Oscillation theorems for Sturm-Liouville problems with distribution potentials

The Sturm-Liouville problem

$\begin{array}{*{20}c} { - y'' + q(x)y = \lambda y,} \\ {y(0) = y(1) = 0} \\ \end{array} $

is considered with a singular potential q(x) representing the derivative of a real function from the space L ₂[0, 1] in the distributional sense. Two approaches are developed for the study of oscillation properties of eigenfunctions of this problem. The first approach is based on generalization of methods of the Sturm theory. The second one is based on development of variational principles.

     

Synthesis of amorpha-4,11-diene from dihydroartemisinic acid

Amorphadiene is a natural product involved in the biosynthesis of the antimalarial drug artemisinin. A convenient four-step synthesis of amorphadiene, starting from commercially available dihydroartemisinic acid, is reported. The targeted molecule is isolated with an overall yield of 85% on a multi-gram scale in four steps with only one chromatography.     

Photoluminescence of polycrystalline CuIn0.5Ga0.5Te2 thin films grown by flash evaporation

Polycrystalline CuIn_0.5Ga_0.5Te₂ films were deposited by flash evaporation from ingot prepared by reacting, in stoichiometric proportions, high purity Cu, In, Ga and Te elements in vacuum sealed quartz. The as-obtained films were characterized by X – ray diffraction (XRD), transmission electron microscopy (TEM) combined with energy dispersive spectroscopy (EDS). XRD and TEM results showed that the layer has a chalcopyrite-type structure, predominantly oriented along (112) planes, with lattice parameters a?=?0.61?nm and c?=?1.22?nm. The optical properties in the near - infrared and visible range 600–2400?nm have been studied. The analysis of absorption coefficient yielded an energy gap value of 1.27?eV. Photoluminescence analysis of as-grown sample shows two main emission peaks located at 0.87 and 1.19?eV at 4?K.     

Synthetic signal injection using inductive coupling

The limited bandwidths of volume selective RF pulses in localized in vivo MRS experiments introduce spatial artifacts that complicate spectral quantification of J-coupled metabolites. These effects are commonly referred to as a spatial interference or "four compartment" artifacts and are more pronounced at higher field strengths. The main focus of this study is to develop a generalized approach to numerical simulations that combines full density matrix calculations with 3D localization to investigate the spatial artifacts and to provide accurate prior knowledge for spectral fitting. Full density matrix calculations with 3D localization using experimental pulses were carried out for PRESS (TE=20, 70 ms), STEAM (TE=20, 70 ms) and LASER (TE=70 ms) pulse sequences and compared to non-localized simulations and to phantom solution data at 4 T. Additional simulations at 1.5 and 7 T were carried out for STEAM and PRESS (TE=20 ms). Four brain metabolites that represented a range from weak to strong J-coupling networks were included in the simulations (lactate, N-acetylaspartate, glutamate and myo-inositol). For longer TE, full 3D localization was necessary to achieve agreement between the simulations and phantom solution spectra for the majority of cases in all pulse sequence simulations. For short echo time (TE=20 ms), ideal pulses without localizing gradients gave results that were in agreement with phantom results at 4 T for STEAM, but not for PRESS (TE=20). Numerical simulations that incorporate volume localization using experimental RF pulses are shown to be a powerful tool for generation of accurate metabolic basis sets for spectral fitting and for optimization of experimental parameters.     

Warm modified Chaplygin gas shaft inflation

In this paper, we examine the possible realization of a new inflation family called “shaft inflation” by assuming the modified Chaplygin gas model and a tachyon scalar field. We also consider the special form of the dissipative coefficient \(\Gamma ={a_0}\frac{T^{3}}{\phi ^{2 }}\) and calculate the various inflationary parameters in the scenario of strong and weak dissipative regimes. In order to examine the behavior of inflationary parameters, the \(n_s \)–\( \phi ,\, n_s \)–r, and \(n_s \)–\( \alpha _s\) planes (where \(n_s,\, \alpha _s,\, r\), and \(\phi \) represent the spectral index, its running, tensor-to-scalar ratio, and scalar field, respectively) are being developed, which lead to the constraints \(r< 0.11\), \(n_s=0.96 \pm 0.025\), and \(\alpha _s =-0.019 \pm 0.025\). It is quite interesting that these results of the inflationary parameters are compatible with BICEP2, WMAP \((7+9)\) and recent Planck data.     

Evaluation of Seven Essential Oils as Seed Treatments against Seedborne Fungal Pathogens of Cucurbita maxima

Essential oils are gaining interest as environmentally friendly alternatives to synthetic fungicides for management of seedborne pathogens. Here, seven essential oils were initially tested in vivo for disinfection of squash seeds (Cucurbita maxima) naturally contaminated by Stagonosporopsis cucurbitacearum, Alternaria alternata, Fusarium fujikuro, Fusarium solani, Paramyrothecium roridum, Albifimbria verrucaria, Curvularia spicifera, and Rhizopus stolonifer. The seeds were treated with essential oils from Cymbopogon citratus, Lavandula dentata, Lavandula hybrida, Melaleuca alternifolia, Laurus nobilis, and Origanum majorana (#1 and #2). Incidence of S. cucurbitacearum was reduced, representing a range between 67.0% in L. nobilis to 84.4% in O. majorana #2. Treatments at 0.5 mg/mL essential oils did not affect seed germination, although radicles were shorter than controls, except with C. citratus and O. majorana #1 essential oils. Four days after seeding, seedling emergence was 20%, 30%, and 10% for control seeds and seeds treated with C. citratus essential oil (0.5 mg/mL) and fungicides (25 g/L difenoconazole plus 25 g/L fludioxonil). S. cucurbitacearum incidence was reduced by ~40% for plantlets from seeds treated with C. citratus essential oil. These data show the effectiveness of this essential oil to control the transmission of S. cucurbitacearum from seeds to plantlets, and thus define their potential use for seed decontamination in integrated pest management and organic agriculture.     

A three field stabilized finite element method for the Stokes equationsUne méthode d'éléments finis stabilisée à trois champs pour les équations de Stokes

We consider in this work the boundary value problem for Stokes equations on a two dimensional domain in cases where non-standard boundary conditions are given. We study the cases where pressure and normal or tangential components of the velocity are given in different parts of the boundary and solve the problem with a minimal regularity. We introduce the problem and its variational formulation which is a mixed one. The principal unknowns are the pressure and the vorticity, the multiplier is the velocity. We present the numerical discretization which needs some stabilization. We prove the convergence and the behavior of the a priori error estimates. Some numerical tests are also presented. To cite this article: M. Amara et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 603–608.     

Evaluation of an ab initio quantum mechanical/molecular mechanical hybrid-potential link-atom method

 Hybrid potentials have become a common tool in the study of many condensed-phase processes and are the subject of much active research. An important aspect of the formulation of a hybrid potential concerns how to handle covalent bonds between atoms that are described with different potentials and, most notably, those at the interface of the quantum mechanical (QM) and molecular mechanical (MM) regions. Several methods have been proposed to deal with this problem, ranging from the simple link-atom method to more sophisticated hybrid-orbital techniques. Although it has been heavily criticized, the link-atom method has probably been the most widely used in applications, especially with hybrid potentials that use semiempirical QM methods. Our aim in this paper has been to evaluate the link-atom method for ab initio QM/MM hybrid potentials and to compare the results it gives with those of previously published studies. Given its simplicity and robustness, we find that the link-atom method can produce results of comparable accuracy to other methods as long as the charge distribution on the MM atoms at the interface is treated appropriately. Received: 27 September 2002 / Accepted: 21 October 2002 / Published online: 8 January 2003 Correspondence to: M. J. Field e-mail: mjfield@ibs.fr Acknowledgements. The authors thank the Institut de Biologie Structurale – Jean-Pierre Ebel, the Commissariat à l'Energie Atomique and the Centre National de la Recherche Scientifique for support of this work.