Approximation of multi-scale elliptic problems using patches of finite elements

In this paper we present a method to solve numerically elliptic problems with multi-scale data using multiple levels of not necessarily nested grids. The method consists in calculating successive corrections to the solution in patches whose discretizations are not necessarily conforming. It resembles the FAC method (see Math. Comp. 46 (174) (1986) 439–456) and its convergence is obtained by a domain decomposition technique (see Math. Comp. 57 (195) (1991) 1–21). However it is of much more flexible use in comparison to the latter. To cite this article: R. Glowinski et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Study of removal processes of <Superscript>7</Superscript>Be and <Superscript>137</Superscript>Cs from the atmosphere

In order to understand better the way in which radioactive contamination may be transferred from the atmosphere to other ecological compartments it is necessary to obtain information of the deposition mechanisms of radionuclides. Concentration and speciation of ¹³⁷Cs and ⁷Be in the atmospheric aerosol and deposition were studied. The mixed deposition velocities of water-soluble and insoluble ¹³⁷Cs and ⁷Be were determined. The relation between activity concentrations of insoluble ⁷Be in the atmosphere and its amount in deposition was observed. It is supposed that in the deposition process of radiocesium the precipitation plays an important role in scavenging of water-soluble radiocesium by falling raindrops, in contrast to insoluble ¹³⁷Cs where the dry deposition becomes predominant.     

Convective Heat Transfer past Small Cylindrical Bodies

Convective heat transfer from an array of small, cylindrical bodies of arbitrary shape in an unbounded, two-dimensional domain is a singular perturbation problem involving an infinite logarithmic expansion in the small parameter ε, representing the order of magnitude of the size of the bodies. Using the method of matched asymptotic expansions, we formulate a hybrid asymptotic-numerical method to solve for the dimensionless, steady-state temperature. We assume that the velocity field of the fluid surrounding the bodies is arbitrary but known. From our asymptotic solution for an arbitrary velocity field, we present the results for two special cases: a uniform flow field and a simple shear flow field. We demonstrate the asymptotic results of the hybrid method through a number of examples and, in a particular case, we compare these results to an exact analytical solution.     

Risk management of a bond portfolio using options

In this paper, we elaborate a formula for determining the optimal strike price for a bond put option, used to hedge a position in a bond. This strike price is optimal in the sense that it minimizes, for a given budget, either Value-at-Risk or Tail Value-at-Risk. Formulas are derived for both zero-coupon and coupon bonds, which can also be understood as a portfolio of bonds. These formulas are valid for any short rate model that implies an affine term structure model and in particular that implies a lognormal distribution of future zero-coupon bond prices. As an application, we focus on the Hull-White one-factor model, which is calibrated to a set of cap prices. We illustrate our procedure by hedging a Belgian government bond, and take into account the possibility of divergence between theoretical option prices and real option prices. This paper can be seen as an extension of the work of Ahn and co-workers [Ahn, D., Boudoukh, J., Richardson, M., Whitelaw, R., 1999. Optimal risk management using options. J. Financ. 54, 359-375], who consider the same problem for an investment in a share.     

Analysis of the manufacturing lead time in a production system with non-renewal batch input,threshold policy and post-operation

In this paper, we analyze the manufacturing lead time in a production system with BMAP (Batch Markovian Arrival process) input and post-operation operated under the N-policy. We use the factorization principle to derive the waiting time distribution (hence the manufacturing lead time) and the mean performance measures. A numerical example is provided.     

Base-Catalyzed Reaction of Cyanoalkylphosphonates with Methanol

The equilibrium conversion of nitriles in the reaction of cyanoalkylphosphonates with methanol in the presence of sodium methylate, as determined by potentiometric titration with perchloric acid in nitromethane, varies from 58 to 17.7%. The practical yields of imidates were evaluated by a preparative procedure of isolation of purified imidates from the reaction mixtures (56-14%). Because of the low conversions of nitriles, the reaction is expedient to use only for preparing alkyl (dialkoxyphosphoryl)acetimidates.     

Identification,synthesis and conformational study of a CN(R,S) synthon by-product: (5R, 10R)-5,10-diphenyl-1,6-diaza-3,8-dioxabicyclo[4.4.1]undecane

The title compound, containing a new heterocyclic skeleton, was identified by X-ray crystallography as the product of condensation of (R)-phenylglycinol with an excess of formaldehyde. The molecule adopts a rigid double twist-chair conformation in both solid and solution states.