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1. Cauchy inequality(ndimension and 2order Cauchy inequality)
"... Cauchy inequality is a very important inequality in mathematics and physics, especially has wild application in resolving the proof of inequalities, which has significance for researching inequalities in mathematics. This paper promotes the original Cauchy inequality. The original ndimension and 2 ..."
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Cauchy inequality is a very important inequality in mathematics and physics, especially has wild application in resolving the proof of inequalities, which has significance for researching inequalities in mathematics. This paper promotes the original Cauchy inequality. The original ndimension and 2
Strengthened Cauchy inequality in anisotropic meshes and application to an . . .
, 2001
"... In this document, we show an aposteriori error estimator which is efficient and reliable even on highly stretched meshes for the CrouzeixRaviart/P 0 pair. It relies on hierarchical space splitting whose main ingredient is the strengthened CauchySchwarz inequality. We demonstrate a method to enric ..."
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Cited by 8 (3 self)
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In this document, we show an aposteriori error estimator which is efficient and reliable even on highly stretched meshes for the CrouzeixRaviart/P 0 pair. It relies on hierarchical space splitting whose main ingredient is the strengthened CauchySchwarz inequality. We demonstrate a method
Cauchy Inequality and the Space of Measured Laminations, I
, 2000
"... 1.1. This is the first of two papers addressing a Cauchy type inequality for the geometric intersection number between two 1dimensional submanifolds in a surface. As a consequence, we reestablish some of the basic results in Thurston’s theory of measured laminations. In this paper, we consider surf ..."
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1.1. This is the first of two papers addressing a Cauchy type inequality for the geometric intersection number between two 1dimensional submanifolds in a surface. As a consequence, we reestablish some of the basic results in Thurston’s theory of measured laminations. In this paper, we consider
A Limited Memory Algorithm for Bound Constrained Optimization
 SIAM Journal on Scientific Computing
, 1994
"... An algorithm for solving large nonlinear optimization problems with simple bounds is described. ..."
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Cited by 557 (9 self)
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An algorithm for solving large nonlinear optimization problems with simple bounds is described.
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 550 (3 self)
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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 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 an offline algorithm that computes, for any set of jobs, a minimumenergy schedule. We then consider some online algorithms and their competitive performance for the power function P(s) = sp where p 3 2. It is shown that one natural heuristic, called the Average Rate heuristic, uses at most a constant times the minimum energy required. The analysis involves bounding the largest eigenvalue in matrices of a special type.
Near Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
, 2004
"... Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear m ..."
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Cited by 1513 (20 self)
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Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear measurements do we need to recover objects from this class to within accuracy ɛ? This paper shows that if the objects of interest are sparse or compressible in the sense that the reordered entries of a signal f ∈ F decay like a powerlaw (or if the coefficient sequence of f in a fixed basis decays like a powerlaw), then it is possible to reconstruct f to within very high accuracy from a small number of random measurements. typical result is as follows: we rearrange the entries of f (or its coefficients in a fixed basis) in decreasing order of magnitude f  (1) ≥ f  (2) ≥... ≥ f  (N), and define the weakℓp ball as the class F of those elements whose entries obey the power decay law f  (n) ≤ C · n −1/p. We take measurements 〈f, Xk〉, k = 1,..., K, where the Xk are Ndimensional Gaussian
Regression quantiles
 Econometrica
, 1978
"... Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at ..."
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Cited by 870 (19 self)
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
Bid, ask and transaction prices in a specialist market with heterogeneously informed traders
 Journal of Financial Economics
, 1985
"... The presence of traders with superior information leads to a positive bidask spread even when the specialist is riskneutral and makes zero expected profits. The resulting transaction prices convey information, and the expectation of the average spread squared times volume is bounded by a number th ..."
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Cited by 1217 (5 self)
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The presence of traders with superior information leads to a positive bidask spread even when the specialist is riskneutral and makes zero expected profits. The resulting transaction prices convey information, and the expectation of the average spread squared times volume is bounded by a number that is independent of insider activity. The serial correlation of transaction price differences is a function of the proportion of the spread due to adverse selection. A bidask spread implies a divergence between observed returns and realizable returns. Observed returns are approximately realizable returns plus what the uninformed anticipate losing to the insiders. 1.
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