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ACKNOWLEDGEMENTS
, 2003
"... Dr. Manfred Huber has been a great thesis advisor. I thank him for giving me an opportunity to work for him and for all the calm explanations. He helped me by shaping my critical thinking as well as by improving my expressive skills. I would like to thank Dr. Farhad Kamangar and Dr. Lynn Peterson fo ..."
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for serving on my committee. I would like to thank Dr. Zaruba, Dr. Alp and Mr. David Levine for everything that they have taught me. I extend my appreciation to my friends—Raman, Vivek, Shashank, Amit, Birj, Gaurav and the rest—for their support and humor through all the conflicts of these past two years
NONINTERSECTING BROWNIAN EXCURSIONS
, 2007
"... We consider the process of n Brownian excursions conditioned to be nonintersecting. We show the distribution functions for the top curve and the bottom curve are equal to Fredholm determinants whose kernel we give explicitly. In the simplest case, these determinants are expressible in terms of Painl ..."
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Cited by 31 (0 self)
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We consider the process of n Brownian excursions conditioned to be nonintersecting. We show the distribution functions for the top curve and the bottom curve are equal to Fredholm determinants whose kernel we give explicitly. In the simplest case, these determinants are expressible in terms
On Schur properties of random subsets of integers
 J. NUMBER THEORY
, 1996
"... A classic result of I. Schur [9] asserts that for every r 2 and for n sufficiently large, if the set [n]=[1, 2,..., n] is partitioned into r classes, then at least one of the classes contains a solution to the equation x+ y=z. Any such solution with x{y will be called a Schur triple. Let us say that ..."
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Cited by 22 (2 self)
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A classic result of I. Schur [9] asserts that for every r 2 and for n sufficiently large, if the set [n]=[1, 2,..., n] is partitioned into r classes, then at least one of the classes contains a solution to the equation x+ y=z. Any such solution with x{y will be called a Schur triple. Let us say
EXAMPLES OF SCALARFLAT HYPERSURFACES IN R n+1
, 812
"... ABSTRACT. Given a hypersurface M of null scalar curvature in the unit sphere S n, n≥ 4, such that its second fundamental form has rank greater than 2, we construct a singular scalarflat hypersurface in R n+1 as a normal graph over a truncated cone generated by M. Furthermore, this graph is 1stable ..."
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ABSTRACT. Given a hypersurface M of null scalar curvature in the unit sphere S n, n≥ 4, such that its second fundamental form has rank greater than 2, we construct a singular scalarflat hypersurface in R n+1 as a normal graph over a truncated cone generated by M. Furthermore, this graph is 1
A O(n 8)×O(n 7) Linear Programming Model of the Quadratic Assignment Problem
, 802
"... Abstract: In this paper, we propose a linear programming (LP) formulation of the Quadratic Assignment Problem (QAP) with O(n 8) variables and O(n 7) constraints, where n is the number of assignments. A small experimentation that was undertaken in order to gain some rough indications about the comput ..."
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Abstract: In this paper, we propose a linear programming (LP) formulation of the Quadratic Assignment Problem (QAP) with O(n 8) variables and O(n 7) constraints, where n is the number of assignments. A small experimentation that was undertaken in order to gain some rough indications about
A O(n 8)×O(n 7) Linear Programming Model of the Traveling Salesman Problem
, 803
"... Abstract: In this paper, we propose a new linear programming (LP) formulation of the Traveling Salesman Problem (TSP). The proposed model has O(n 8) variables and O(n 7) constraints, where n is the number of cities. Our numerical experimentation shows that computational times for the proposed linear ..."
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Abstract: In this paper, we propose a new linear programming (LP) formulation of the Traveling Salesman Problem (TSP). The proposed model has O(n 8) variables and O(n 7) constraints, where n is the number of cities. Our numerical experimentation shows that computational times for the proposed
Towards Efficient Nx Contingency Selection Using Group Betweenness Centrality
"... Abstract—The goal of N − x contingency selection is to pick a subset of critical cases to assess their potential to initiate a severe crippling of an electric power grid. Even for a moderatesized system there can be an overwhelmingly large number of contingency cases that need to be studied. The num ..."
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Abstract—The goal of N − x contingency selection is to pick a subset of critical cases to assess their potential to initiate a severe crippling of an electric power grid. Even for a moderatesized system there can be an overwhelmingly large number of contingency cases that need to be studied
Characteristics and existence of isometric embeddings
"... Let (Mn, ds 2) be an ndimensional Riemannian manifold. A wellknown problem is to prove the existence of a local Coo isometric embedding 7"n(n + l) (Mn, ds2) /2. (1) By this we mean that there is a smooth isometric embedding of a neighborhood of a given point x0 M; to simplify notation, we sha ..."
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Cited by 10 (1 self)
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Let (Mn, ds 2) be an ndimensional Riemannian manifold. A wellknown problem is to prove the existence of a local Coo isometric embedding 7"n(n + l) (Mn, ds2) /2. (1) By this we mean that there is a smooth isometric embedding of a neighborhood of a given point x0 M; to simplify notation, we
Results 1  10
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223