Convergence and superconvergence analyses of HDG methods for time fractional diffusion problems

We study the hybridizable discontinuous Galerkin (HDG) method for the spatial discretization of time fractional diffusion models with Caputo derivative of order 0 < α < 1. For each time t ∈ [0, T], when the HDG approximations are taken to be piecewise polynomials of degree k ≥ 0 on the spatial domain Ω, the approximations to the exact solution u in the L _∞(0, T; L ₂(Ω))-norm and to ?u in the \(L_{\infty }(0, \textit {T}; \mathbf {L}_{2}({\Omega }))\)-norm are proven to converge with the rate h ^k+1 provided that u is sufficiently regular, where h is the maximum diameter of the elements of the mesh. Moreover, for k ≥ 1, we obtain a superconvergence result which allows us to compute, in an elementwise manner, a new approximation for u converging with a rate h ^k+2 (ignoring the logarithmic factor), for quasi-uniform spatial meshes. Numerical experiments validating the theoretical results are displayed.     

Computational Design,Synthesis and Application of a New Selective Molecularly Imprinted Polymer for Electrochemical Detection

A computational approach was developed to find a suitable functional monomer to design a new molecularly imprinted polymer (MIP), based on which methacyrlic acid (MAA) was selected as a functional monomer to synthesize the molecular imprinted and non‐imprinted polymers. All calculations were carried out using Gaussian 03 software based on the application of Hartree?Fock (HF) method with 6‐31G (d) basis set. The performance of the MIPs prepared with different ratios of MAA was then evaluated using equilibrium rebinding assays. The MIP with the highest binding capacity was chosen as recognition material for the fabrication of new PVC sensors and their responses were compared with each other and with previously reported modifiers in literature. The addition of the ionic surfactant (TFPB) was found to have a synergistic effect on the response mechanism of the electrodes. The results of the MIP modified sensors show that they provide an improved electrode slope, wider pH range and a highly extended life time reaching 7 months compared to 2–4 weeks in case of traditional ion‐exchangers reported in literature, besides, being successfully applied for measurements in biological samples.     

Spectroscopic investigation of the charge-transfer interactions between 1,4,7-trimethyl-1,4,7-triazacyclononane and the acceptors iodine, TCNE, TCNQ and chloranil

The interaction of the interesting polynitrogen cyclic base 1,4,7-trimethyl-1,4,7-triazacyclononane (TMTACN) with the sigma-acceptor iodine and pi-acceptors tetracyanoethylene (TCNE), 7,7,8,8-tetracyanoquinodimethane (TCNQ) and tetrachloro-p-benzoquinone (chloranil) have been studied spectrophotometrically and cyclic voltametrically in chloroform at 20 degrees C. Based on the obtained data, the formed charge-transfer complexes were formulated as [(TMTACN)I](+).I(3)(-), [(TMTACN)(TCNE)(5)], [(TMTACN)(TCNQ)(3)] and [(TMTACN)(chloranil)(3)] where the stoichiometry of the reactions, donor:acceptor molar ratios, were shown to equal 1:2 for iodine complex, 1:3 for chloranil and TCNQ complexes and 1:5 for TCNE complex.     

Non Deterministic Classical Logic: The λμ++ ‐calculus

In this paper, we present an extension of λμ‐calculus called λμ⁺⁺‐calculus which has the following properties: subject reduction, strong normalization, unicity of the representation of data and thus confluence only on data types. This calculus allows also to program the parallel‐or.     

A generalized equation for rheology of emulsions and suspensions of deformable particles subjected to simple shear at low Reynolds number

We present analyses to provide a generalized rheological equation for suspensions and emulsions of non-Brownian particles. These multiparticle systems are subjected to a steady straining flow at low Reynolds number. We first consider the effect of a single deformable fluid particle on the ambient velocity and stress fields to constrain the rheological behavior of dilute mixtures. In the homogenization process, we introduce a first volume correction by considering a finite domain for the incompressible matrix. We then extend the solution for the rheology of concentrated system using an incremental differential method operating in a fixed and finite volume, where we account for the effective volume of particles through a crowding factor. This approach provides a self-consistent method to approximate hydrodynamic interactions between bubbles, droplets, or solid particles in concentrated systems. The resultant non-linear model predicts the relative viscosity over particle volume fractions ranging from dilute to the the random close packing in the limit of small deformation (capillary or Weissenberg numbers) for any viscosity ratio between the dispersed and continuous phases. The predictions from our model are tested against published datasets and other constitutive equations over different ranges of viscosity ratio, volume fraction, and shear rate. These comparisons show that our model, is in excellent agreement with published datasets. Moreover, comparisons with experimental data show that the model performs very well when extrapolated to high capillary numbers (C a?1). We also predict the existence of two dimensionless numbers; a critical viscosity ratio and critical capillary numbers that characterize transitions in the macroscopic rheological behavior of emulsions. Finally, we present a regime diagram in terms of the viscosity ratio and capillary number that constrains conditions where emulsions behave like Newtonian or Non-Newtonian fluids.     

Determination of diethylhexyl phtalate in water by solid phase microextraction coupled to high performance liquid chromatography

Difficulties detected in the determination of the diethylhexylphthalate (DEHP) at trace levels by gas chromatography–mass spectrometry (GC–MS) using SPME, due to its ubiquitous distribution in the environment has been overcome and a new method for the determination of DEHP in drinking water has been proposed. The method is based on solid phase microextraction (SPME) coupled to high-performance liquid chromatography (HPLC). Detection was carried out spectrophotometrically. Calibration graph was linear in the range 10–110 μg/L with a regression coefficient of r² = 0.998 and a detection limit of 0.6 μg/L. The relative standard deviation was 5 and 2% (n = 4) for chromatographic areas and retention times, respectively. The usefulness of the SPME–HPLC technique was confirmed.     

Synthesis and preliminary investigations of the siRNA delivery potential of novel, single-chain rigid cationic carotenoid lipids

The success of nucleic acid delivery requires the development of safe and efficient delivery vectors that overcome cellular barriers for effective transport. Herein we describe the synthesis of a series of novel, single-chain rigid cationic carotenoid lipids and a study of their preliminary in vitro siRNA delivery effectiveness and cellular toxicity. The efficiency of siRNA delivery by the single-chain lipid series was compared with that of known cationic lipid vectors, 3β-[N-(N',N'-dimethylaminoethane)carbamoyl]-cholesterol (DC-Chol) and 1,2-dimyristoyl-sn-glyceryl-3-phosphoethanolamine (EPC) as positive controls. All cationic lipids (controls and single-chain lipids) were co-formulated into liposomes with the neutral co-lipid, 1,2-dioleolyl-sn-glycerol-3-phosphoethanolamine (DOPE). Cationic lipid-siRNA complexes of varying (+/-) molar charge ratios were formulated for delivery into HR5-CL11 cells. Of the five single-chain carotenoid lipids investigated, lipids 1, 2, 3 and 5 displayed significant knockdown efficiency with HR5-CL11 cells. In addition, lipid 1 exhibited the lowest levels of cytotoxicity with cell viability greater than 80% at all (+/-) molar charge ratios studied. This novel, single-chain rigid carotenoid-based cationic lipid represents a new class of transfection vector with excellent cell tolerance, accompanied with encouraging siRNA delivery efficiency.     

Effect of Efflorescence Formation on Drying Kinetics of Porous Media

We study experimentally the evaporation of an aqueous NaCl solution with efflorescence formation in hydrophilic or hydrophobic two-dimensional model porous media. The efflorescence formation only marginally affects the invasion patterns but greatly modifies the drying kinetics compared to pure water. Two mechanisms are identified for explaining the impact of efflorescence formation on drying kinetics. It is shown that the efflorescence contributes to increase the evaporation rate compared to drying with pure water, a surprising result since the water activity is reduced in the presence of dissolved salt. This effect is explained by the efflorescence liquid capillary pumping effect associated with the porous nature of the efflorescence. Then, we identify a second phase where the efflorescence dries out and acts as a vapour diffusion barrier, leading to a dramatic reduction of evaporation rate.     

La valeur d'un entier classique en \lambda\mu-calcul

In this paper, we present three methods to give the value of a classical integer in -calculus. The first method is an external method and gives the value and the false part of a normal classical integer. The second method uses a new reduction rule and gives as result the corresponding Church integer. The third method is the M. Parigot's method which uses the J.L. Krivine's storage operators.

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Re?u le 4 Septembre 1995