Polytopes of high rank for the alternating groups

There is a well-known correspondence between abstract regular polytopes and string C-groups. In this paper, for each d?3, a string C-group with d generators, isomorphic to an alternating group of degree n is constructed (for some n?9), or equivalently an abstract regular d-polytope, is produced with automorphism group Alt(n). A method that extends the CPR graph of a polytope to a different CPR graph of a larger (or possibly isomorphic) polytope is used to prove that various groups are themselves string C-groups.     

Finite elements for a prefractal transmission problem

In this Note we deal with the finite element approximation of a transmission problem across a prefractal curve approximating the von Koch fractal curve. We construct a mesh adapted to the geometric shape of the interface and we refine it consistently with some estimates in suitable weighted Sobolev spaces. In these spaces we also obtain an approximation error estimate. To cite this article: P. Bagnerini et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

An analytic approach to stochastic Volterra equations with completely monotone kernels

We apply the semigroup setting of Desch and Miller to a class of stochastic integral equations of Volterra type with completely monotone kernels with a multiplicative noise term; the corresponding equation is an infinite dimensional stochastic equation with unbounded diffusion operator that we solve with the semigroup approach of Da Prato and Zabczyk. As a motivation of our results, we study an optimal control problem when the control enters the system together with the noise.      

Highly symmetric hypertopes

We study incidence geometries that are thin and residually connected. These geometries generalise abstract polytopes. In this generalised setting, guided by the ideas from the polytope theory, we introduce the concept of chirality, a property of orderly asymmetry occurring frequently in nature as a natural phenomenon. The main result in this paper is that automorphism groups of regular and chiral thin residually connected geometries need to be C-groups in the regular case and \({C^+}\)-groups in the chiral case.     

On an Elliptical Trust-Region Procedure for Ill-Posed Nonlinear Least-Squares Problems

In this paper, we address the stable numerical solution of ill-posed nonlinear least-squares problems with small residual. We propose an elliptical trust-region reformulation of a Levenberg–Marquardt procedure. Thanks to an appropriate choice of the trust-region radius, the proposed procedure guarantees an automatic choice of the free regularization parameters that, together with a suitable stopping criterion, ensures regularizing properties to the method. Specifically, the proposed procedure generates a sequence that even in case of noisy data has the potential to approach a solution of the unperturbed problem. The case of constrained problems is considered, too. The effectiveness of the procedure is shown on several examples of ill-posed least-squares problems.     

Preferential sites for InAsP/InP quantum wire nucleation using molecular dynamics

In this paper, stress fields at the surface of the capping layer of self-assembled InAsP quantum wires grown on an InP (001) substrate have been determined from atomistic models using molecular dynamics and Stillinger-Weber potentials. To carry out these calculations, the quantum wire compositional distribution was extracted from previous works, where the As and P distributions were determined by electron energy loss spectroscopy and high-resolution aberration-corrected Z-contrast imaging. Preferential sites for the nucleation of wires on the surface of the capping layer were studied and compared with (i) previous simulations using finite element analysis to solve anisotropic elastic theory equations and (ii) experimentally measured locations of stacked wires. Preferential nucleation sites of stacked wires were determined by the maximum stress location at the MD model surface in good agreement with experimental results and those derived from finite element analysis. This indicates that MD simulations based on empirical potentials provide a suitable and flexible tool to study strain dependent atom processes.     

A Schiff base expanded porphyrin macrocycle that acts as a versatile binucleating ligand for late first-row transition metals

The coordination chemistry of the Schiff base polypyrrolic octaaza macrocycle 1 toward late first-row transition metals was investigated. Binuclear complexes with the divalent cations Ni(II), Cu(II), and Zn(II) and with the monovalent cation Cu(I) were prepared and characterized. Air oxidation of the Cu(I) ions in the latter complex to their divalent oxidation state resulted in a change in the coordination mode relative to the macrocycle.     

Acetone powder from dormant seeds of Ricinus communis L

The influence of several factors on the hydrolytic activity of lipase, present in the acetone powder from dormant castor seeds (Ricinus communis) was evaluated. The enzyme showed a marked specificity for short-chain substrates. The best reaction conditions were an acid medium, Triton X-100 as the emulsifying agent and a temperature of 30 degrees C. The lipase activity of the acetone powder of different castor oil genotypes showed great variability and storage stability of up to 90%. The toxicology analysis of the acetone powder from genotype Nordestina BRS 149 showed a higher ricin (toxic component) content, a lower 2S albumin (allergenic compound) content, and similar allergenic potential compared with untreated seeds.     

Photochemistry of Hantzsch 1,4-dihydropyridines and pyridines

The photochemistry of some Hantzsch 4-phenyl-1,4-dihydropyridines bearing a substituent on the phenyl ring (the three isomeric chloro derivatives and the 4′-nitro derivative) has been studied. All of these compounds underwent inefficient aromatization to the corresponding pyridines (quantum yield <10⁻⁴ at 366 nm, <10⁻² at 254 nm). This process is scarcely affected by molecular oxygen and is initiated by proton transfer (from C₄-H), probably to the solvent, from the excited singlet. In turn, the thus formed pyridines were photoreactive with comparable or higher efficiency. Thus, the 4-(3′-chlorophenyl) and 4-(4′-chlorophenyl) Hantzsch pyridines underwent positional rearrangement to form two isomers each. The reaction occurs via Dewar benzene--prismane path. In the case of the minor isomer a further 1,3-shift take place at the Dewar benzene level. The 4-(2′-chlorophenyl) derivative underwent C-Cl bond homolysis, which led to cyclization of the phenyl group onto one of the ester groups forming a pyrane ring.     

Optimization of matrix solid-phase dispersion conditions for UV filters determination in biota samples

A low solvent consumption method for the determination of eight ultraviolet (UV) filters, displaying low to medium polarities, in freeze-dried samples of marine bivalves and fish is proposed. Matrix solid-phase dispersion (MSPD) and gas chromatography with mass spectrometry (GC-MS) were used as sample preparation and determination techniques, respectively. This work describes the influence of several parameters (type and amount of dispersant and clean-up sorbents, as well as elution solvent) on the yield and the selectivity of the MSPD extraction. Under optimized conditions, samples (0.5?g) were ground with 2?g of Florisil in a mortar with a pestle and transferred into a polypropylene syringe, which contained 1?g of C18 as clean-up sorbent. Analytes were eluted with 5?mL of acetonitrile. This extract was concentrated to dryness, re-constituted with 1?mL of ethyl acetate and injected in the GC-MS system without any further clean-up. The global average recoveries, measured for three different biota samples, spiked at three different levels (between 50 and 1000?ng?g^?1), ranged from 80% to 101% with associated standard deviations below 10%. The inter-day precision of the method varied from 4% to 15% and the achieved LOQs (defined for a signal to noise ratio of 10) ranged from 4 to 28?ng?g^?1, referred to the freeze-dried matrix. Octocrylene (OCR) was found in some samples of fish and mussels at concentrations between 15 and 20?ng?g^?1, referred to dry mass.