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Second Marine Division, 1940-1999
Since 1941, the 2nd Marine Division has written a record of unparalleled success through their courage, spirit, dedication and above all, their sacrifice. Volume II continues the history of the 2nd Marine Division, written by Art Sharp, former Follow Me"" editor. Displays the triumphs they shared through a written history with hundreds of photographs. Features Second Marine Division Association history and information, past presidents, past reunions, Second Marine Division Lineage, Unit Citation, Medal of Honor recipients, Distinguished Service Award recipients, special feature stories written by Second Marine Division members, biographies and an association roster.""
Density of Prime Divisors of Linear Recurrences
A general density theory of the set of prime divisors of a certain family of linear recurring sequences with constant coefficients, a family which is defined for any order recursion, is built up from the work of Lucas, Laxton, Hasse, and Lagarias. In particular, in this theory the notion of the rank of a prime divisor as well as the notion of a Companion Lucas sequence (Lucas), the group associated with a given second-order recursion (Laxton), and the effective computation of densities (Hasse and Lagarias) are first combined and then generalized to any order recursion.
Triangular Algebras and Ideals of Nest Algebras
Immersive environments such as virtual reality technology makes possible can respond to their audiences, so that each person's experience of the environment is unique. This volume brings together 11 essays along with artists' projects produced at the Banff Centre for the Arts in Canada to explore issues raised by the creation of virtual environments. The essays approach the social and cultural implications of cyberspace from the perspective of cultural studies, communications, art history, art criticism, English, and women's studies; while artists who created nine virtual worlds at the Banff Centre discuss what they have tried to accomplish in both theoretical and technical terms. With 64 illustrations, including 18 color plates. Annotation copyright by Book News, Inc., Portland, OR
$C^*$-Algebra Extensions of $C(X)$
We show that the Weyl-von Neumann theorem for unitaries holds for [lowercase Greek]Sigma-unital [italic capital]A[italic capital]F-algebras and their multiplier algebras.
Orthogonal Decompositions and Functional Limit Theorems for Random Graph Statistics
We define an orthogonal basis in the space of real-valued functions of a random graph, and prove a functional limit theorem for this basis. Limit theorems for other functions then follow by decomposition. The results include limit theorems for the two random graph models [italic]G[subscript italic]n, [subscript italic]p and [italic]G[subscript italic]n, [subscript italic]m as well as functional limit theorems for the evolution of a random graph and results on the maximum of a function during the evolution. Both normal and non-normal limits are obtained. As examples, applications are given to subgraph counts and to vertex degrees.
Gauge Theory on Compact Surfaces
In this paper we develop a concrete description of connections on principal bundles, possibly non-trivial, over compact surfaces and use this description to construct the Yang-Mills measure which underlies the Euclidean quantum theory of gauge fields, involving compact gauge groups, on compact connected two-dimensional Riemannian manifolds (possibly with boundary). Using this measure we compute expectation values of important random variables, the Wilson loops variables, corresponding to a broad class of configurations of loops on the surface.
Markov Fields over Countable Partially Ordered Sets: Extrema and Splitting
Various notions of the Markov property relative to a partial ordering have been proposed by both physicists and mathematicians. This work develops techniques for stying Markov fields on partially ordered sets. We introduce random transformations of the index set which preserves the Markov property of the field. These transformations yield new classes of Markov fields starting from relatively simple ones. Examples include a model for crack formation and a model for the distribution of fibres in a composite material.
