On the performance of peeling algorithms

The peeling of a d-dimensional set of points is usually performed with successive calls to a convex hull algorithm; the optimal worst-case convex hull algorithm, known to have an O(n^˙ Log (n)) execution time, may give an O(n^˙n^˙ Log (n)) to peel all the set; an O(n^˙n) convex hull algorithm, m being the number of extremal points, is shown to peel every set with an O(n-n) time, and proved to be optimal; an implementation of this algorithm is given for planar sets and spatial sets, but the latter give only an approximate O(n^˙n) performance.     

Synthesis,properties, and crystal structure of a novel 3-hydroxy-(4<Emphasis Type="Italic">H</Emphasis>)-benzopyran-4-one containing copper(II) complex,and its oxygenation and relevance to quercetinase

The preparation, spectroscopic properties, and crystal structure of [Cu(ind)(mco)] [ind is the anion of 1,3-bis(2-pyridylimino)isoindoline and mco is the anion of 3-hydroxy-(4H)-benzopyran-4-one] are reported. The complex exhibits a distorted square pyramidal geometry. The oxygenation of the title compound results in oxidative cleavage of the heterocyclic ring to give the (acetylsalicylato)copper(II) complex [Cu(asp)(ind)] (asp is the anion of acetylsalicylic acid) and CO as primary products, which reaction resembles the enzymatic reaction of quercetinase.     

Contractivity and Analyticity in l p of Some Approximation of the Heat Equation

We consider the lumped mass method with piecewise linear finite elements in two dimensions. When the triangulation is of Delaunay type it is known that the discrete scheme satisfies a maximum principle. In this work we pursue the analysis and prove that the discrete semi-group is l ^p contractive in a sector, which implies smoothing effects and provide some resolvent estimates.     

Ueber Verbesserungen an seinem Normalbarometer

Ohne Zusammenfassung     

New Results on the Queens_n 2 Graph Coloring Problem

For the Queens_n ² graph coloring problems no chromatic numbers are available for n > 9 except where n is not a multiple of 2 or 3. In this paper we propose an exact algorithm that takes advantage of the particular structure of these graphs. The algorithm works on the independent sets of the graph rather than on the vertices to be colored. It combines branch and bound, for independent set assignment, with a clique based filtering procedure. A first experimentation of this approach provided the coloring number values ranging for n = 10 to n = 14.     

Error Bounds and Implicit Multifunction Theorem in Smooth Banach Spaces and Applications to Optimization

In this paper we provide an error bound estimate and an implicit multifunction theorem in terms of smooth subdifferentials and abstract subdifferentials. Then, we derive a subdifferential calculus and Fritz–John type necessary optimality conditions for constrained minimization problems.     

On the asymptotic behaviour of elliptic problems with periodic data

We study the asymptotic behaviour of the solution of elliptic problems with periodic data when the size of the domain on which the problem is set becomes unbounded. To cite this article: M. Chipot, Y. Xie, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Fixed mesh approximation of ordinary differential equations with impulses

When trains of impulse controls are present on the right-hand side of a system of ordinary differential equations, the solution is no longer smooth and contains jumps which can accumulate at several points in the time interval. In technological and physical systems the sum of the absolute value of all the impulses is finite and hence the total variation of the solution is finite. So the solution at best belongs to the space BV of vector functions with bounded variation. Unless variable node methods are used, the loss of smoothness of the solution would a priori make higher-order methods over a fixed mesh inactractive. Indeed in general the order of -convergence is and the nodal rate is . However in the linear case -convergence rate remains but the nodal rate can go up to by using one-step or multistep scheme with a nodal rate up to when the solution belongs to . Proofs are given of error estimates and several numerical experiments confirm the optimality of the estimates. Received March 15, 1996 / Revised version received January 3, 1997     

Pricing and distributed QoS control for elastic network traffic

We study a processor-sharing model in which users choose between a high- and a low-priority service, based on their utility functions and prices charged by the service provider. The latter aims at revenue maximization. The model is motivated by file transmissions in data networks with distributed congestion control.