Stemmosides C and D, two novel unusual pregnane glycosides from Solenostemma argel: structural elucidation and configurational study by a combined NMR-quantum mechanical strategy

Stemmosides C and D, two novel pregnane glycosides characterized by an unusual C-17 side chain were isolated from the pericarps of Solenostemma argel. In addition, stemmoside D displays an uncommon 14β proton configuration, apparently being the first pregnane isolated from plants known to have a 15 keto, cis CD ring junction. Their structures have been established by ESIMS and NMR experiments. The relative configuration of the molecules was determined using a strategy based on the simulation of ¹H, ¹³C, and J coupling NMR parameters. DFT calculations of ¹H and ¹³C chemical shifts, and of the ¹H homonuclear spin–spin coupling constants were performed with the mPW1PW91 functional using the 6-31G(d,p) basis set on the fully optimized geometries of all the possible stereoisomers.     

A new flavonol glycoside from the aerial parts of Astragalus vulneraria

A new flavonol glycoside, isorhamnetin 3-O-beta-D-apiofuranosyl-(1-->2)-alpha-L-rhamnopyranosyl-(1-->6)]-beta-D-galactopyranoside, and the known diglycoside, isorhamnetin 3-O-alpha-L-rhamnopyranosyl-(1-->6)-beta-D-galactopyranoside were isolated from the aerial parts of Astragalus vulneraria. Characterization of the two compounds was done by spectroscopic methods (1D and 2D NMR, and FAB-MS).     

Stable tangential family germs and singularities of their envelopes

A tangential family is a system of regular curves emanating tangentially from another regular curve. We classify tangential family germs which are stable under deformations among tangential families and we study singularities of their envelopes. We also discuss some applications of our results to Differential Geometry. To cite this article: G. Capitanio, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Spectrally accurate energy‐preserving methods for the numerical solution of the “good” Boussinesq equation

In this paper we study the geometric numerical solution of the so called “good” Boussinesq equation. This goal is achieved by using a convenient space semi‐discretization, able to preserve the corresponding Hamiltonian structure, then using energy‐conserving Runge–Kutta methods in the Hamiltonian boundary value method class for the time integration. Numerical tests are reported, confirming the effectiveness of the proposed method.     

2-D Numerical Modeling of Bioremediation in Heterogeneous Saturated Soils

This paper presents a numerical solution approach for an existing model for simulating transport and biodegradation in saturated porous media. The discrete approximation makes use of an appropriate blending of mixed-hybrid finite-element and shock-capturing finite-volume schemes. The model is applied for simulating enhanced-bioremediation of highly heterogeneous porous media contaminated by organic pollutants. Injection of water enriched in dissolved oxygen (DO) is considered for accelerating contaminant degradation and concentration of both organic pollutant (substrate) and DO. Heterogeneity is found to produce pools of contaminants which strongly affect DO delivery and, then, the degradation of the organic contaminant. A set of numerical results on representative situations illustrates the effectiveness and the robustness of the present approach. The computational efficiency of the present approach is also estimated in terms of CPU costs and memory requirements.     

Null Space Algorithm and Spanning Trees in Solving Darcy's Equation

A Null Space algorithm is considered to solve the augmented system produced by the mixed finite element approximation of Darcy's Law. The method is based on the combination of a LU factorization technique for sparse matrices with an iterative Krylov solver. The computational efficiency of the method relies on the use of spanning trees to compute the LU factorization without fill-in and on a suitable stopping criterion for the iterative solver. We experimentally investigate its performance on a realistic set of selected application problems.This revised version was published online in October 2005 with corrections to the Cover Date.     

Simple tangential family germs and perestroikas of their envelopes

A tangential family is a 1-parameter system of regular curves emanating tangentially from another regular curve. We classify simple tangential family germs up to A-equivalence. We describe perestroikas of envelopes of simple tangential family germs of small codimension under small deformations of the germ among tangential families.