A Meshless Solution Technique for the Solution of 3D Unsaturated Zone Problems,Based on Local Hermitian Interpolation with Radial Basis Functions

Recent developments in meshless numerical methods have led to algorithms that can be used to solve arbitrarily large problems without the support of a connected mesh, and without the computational cost and numerical ill-conditioning issues usually associated with such solution techniques. This work applies the Local Hermitian Interpolation (LHI) method, based on local interpolation with Radial Basis Functions (RBFs), to the solution of 3D unsaturated porous media problems. The proposed implementation is capable of handling real soil properties, provided either as an analytical function or as a series of pointwise measurements. The technique is implemented with implicit and explicit timestepping, and is validated against two transient Richards’ equation models, of which one has a known analytical solution. In addition, a real-world infiltration problem based on a saturated–unsaturated formulation is modelled, using a realistic variation of soil properties with water-pressure.     

Under load strain partition of a ceramic matrix composite using an ultrasonic method

A method for carrying out strain partition under load is described. An ultrasonic device and a suitable extensometer are used simultaneously. Applied to a ceramic matrix composite, it allows one to evaluate the contribution of the various damage mechanisms on its highly nonlinear behavior.     

Interval dimension and MacNeille completion

Equality between the interval dimensions of a poset and its MacNeille completion, announced in [7], has been obtained by the authors as a byproduct of their study of Galois lattices in [8]. The purpose of this note is to give a direct proof, similar to the classical proof of Baker's result stating that the dimension (in the Dushnik-Miller sense) of a poset and its MacNeille completion are the same.Supported by French PRC Math-Info.     

Cytosporins F–K,new epoxyquinols from the endophytic fungus Pestalotiopsis theae

Chemical investigation of an endophytic fungus, Pestalotiopsis theae, isolated from the leaves of Turraeanthus longipes (Meliaceae) collected in Cameroon, resulted in the isolation of six new epoxyquinols, cytosporins F–K (2–7), together with the known cytosporin D (1). The structures of the new compounds were unambiguously determined by analysis of the 1D, 2D NMR, and HRMS spectra. Cytosporins G–K (3–7) are the first cytosporins with a hydroxyl substituted C₇ side chain, while cytosporins F–I (2–5) contain a 13-acetoxyl group that was not reported previously. A plausible biosynthetic pathway for the cytosporin derivatives is proposed.