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Soren S Nielson, Andrea Consiglio

This companion book thoroughly describes the actual implementation of the majority of the models developed in Practical Financial Optimization, in the General Algebraic Modelling System, GAMS. In addition, the volume contains executable versions of these models, and a CD containing the software needed to execute them.

High Quality Content by WIKIPEDIA articles! In mathematics and abstract algebra, a relation algebra is a residuated Boolean algebra equipped with an involution called "converse". The motivating example of a relation algebra is the algebra 2X? of all binary relations on a set X, with R?S interpreted as the usual composition of binary relations and the converse of R as the inverse relation. Relation algebra emerged in the 19th century work of Augustus De Morgan and Charles Peirce, which culminated in the algebraic logic of Ernst Schroder. The present-day purely equational form or relation algebra was developed by Alfred Tarski and his students, starting in the 1940s.

High Quality Content by WIKIPEDIA articles! A scale-free network is a network whose degree distribution follows a power law, at least asymptotically. That is, the fraction Pk of nodes in the network having k connections to other nodes goes for large values of k as Pk ~ k?? where ? is a constant whose value is typically in the range 2<?<3, although occasionally it may lie outside these bounds. Scale-free networks are noteworthy because many empirically observed networks appear to be scale-free, including the protein networks, citation networks, and some social networks.

High Quality Content by WIKIPEDIA articles! The spectrum of a C*-algebra or dual of a C*-algebra A, denoted A, is the set of unitary equivalence classes of irreducible *-representations of A. A *-representation ? of A on a Hilbert space H is irreducible if, and only if, there is no closed subspace K different from H and {0} which is invariant under all operators ?(x) with x ? A. We implicitly assume that irreducible representation means non-null irreducible representation, thus excluding trivial (i.e. identically 0) representations on one-dimensional spaces. As explained below, the spectrum A is also naturally a topological space; this generalizes the notion of the spectrum of a ring.

In mathematics and computer science, graph theory is the study of graphs : mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of vertices. A graph may be undirected , meaning that there is no distinction between the two vertices associated with each edge or its edges may be directed from one vertex to another; see graph (mathematics) for more detailed definitions and for other variations in the types of graphs that are commonly considered. The graphs studied in graph theory should not be confused with "graphs of functions" and other kinds of graphs.

Roger W. Carter

Now available in paperback––the standard introduction to the theory of simple groups of Lie type. In 1955, Chevalley showed how to construct analogues of the complex simple Lie groups over arbitrary fields. The present work presents the basic results in the structure theory of Chevalley groups and their twisted analogues.

Raymond H. Myers, Douglas C. Montgomery, G. Geoffrey Vining, Timothy J. Robinson

Praise for the First Edition "The obvious enthusiasm of Myers, Montgomery, and Vining and their reliance on their many examples as a major focus of their pedagogy make Generalized Linear Models a joy to read. Every statistician working in any area of applied science should buy it and experience the excitement of these new approaches to familiar activities." ?Technometrics Generalized Linear Models: With Applications in Engineering and the Sciences, Second Edition continues to provide a clear introduction to the theoretical foundations and key applications of generalized linear models (GLMs). Maintaining the same nontechnical approach as its predecessor, this update has been thoroughly extended to include the latest developments, relevant computational approaches, and modern examples from the fields of engineering and physical sciences. This new edition maintains its accessible approach to the topic by reviewing the various types of problems that support the use of...

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.

Ernest F. Haeussler, Richard S. Paul, Richard J. Wood

Haeussler, Paul, and Wood establish a strong algebraic foundation that sets this text apart from other applied mathematics texts, paving the way for readers to solve real-world problems that use calculus. Emphasis on developing algebraic skills is extended to the exercises–including both drill problems and applications. The authors work through examples and explanations with a blend of rigor and accessibility. In addition, they have refined the flow, transitions, organization, and portioning of the content over many editions to optimize learning for readers. The table of contents covers a wide range of topics efficiently, enabling readers to gain a diverse understanding. ALGEBRA; Review of Algebra; Applications and More Algebra; Functions and Graphs; Lines, Parabolas, and Systems; Exponential and Logarithmic Functions; FINITE MATHEMATICS; Mathematics of Finance; Matrix Algebra; Linear Programming; Introduction to Probability and Statistics; Additional Topics in Probability;...

John Cassidy

How did we get to where we are? John Cassidy shows that the roots of our most recent financial failure lie not with individuals, but with an idea - the idea that markets are inherently rational. He gives us the big picture behind the financial headlines, tracing the rise and fall of free-market ideology from Adam Smith to Milton Friedman and Alan Greenspan. Full of wit, sense and, above all, a deep understanding, "How Markets Fail: The Logic of Economic Calamities" argues for the end of "utopian" economics, and the beginning of a pragmatic, reality-based way of thinking.