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Krishan L. Duggal, Bayram Sahin

This is the first systematic account of the main results in the theory of lightlike submanifolds of semi-Riemannian manifolds which have a geometric structure, such as almost Hermitian, almost contact metric or quaternion Kahler. Using these structures, the book presents interesting classes of submanifolds whose geometry is very rich. The book also includes hypersurfaces of semi-Riemannian manifolds, their use in general relativity and Osserman geometry, half-lightlike submanifolds of semi-Riemannian manifolds, lightlike submersions, screen conformal submersions, and their applications in harmonic maps. Basic constructions and definitions are presented as preliminary background in every chapter. The presentation explores applications and suggests several open questions. This self-contained monograph provides up-to-date research in lightlike geometry and is intended for graduate students and researchers just entering this field.

High Quality Content by WIKIPEDIA articles! In geometry, a Schwarz triangle is a spherical triangle that can be used to tile a sphere. Each Schwarz triangle defines a finite group ? its triangle group. A Schwarz triangle is represented by three rational numbers (p q r) each representing the angle at a vertex. The value n/d means the vertex angle is d/n of the half-circle. "2" means a right triangle. A Schwarz triangle is represented graphically by a triangular graph. Each node represents an edge (mirror) of the Schwarz triangle. Each edge is labeled by a rational value corresponding to the reflection order, being ?/vertex angle.

Robert P. Crease

a??Any reader who aspires to be scientifically literate will find this a good starting place.a??a??Publishers Weekly While we may be familiar with some of sciencea??s greatest equations, we may not know that each and every equation emerged not in a??Eureka!a?? moments but in years of cultural developments and scientific knowledge. With vignettes full of humor, drama, and eccentricity, philosopher and science historian Robert P. Crease shares the stories behind ten of historya??s greatest equations, from the a??first equation,a?? 1 + 1 = 2, which promises a rational, well-ordered world, to Heisenberga??s uncertainty principle, which reveals the limitations of human knowledge. For every equation, Crease provides a brief account of who discovered it, what dissatisfactions lay behind its discovery, and what the equation says about the nature of our world. 43 illustrations.

Marcel Berger

Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces, convex sets, etc., crucial ideas and above all abstract concepts needed for attaining the results are elucidated. These are conceptual notions, each built "above" the preceding and permitting an increase in abstraction, represented metaphorically by Jacob's ladder with its rungs: the 'ladder' in the Old Testament, that angels ascended and descended... In all this, the aim of the book is to...

Ralf Korn, Elke Korn, Gerald Kroisandt

Offering a unique balance between applications and calculations, Monte Carlo Methods and Models in Finance and Insurance incorporates the application background of finance and insurance with the theory and applications of Monte Carlo methods. It presents recent methods and algorithms, including the multilevel Monte Carlo method, the statistical Romberg method, and the Heath–Platen estimator, as well as recent financial and actuarial models, such as the Cheyette and dynamic mortality models. The authors separately discuss Monte Carlo techniques, stochastic process basics, and the theoretical background and intuition behind financial and actuarial mathematics, before bringing the topics together to apply the Monte Carlo methods to areas of finance and insurance. This allows for the easy identification of standard Monte Carlo tools and for a detailed focus on the main principles of financial and insurance mathematics. The book describes high-level Monte Carlo methods for standard...

P-C. G. Vassiliou

Stochastic finance and financial engineering have been rapidly expanding fields of science over the past four decades, mainly due to the success of sophisticated quantitative methodologies in helping professionals manage financial risks. In recent years, we have witnessed a tremendous acceleration in research efforts aimed at better comprehending, modeling and hedging this kind of risk. These two volumes aim to provide a foundation course on applied stochastic finance. They are designed for three groups of readers: firstly, students of various backgrounds seeking a core knowledge on the subject of stochastic finance; secondly financial analysts and practitioners in the investment, banking and insurance industries; and finally other professionals who are interested in learning advanced mathematical and stochastic methods, which are basic knowledge in many areas, through finance. In Volume 2 we study continuous time models by presenting the necessary material from...

High Quality Content by WIKIPEDIA articles! In mathematics, a regular polytope is a polytope whose symmetry is transitive on its flags, thus giving it the highest degree of symmetry. All its elements or j-faces (for all 0 ? j ? n, where n is the dimension of the polytope) ? cells, faces and so on ? are also transitive on the symmetries of the polytope, and are regular polytopes of dimension ? n. Regular polytopes are the generalized analog in any number of dimensions of regular polygons (for example, the square or the regular pentagon) and regular polyhedra (for example, the cube). The strong symmetry of the regular polytopes gives them an aesthetic quality that interests both non-mathematicians and mathematicians.

High Quality Content by WIKIPEDIA articles! In calculus, a branch of mathematics, the second derivative test is a criterion often useful for determining whether a given stationary point of a function is a local maximum or a local minimum using the value of the second derivative at the point. In calculus, the second derivative of a function ? is the derivative of the derivative of ?. Roughly speaking, the second derivative measures how the rate of change of a quantity is itself changing; for example, the second derivative of the position of a vehicle with respect to time is the instantaneous acceleration of the vehicle, or the rate at which the velocity of the vehicle is changing. On the graph of a function, the second derivative corresponds to the curvature or concavity of the graph. The graph of a function with positive second derivative curves upwards, while the graph of a function with negative second derivative curves downwards.

Anthony Kelly

Game theory is a key element in most decision making processes involving two or more people or organizations. This book explains how game theory can predict the outcome of complex decision making processes, and how it can help to improve negotiation and decision-making skills. It is grounded in well-established theory, yet the wide-ranging international examples used to illustrate its application offer a fresh approach to what is becoming an essential weapon in the armory of the informed manager. The book is accessibly written, explaining in simple terms the underlying mathematics behind games of skill. It analyzes more sophisticated topics such as zero-sum games, mixed-motive games, and multi-person games, coalitions and power. Clear examples and helpful diagrams are used throughout, and the mathematics is kept to a minimum. Written for managers, students and decision-makers in every field.

Kirk Trigsted, Randall Gallaher, Kevin Bodden

Normal 0 false false false Intermediate Algebra by Trigsted, Gallaher, and Bodden is the first online, completely “clickable” Intermediate Algebra text to take full advantage of MyMathLab’s features and benefits. Like many instructors, Kirk Trigsted experienced marked improvement in student learning when teaching with MyMathLab. After observing that most students started their assignments by going directly to the exercises in MyMathLab without first consulting their textbooks, he was inspired to design an eText and course to better meet the needs and expectations of students. The coupling of a true eText with a fully designed course structure within MyMathLab provides a seamless learning experience for readers. Most importantly, the Trigsted MyMathLab course drives students into the book, before starting their homework. Foundations; Equations and Inequalities in One Variable; Graphs and Functions; Systems of Linear Equations and Inequalities; Polynomial Expressions and...