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Dynamic speed scaling to manage energy and temperature
 In IEEE Syposium on Foundations of Computer Science
, 2004
"... We first consider online speed scaling algorithms to minimize the energy used subject to the constraint that every job finishes by its deadline. We assume that the power required to run at speed ¡ is ¢¤ £. We provide a tight bound on the competitive ratio of the previously proposed Optimal Availabl ..."
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Cited by 113 (14 self)
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We first consider online speed scaling algorithms to minimize the energy used subject to the constraint that every job finishes by its deadline. We assume that the power required to run at speed ¡ is ¢¤ £. We provide a tight bound on the competitive ratio of the previously proposed Optimal Available algorithm. This improves the best known competitive ratio by a factor � � of. We then introduce a new online algorithm, and show that this algorithm’s competitive ratio is at � £ �� � £ �¨����¥�¥����� � most. This competitive ratio is significantly better and is � ������� approximately for large �. Our result is essentially tight for large �. In particular, as � approaches infinity, we show that any algorithm must have competitive ratio �� � (up to lower order terms). We then turn to the problem of dynamic speed scaling to minimize the maximum temperature that the device ever reaches, again subject to the constraint that all jobs finish by their deadlines. We assume that the device cools according to Fourier’s law. We show how to solve this problem in polynomial time, within any error bound, using the Ellipsoid algorithm. 1.
Explicit Constants for Rellich Inequalities in ...
, 1997
"... Introduction Let\Omega be a bounded region in a complete Riemannian manifold with smooth boundary @ Let C 1 (\Omega ); C 1 0 (\Omega\Gamma and C 1 c (\Omega\Gamma denote respectively the space of smooth functions on\Omega , the subspace consisting of such functions which vanish on @ and the su ..."
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Cited by 15 (2 self)
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Introduction Let\Omega be a bounded region in a complete Riemannian manifold with smooth boundary @ Let C 1 (\Omega ); C 1 0 (\Omega\Gamma and C 1 c (\Omega\Gamma denote respectively the space of smooth functions on\Omega , the subspace consisting of such functions which vanish on @ and the subspace of such functions which vanish in a neighbourhood of @ \Omega\Gamma For those whose main interest is in spectral theory in Euclidean space we mention that our main results are also new in that context. We investigate the existence and explicit determination of constants c and weights X and Y on\Omega such that the Rellich inequality Z \Omega Xjuj p c Z \Omega Y
A geometrical version of Hardy's inequality for ...
"... The aim of this article is to prove a Hardy type inequality, concerning functions in (# for some , involving the volume of# and the distance to the boundary of # The inequality is a generalization of a recently proved inequality by M.HoffmannOstenhof, T.HoffmannOstenhof and A.Laptev [9], w ..."
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Cited by 2 (1 self)
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The aim of this article is to prove a Hardy type inequality, concerning functions in (# for some , involving the volume of# and the distance to the boundary of # The inequality is a generalization of a recently proved inequality by M.HoffmannOstenhof, T.HoffmannOstenhof and A.Laptev [9], which dealt with the special case p = 2.
The HardyRellich Inequality for . . .
 PROC. ROY. SOC. EDINBURGH SECT. A
, 1999
"... The HardyRellich inequality given here generalizes a Hardy inequality of Davies [2], from the case of the Dirichlet Laplacian of a region\Omega ` R N to that of the higher order polyharmonic operators with Dirichlet boundary conditions. The inequality yields some immediate spectral information f ..."
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The HardyRellich inequality given here generalizes a Hardy inequality of Davies [2], from the case of the Dirichlet Laplacian of a region\Omega ` R N to that of the higher order polyharmonic operators with Dirichlet boundary conditions. The inequality yields some immediate spectral information for the polyharmonic operators and also bounds on the trace of the associated semigroups and resolvents.
HARDY’S INTEGRAL INEQUALITY FOR COMMUTATORS OF HARDY OPERATORS
, 2006
"... ABSTRACT. The authors establish the Hardy integral inequality for commutators generated by Hardy operators and Lipschitz functions. Key words and phrases: Hardy’s integral inequality, Commutator, Hardy operator, Lipschitz function. ..."
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ABSTRACT. The authors establish the Hardy integral inequality for commutators generated by Hardy operators and Lipschitz functions. Key words and phrases: Hardy’s integral inequality, Commutator, Hardy operator, Lipschitz function.
2005:45issn: 14021757isrn: ltulic 05 ⁄45 seWeight Characterizations of Discrete Hardy and Carleman Type Inequalities
, 2005
"... This thesis deals with some generalizations of the discrete Hardy and Carleman type inequalities and the relations between them. In Chapter 1 we give an introduction and overview of the area that serves as a frame for the rest of the thesis. In particular, a fairly complete description of the develo ..."
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This thesis deals with some generalizations of the discrete Hardy and Carleman type inequalities and the relations between them. In Chapter 1 we give an introduction and overview of the area that serves as a frame for the rest of the thesis. In particular, a fairly complete description of the development of discrete Hardy and Carleman type inequalities in one and more dimensions can be found in this chapter. In Chapter 2 we consider some scales of weight characterizations for the onedimensional discrete Hardy inequality for the case 1 <p ≤ q<∞. These characterizations contain a parameter s and as endpoint results we obtain the usual characterizations of Muckenhoupt or Bennett type. As limit cases some weight characterizations of Carleman type inequalities are obtained for the case 0 <p ≤ q<∞. In Chapter 3 we present and discuss a new scale of weight characterizations for a twodimensional discrete Hardy type inequality and its limit twodimensional Carleman type inequality. In Chapter 4 we generalize the work done in Chapters 2 and 3 and present, prove and discuss the corresponding general ndimensional versions. In Chapter 5 we introduce the study of the general Hardy type inequality n∑
der Rheinischen Friedrich–Wilhelms–Universität Bonn vorgelegt von Hans Knüpfer aus Heidelberg
"... Classical solutions for a thin–film equation ..."