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 pro-posed 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.

We give conditions under which a function F (t; x; u; 0 ; ) satisfies the relation @t + @ @F @x along the Pontryagin extremals (x( ); u( ); 0 ; ( )) of an optimal control problem, where H is the corresponding Hamiltonian. The relation generalizes the well known fact that the equality holds along the extremals of the problem, and that in the autonomous case H constant. As applications of the new relation, methods for obtaining conserved quantities along the Pontryagin extremals and for characterizing problems possessing given constants of the motion are obtained.

Abstract This thesis deals with the problem of recovering the local structure of surfaces from discrete range data. It is assumed that this recovery is done mostly in a bottom-up fashion, that is, without the help of a priori knowledge about the viewed surface. Because the problem is ill-posed, we nevertheless need to place constraints on the recovered structure to get a unique solution. In a bottom-up approach, these constraints must come from generic assumptions that apply to all surfaces. Many methods of bottom-up surface reconstruction have been proposed up to now, some of them dealing with intensity surfaces, some with range surfaces. Each of these methods either explicitly or implicitly applies a set of constraints on the data. The way in which the constraints are applied also varies from method to method. The main contribution of this thesis is some success at unifying a number of those methods under a common formalism of energy minimization, which will permit to better compare the choice of constraints between methods. We also show that the most successful surface reconstruction methods form idempotent operators, which we argue is to be expected. One method, Sander's curvature consistency, is studied in more detail than the others because it has not been studied much elsewhere yet. ii TABLE OF CONTENTS TABLE OF CONTENTS Abstract : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 LIST OF FIGURES : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : iv Abstract : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 Sommaire : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 Acknowledgements : : :...

practical algorithm for generatlng smooth

Abstract. Speed scaling is a power management technique that involves dynamically changing the speed of a processor. We study policies for setting the speed of the processor for both of the goals of minimizing the energy used and the maximum temperature attained. The theoretical study of speed scaling policies to manage energy was initiated in a seminal paper by Yao et al. [1995], and we adopt their setting. We assume that the power required to run at speed s is P(s) = s α for some constant α>1. We assume a collection of tasks, each with a release time, a deadline, and an arbitrary amount of work that must be done between the release time and the deadline. Yao et al. [1995] gave an offline greedy algorithm YDS to compute the minimum energy schedule. They further proposed two online algorithms Average Rate (AVR) and Optimal Available (OA), and showed that AVR is 2 α−1 α α-competitive with respect to energy. We provide a tight α α bound on the competitive ratio of OA with respect to energy. We initiate the study of speed scaling to manage temperature. We assume that the environment has a fixed ambient temperature and that the device cools according to Newton’s law of cooling. We observe that the maximum temperature can be approximated within a factor of two by the maximum energy used over any interval of length 1/b, where b is the cooling parameter of the

We obtain regularity conditions of a new type of problems of the calculus of variations with secondorder derivatives. As a corollary, we get non-occurrence of the Lavrentiev phenomenon. Our main result asserts that autonomous integral functionals of the calculus of variations with a Lagrangian having superlinearity partial derivatives with respect to the higher-order derivatives admit only minimizers with essentially bounded derivatives.