Characterization of Trimmed NURBS Surface Boundaries Using Topological Criteria

This paper presents an approach based on topology for the determination of characteristics and properties of curves used in the trimming of NURBS surfaces. Through discrete subdivision and topological criteria, a method is presented to determine characteristics of the boundary; such as whether the set of trimming curves forms a set of closed loops, whether trimming curves contain singularities or self intersections, and whether the boundary is simply connected. A surface mesh partitionning the parameter space is used, formed of isoparametric lines in both parametric directions. Topological properties of the cells of this mesh and their intersections with the trimming curves allow to localize the boundary. Topological treatment of this localization allows to define the interior and exterior of the face, and to refine the boundary localization. Singularities and self intersections of the boundary as well as voids in the face are investigated through the study of topological properties of neighbors. As an application, an algorithm for point localization is presented that very rapidly allows to determine whether a given point in parameter space lies inside, on the boundary or outside of the trimmed surface.     

Approximation diophantienne sur les courbes elliptiques à multiplication complexe

Let $\text{E}$ be an elliptic curve with complex multiplication, defined over $\text{Q}$. We consider linear forms on $\text{Lie}\text{(}\text{E}{}^{\mathrm{n}}\text{)}$ with coefficients in the CM field of $\text{E}$. Within this framework, we present a new measure of linear independence for elliptic logarithms in (logb)(loga)ⁿ. Like recent advances in this domain (works by Ably, David, Hirata-Kohno), our result is best possible in terms of the height of the linear forms (logb) while providing a better estimate in the height of algebraic points considered (loga), removing a term in logloga. To cite this article: M. Ably, É. Gaudron, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Estimating market shares in each market segment using the information entropy concept

Sales data of a certain product for the various competitors are usually available at the aggregate level. However these data give no clue to the heterogeneities in the sales pattern across different market segments. Heterogeneities are caused by different purchasing behavior in each market segment; as a purchaser in a segment will be attracted to the attributes of the product most important to that segment. This concept can be formalized via a simple attraction model that utilizes an elasticity measure for each quality or price attribute [G.S. Carpenter, L.G. Cooper, D.M. Hanssens, D.F. Midgley, Modeling asymmetric competition, Marketing Science 7 (4) (1998) 393–412]. Assessment of these elasticities is not difficult since customer response – in each market segment – to perception of quality and price is tracked by most firms [J. Ross, D. Georgoff, A survey of productive and quality issues in manufacturing. The state of the industry, Industrial Management 3 (5) (1991) 22–25]. This paper attempts to formulate a generic framework based on the information entropy concept that utilizes such an attraction model to estimate competitors’ sales in each market segment.     

Near-optimal design of Global Positioning System (GPS) networks using the Tabu Search technique

This paper describes an optimization technique based on an heuristic procedure which is applied to analyse and improve the efficiency of the design of Global Positioning System (GPS) surveying networks. GPS is a valuable survey tool because of its ability to increase the accuracy, speed and flexibility of a survey. A GPS network can be defined as a number of stations, which are co-ordinated by a series of sessions, formed by placing receivers on stations. The goal is to select the best order in which these sessions can be organised to give the best possible schedule. Generally, solving large networks to optimality requires impractical computational time. This paper proposes a Tabu Search technique which provides optimal or near-optimal solutions for large networks with an acceptable amount of computational effort. Computational results for several case studies with known and unknown optimal schedules have been presented to assess the performance of the proposed technique.     

Rheological properties of polyacrylates used as synthetic road binders

Most adhesives and binders, including bitumen for asphalt mixture production, are presently produced from petrochemicals after the refining of crude oil. The fact that crude oil reserves are a finite resource means that in the future, it may become necessary to produce these materials from alternative and probably renewable sources. Suitable resources of this kind may include polysaccharides, plant oils and proteins. This paper deals with the synthesis of polymer binders from monomers that could, in future, be derived from renewable resources. These binders consist of polyethyl acrylate (PEA) of different molecular weight, polymethyl acrylate (PMA) and polybutyl acrylate (PBA), which were synthesised from ethyl acrylate, methyl acrylate and butyl acrylate, respectively, by atom transfer radical polymerisation. The rheological properties of these binders were determined by means of oscillatory testing using a dynamic shear rheometer and combinations of stress/strain, temperature and frequency sweeps. The results indicate that PEA can be produced to have rheological properties similar to that of ‘soft’ 100/150 penetration grade bitumen, PMA with similar rheological properties to that of ‘hard’ 10/20 penetration grade bitumen, while PBA, due to its highly viscous nature and low dynamic moduli, cannot be used on its own as a binder. The synthetic polymers were found to be thermo-rheologically simple, and the shift factors, used to produce the dynamic moduli master curves, were found to fit an Arrhenius function.     

Oxidation of Aromatic Amines to Quinones by Iodic Acid under Microwave Irradiation in the Presence of Montmorillonite K10 and Silica Gel

A variety of aromatic amines are oxidized to their corresponding quinones in excellent yields by supported iodic acid under microwave irradiation and solvent free conditions.     

Osmium(VIII)-catalyzed oxidation of pentamethylene sulfide

Although pentamethylene sulfide (tetrahydrothiopyran) lacks acidic hydrogen, Os^VIII has been found to catalyze its oxidation by alkaline K₃Fe(CN)₆ to produce 3-hydroxypentamethylene sulfide as the only product. The kinetics reveal first-order dependence on ferricyanide and Os^VIII, and zero order on pentamethylene sulfide and OH^–. The effects of introduced electrolytes, K₄Fe(CN)₆, relative permittivity and temperature have also been studied. On the basis of kinetic evidence, a mechanism that involves anation of the osmium catalyst (sulfide/water interchange) followed by intramolecular proton abstraction, followed by an electron transfer step has been proposed and discussed.     

An existence result for a quadrature surface free boundary problem

The aim of this paper is to present two different approachs in order to obtain an existence result to the so-called quadrature surface free boundary problem. The first one requires the shape derivative calculus while the second one depends strongly on the compatibility condition of the Neumann problem. A necessary and sufficient condition of existences is given in the radial case.     

Theoretical estimates for proton-NMR spin–lattice relaxation rates of heterometallic spin rings

Heterometallic molecular chromium wheels are fascinating new magnetic materials. We reexamine the available experimental susceptibility data on MCr₇ wheels in terms of a simple isotropic Heisenberg Hamiltonian for M=Fe, Ni, Cu, and Zn and find in that FeCr₇ needs to be described with an iron–chromium exchange that is different from all other cases. In a second step we model the behavior of the proton spin lattice relaxation rate as a function of applied magnetic field for low temperatures as it is measured in nuclear magnetic resonance (NMR) experiments. It appears that CuCr₇ and NiCr₇ show an unexpectedly reduced relaxation rate at certain level crossings.