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Speed scaling to manage energy and temperature
 Journal of the ACM
"... 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 s is P s s. We provide a tight bound on the competitive ratio of the previously proposed Optimal A ..."
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Cited by 146 (15 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 s is P s s. 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 e. This competitive ratio is significantly better and is approximately e for large . Our result is essentially tight for large . In particular, as approaches infinity, we show that any algorithm must have competitive ratio e (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.
Smooth ZeroContact Angle Solutions to a ThinFilm Equation Around the Steady State
"... no. 306 ..."
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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 4 (2 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.
SHARP BOUNDS FOR mLINEAR HARDY AND HILBERT OPERATORS
"... Abstract. The precise norms of mlinear Hardy operators and mlinear Hilbert operators on Lebesgue spaces with power weights are computed. Analogous results are also obtained for Morrey spaces and central Morrey spaces. 1. ..."
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Cited by 2 (1 self)
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Abstract. The precise norms of mlinear Hardy operators and mlinear Hilbert operators on Lebesgue spaces with power weights are computed. Analogous results are also obtained for Morrey spaces and central Morrey spaces. 1.
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.
der Rheinischen Friedrich–Wilhelms–Universität Bonn vorgelegt von Hans Knüpfer aus Heidelberg
"... Classical solutions for a thin–film equation ..."
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doi:10.1155/2007/76329 Research Article On Further Analogs of Hilbert’s Inequality
, 2007
"... similar to Hilbert’s type inequality for integrals. As applications, we give its equivalent form as well. Copyright © 2007 Yongjin Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in an ..."
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similar to Hilbert’s type inequality for integrals. As applications, we give its equivalent form as well. Copyright © 2007 Yongjin Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1.
MaxPlanckInstitut für Mathematik in den Naturwissenschaften Leipzig
, 2014
"... Asymmetric domain walls of small angle in soft ferromagnetic films by ..."