The main result is a proof that the g-vector of a simplicial complex with a convex ear decomposition is an M-vector. This is a generalization of similar results for matroid complexes. We also show that a finite building has a convex ear…
Papers in Discrete Mathematics
Discrete Mathematics papers in Mathematics, G
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This book provides insight in the mathematics of Galerkin finite element method as applied to parabolic equations. The approach is based on first discretizing in the spatial variables by Galerkin's method, using piecewise polynomial trial functions,…
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Classical Galois theory is a subject generally acknowledged to be one of the most central and beautiful areas in pure mathematics. This text develops the subject systematically and from the beginning, requiring of the reader only basic facts about…
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In the multi-armed bandit problem, a gambler must decide which arm of K non-identical slot machines to play in a sequence of trials so as to maximize his reward. This classical problem has received much attention because of the simple model it…
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We consider the problem of Internet switching, where traffic is generated by selfish users. We study a packetized (TCP-like) traffic model, which is more realistic than the widely used fluid model. We assume that routers have First-In-First-Out…
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We present a novel formulation of the instanton equations in 8-dimensional Yang-Mills theory. This formulation reveals these equations as the last member of a series of gauge-theoretical equations associated with the real division algebras,…
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In most laser applications it is necessary to focus, modify, or shape the laser beam by using lenses and other optical elements. In general, laser-beam propagation can be approximated by assuming that the laser beam has an ideal Gaussian intensity…
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V. V. Kljuev and N. I. Kokovkin-v Sv cerbak v Z. Vyv cisl. Mat. i Mat. Fiz. 5 (1965), 21膒33; ; English translation, Tech. Rep. No. CS 24, Comput. Sci. Dept., Stanford Univ., Stanford, Calif., 1965 have proved that, if one restricts oneself to…
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The paper aims at presenting a didactic and self-contained overview of Gauss-Hermite and Gauss-Laguerre laser beam modes. The usual textbook approach for deriving these modes is to solve the Helmoltz electromagnetic wave equation within the paraxial…
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Kochen and Specker's theorem can be seen as a consequence of Gleason's theorem and logical compactness. Similar compactness arguments lead to stronger results about finite sets of rays in Hilbert space, which we also prove by a direct construction.…
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Cores are, besides connectivity components, one among few concepts that provides us with efficient decompositions of large graphs and networks. In the paper a generalization of the notion of core of a graph based on vertex property function is…
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An approach to unify reproducing kernel methods under one large umbrella and an extension to include time and spatial shifting are proposed. The study is divided into three major topics. The groundwork is set by revisiting the Fourier analysis of…
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This memoir constitutes the author's PhD thesis at Cornell University. It serves both as an expository work and as a description of new research. At the heart of the memoir, we introduce and study a poset NC (k)(W) for each finite Coxeter group W…
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The author describes a probabilistic algorithm that, given a connected, undirected graph G with n vertices, produces a spanning tree of G chosen uniformly at random among the spanning trees of G. The expected running time is O(n log n) per generated…
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Suppose a finite configuration of labeled points p = (p 1 ,. . . ,p n in E d is given along with certain pairs of those points determined by a graph G such that the coordinates of the points of p are generic, i.e., algebraically independent over the…
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The generic initial ideals of a given ideal are rather recent invariants. Not much is known about these objects, and it turns out to be very difficult to compute them. The main purpose of this paper is to study the behaviour of generic initial…
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Sediment and groundwater profiles were compared in two villages of Bangladesh to understand the geochemical and hydrogeological factors that regulate dissolved As concentrations in groundwater. In both villages, fine-grained sediment layers separate…
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We propose a scalable and reliable point-to-point routing algorithm for ad hoc wireless networks and sensor-nets. Our algorithm assigns to each node of the network a virtual coordinate in the hyperbolic plane, and performs greedy geographic routing…
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For many years, scalable routing for wireless communication systems was a compelling but elusive goal. Recently, several routing algorithms that exploit geographic information (e.g., GPSR) have been proposed to achieve this goal. These algorithms…
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(A,E,B)-invariant and (E,A ,B)-invariant subspaces for the two-dimensional singular Roesser model are investigated. These subspaces are related to the existence of the solutions when the boundary conditions are in these subspaces. Also, the…
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