DISCONTINUOUS FINITE ELEMENT METHOD FOR CONVECTION-DIFFUSION EQUATIONS

1. IlltroductionThe finite element approximation of the convection--diffusin equations has been investigated using several different approaches (see e.g. [3] [4] and the references therein).Previous analysis in primal formulation of these problems was done for two types ofapproximation schemes: one which produces a continuous piecewise polynomial approximation and one which produces a piecewise polynomial approximation which arecontinuous for certain number of moments accross interelement edge…     

Synthesis of Unprecedented Sulfonylated Phosphono‐exo‐Glycals Designed as Inhibitors of the Three Mycobacterial Galactofuranose Processing Enzymes

This study reports a new methodology to synthesize exo‐glycals bearing both a sulfone and a phosphonate. This synthetic strategy provides a way to generate exo‐glycals displaying two electron‐withdrawing groups and was applied to eight different carbohydrates from the furanose and pyranose series. The Z/E configurations of these tetrasubstituted enol ethers could be ascertained using NMR spectroscopic techniques. Deprotection of an exo‐glycal followed by an UMP (uridine monophosphate) coupling generated two new UDP (uridine diphosphate)‐galactofuranose analogues. These two Z/E isomers were evaluated as inhibitors of UGM, GlfT1, and GlfT2, the three mycobacterial galactofuranose processing enzymes. Molecule 46‐(E) is the first characterized inhibitor of GlfT1 reported to date and was also found to efficiently inhibit UGM in a reversible manner. Interestingly, GlfT2 showed a better affinity for the (Z) isomer. The three enzymes studied in the present work are not only interesting because, mechanistically, they are still the topic of intense investigations, but also because they constitute very important targets for the development of novel antimycobacterial agents.     

Debenzylative Cycloetherification: An Overlooked Key Strategy for Complex Tetrahydrofuran Synthesis

Tetrahydrofuran (THF) is a major structural feature found in many synthetic and natural products displaying a variety of biological properties. This review summarizes the main synthetic approaches that have been developed to construct tetrahydrofuran moieties involving debenzylative cycloetherification reactions (DBCE). Interestingly, this reaction is regio‐ and stereoselective without the requirement of a selective protection/deprotection strategy. Many applications of this process have been reported, including carbafuranoside synthesis, regioselective deprotection of the benzyl group positioned γ to an alkene, and total synthesis of natural products. The stereochemical outcome and the mechanism of these interesting transformations are also discussed.     

Hölder stability estimates for some inverse pointwise source problems

In this Note we establish a Hölder stability estimate for an inverse pointwise source elliptic problem.     

Thermal convection around obstacles: the case of Sierpinski carpets

Measurements of free convection velocity profiles by laser Doppler velocimetry in a cavity containing Plexiglas reconstructed Sierpinski carpets are compared with computed profiles using the SIMPLER numerical code applied to the Navier–Stokes equations. This first step validates the numerical code into which two thermal conductivities are used (that of the liquid and that of the solid), together with two viscosities (that of the liquid and a fictitious high viscosity of the order of 10³⁰ for the solid). Next, the code is used for a network of Sierpinski carpets, allowing the evaluation of a seepage velocity from the Navier–Stokes equations.     

Calculation of effective index for different dielectric waveguides structures made of PVCi/PMATRIFE polymers at telecom-wavelength \lambda =1.55\,\upmu m

In this paper, a number of polymeric waveguide structures have been analyzed by using two distinct techniques which are: effective index method (EIM) and numerical simulation based on finite difference method (FDM). The main aim of this investigation is the calculation of effective indexes (EI) of the following structures: rib, ridge and buried channel waveguides at telecom wavelength $\lambda =1.55\,\upmu \hbox {m}$ for different dimensions of waveguide cores varying from 1.5–4  $\upmu \hbox {m}$ . Moreover, other optical propagation characteristics such as: confinement factor, normalized and propagation constant have been studied in TE polarisation. Otherwise the effect of the structure parameters and dimensions on the dispersion characteristics has been investigated. On the other hand, the optical field distribution has been computed using commercial software named OlympIOs. The polymers applied in the design of waveguide structures are the PVCi (n = 1,562 $\lambda = {1.55}\,\upmu $ m) used as core layer and the PMATRIFE (n = 1,409 $\lambda = 1.55\,\upmu $ m) used as substrate or cladding layer. The results obtained using EIM and simulation based on FDM show that effective index and field confinement factor of TE fundamental mode increase monotonously with the increasing dimension of core. The obtained results are in good agreement with published data based on other numerical methods.     

Plasmonic properties of silver nanostructures coated with an amorphous silicon-carbon alloy and their applications for sensitive sensing of DNA hybridization

The use of an amorphous silicon-carbon alloy overcoating on silver nanostructures in a localized surface plasmon resonance (LSPR) sensing platform allows for decreasing the detection limit by an order of magnitude as compared to sensors based on gold nanostructures deposited on glass. In addition, silver based multilayer structures show a distinct plasmonic behaviour as compared to gold based nanostructures, which provides the sensor with an increased short-range sensitivity and a decreased long-range sensitivity.     

Synthesis of New Tetraheterocyclic Systems by the Mixed Condensation Reactions on [1,2,4]Triazolo[4,3‐a][1,5]benzodiazepines

We report here a one step synthesis of a new series of bis‐[1,2,4‐triazolo][4,3‐a:3′,4′‐d][1,5]benzodiazepines 3a–e and [1,2,4]oxadiazolo[5,4‐d][1,2,4]triazolo[4,3‐a][1,5]benzodiazepines 5a–c by the condensation reactions of diarylnitrilimines and arylonitrile oxides. This 1,3‐dipolar cycloaddition is completely regioselective. The structure of these products has been confirmed by ¹H, ¹³C NMR and mass spectroscopic.     

Selectfluor and NFSI exo‐Glycal Fluorination Strategies Applied to the Enhancement of the Binding Affinity of Galactofuranosyltransferase GlfT2 Inhibitors

Two complementary methods for the synthesis of fluorinated exo‐glycals have been developed, for which previously no general reaction had been available. First, a Selectfluor‐mediated fluorination was optimized after detailed analysis of all the reaction parameters. A dramatic effect of molecular sieves on the course of the reaction was observed. The reaction was generalized with a set of biologically relevant furanosides and pyranosides. A second direct approach involving carbanionic chemistry and the use of N‐fluorobenzenesulfonimide (NFSI) was performed and this method gave better diastereoselectivities. Assignment of the Z/E configuration of all the fluorinated exo‐glycals was achieved based on the results of HOESY experiments. Furthermore, fluorinated exo‐glycal analogues of UDP‐galactofuranose were prepared and assayed against GlfT2, which is a key enzyme involved in the cell‐wall biosynthesis of major pathogens. The fluorinated exo‐glycals proved to be potent inhibitors as compared with a series of C‐glycosidic analogues of UDP‐Galf, thus demonstrating the double beneficial effect of the exocyclic enol ether functionality and the fluorine atom.