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THE EXISTENCE OF MINIMIZERS OF THE ACTION FUNCTIONAL WITHOUT CONVEXITY ASSUMPTION
"... Abstract. We shall prove the existence of minimizers of the following functional f(u) = R T 0 L(x, u(x), u ′ (x)) dx without convexity assumption. As a consequence of this result and the duality described in [10] we derive the existence of solutions for the Dirichlet problem for a certain different ..."
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Abstract. We shall prove the existence of minimizers of the following functional f(u) = R T 0 L(x, u(x), u ′ (x)) dx without convexity assumption. As a consequence of this result and the duality described in [10] we derive the existence of solutions for the Dirichlet problem for a certain
The Quickhull algorithm for convex hulls
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 1996
"... The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the twodimensional Quickhull Algorithm with the generaldimension BeneathBeyond Algorithm. It is similar to the randomized, incremental algo ..."
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Cited by 713 (0 self)
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is implemented with floatingpoint arithmetic, this assumption can lead to serious errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of “thick ” facets that contain all possible exact convex hulls of the input. A variation
SINGULAR RADON TRANSFORMS AND MAXIMAL FUNCTIONS UNDER CONVEXITY ASSUMPTIONS
, 2002
"... Abstract. We prove variable coefficient analogues of results in [5] on Hilbert transforms and maximal functions along convex curves in the plane. 1. ..."
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Abstract. We prove variable coefficient analogues of results in [5] on Hilbert transforms and maximal functions along convex curves in the plane. 1.
AN ERSATZ EXISTENCE THEOREM FOR FULLY NONLINEAR PARABOLIC EQUATIONS WITHOUT CONVEXITY ASSUMPTIONS
, 2013
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The Extended Linear Complementarity Problem
, 1993
"... We consider an extension of the horizontal linear complementarity problem, which we call the extended linear complementarity problem (XLCP). With the aid of a natural bilinear program, we establish various properties of this extended complementarity problem; these include the convexity of the biline ..."
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Cited by 788 (30 self)
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We consider an extension of the horizontal linear complementarity problem, which we call the extended linear complementarity problem (XLCP). With the aid of a natural bilinear program, we establish various properties of this extended complementarity problem; these include the convexity
Amortized Efficiency of List Update and Paging Rules
, 1985
"... In this article we study the amortized efficiency of the “movetofront” and similar rules for dynamically maintaining a linear list. Under the assumption that accessing the ith element from the front of the list takes 0(i) time, we show that movetofront is within a constant factor of optimum amo ..."
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Cited by 824 (8 self)
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In this article we study the amortized efficiency of the “movetofront” and similar rules for dynamically maintaining a linear list. Under the assumption that accessing the ith element from the front of the list takes 0(i) time, we show that movetofront is within a constant factor of optimum
Robust principal component analysis?
 Journal of the ACM,
, 2011
"... Abstract This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a lowrank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions, it is possible to recover both the lowrank and the ..."
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Cited by 569 (26 self)
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Abstract This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a lowrank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions, it is possible to recover both the low
A scheduling model for reduced CPU energy
 ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE
, 1995
"... The energy usage of computer systems is becoming an important consideration, especially for batteryoperated systems. Various methods for reducing energy consumption have been investigated, both at the circuit level and at the operating systems level. In this paper, we propose a simple model of job s ..."
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Cited by 558 (3 self)
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scheduling aimed at capturing some key aspects of energy minimization. In this model, each job is to be executed between its arrival time and deadline by a single processor with variable speed, under the assumption that energy usage per unit time, P, is a convex function of the processor speed s. We give
Multibump Solutions for a Strongly Indefinite Semilinear Schrödinger Equation Without Symmetry or convexity Assumptions
, 2008
"... In this paper, we study the following semilinear Schrödinger equation with periodic coefficient: −△u + V (x)u = f(x, u), u ∈ H 1 (R N). The functional corresponding to this equation possesses strongly indefinite structure. The nonlinear term f(x, t) satisfies some superlinear growth conditions and ..."
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Cited by 4 (3 self)
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In this paper, we study the following semilinear Schrödinger equation with periodic coefficient: −△u + V (x)u = f(x, u), u ∈ H 1 (R N). The functional corresponding to this equation possesses strongly indefinite structure. The nonlinear term f(x, t) satisfies some superlinear growth conditions and need not be odd or increasing strictly in t. Using a new variational reduction method and a generalized Morse theory, we proved that this equation has infinitely many geometrically different solutions. Furthermore, if the solutions of this equation under some energy level are isolated, then we can show that this equation has infinitely many m−bump solutions for any positive integer m ≥ 2.
Results 1  10
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