic of this book, was the inexactness of the data used to create the models. This phenomenon, inherent in most pratical problems, has been dealt with in several ways. At first, linear programming models used "average” values of inherently vague coefficients, but the optimal solutions of these models were not always optimal for the original problem itself. Later researchers developed the stochastic linear programming approach, but this too has its limitations. Recently, interest has been given to linear programming problems with data given as intervals, convex sets and/or fuzzy sets. The individual results of these studies have been promising, but the literature has not presented a unified theory. Linear Optimization Problems with Inexact Data attempts to present a comprehensive treatment of linear optimization with inexact data, summarizing existing results and presenting new ones within a unifying framework.
Linear Models for Optimal Test Design
Begins with a reflection on the history of test design--the core activity of all educational and psychological testing. It then presents a standard language for modeling test design problems as instances of multi-objective constrained optimization. The main portion of the book discusses test design models for a large variety of problems from the daily practice of testing, and illustrates their use with the help of numerous empirical examples. The presentation includes models for the assembly of tests to an absolute or relative target for their information functions, classical test assembly, test equating problems, item matching, test splitting, simultaneous assembly of multiple tests, tests with item sets, multidimensional tests, and adaptive test assembly. Two separate chapters are devoted to the questions of how to design item banks for optimal support of programs with fixed and adaptive tests. Linear Models for Optimal Test Design, which does not require any specific mathematical background, has been written to be a helpful resource on the desk of any test specialist.
