Tuning the mesh of a mixed method for the stream function Vorticity formulation of the Navier-Stokes equations

Summary In this article we study a new mixed method for the Stokes and Navier-Stokes equations. The method uses two meshes, one very fine for and a coarser one for . Error estimates show that boundary layers do not require to refine the mesh for the stream function as much as for the vorticity when the Reynolds number is large. We prove estimates and study implementation problems.     

Fibrés génériques sur le plan projectif

Sans résumé

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Travail réalisé dans le cadre du groupe Fibres vectoriels du réseau Europrog     

On the a.s. Cesàro-α convergence for stationary or orthogonal random variables

We give a new direct proof of the a.s. convergence of the Cesàro- means of a stationary process (X _n) when 0<<1 andE(X _n ^p )<+ with p>1 and we show that this result does not hold in general for p=1. We also consider similar questions for orthogonal random variables. Finally, we study the a.s. convergence of Riesz harmonic means.     

The Correct Use of "Average" Fluorescence Parameters

When more than one fluorophore is present or when one fluorophore displays a multiple exponential decay "average" fluorescence parameters are derived, which can be combined with "average" lifetimes for further interpretation. However, two kinds of average lifetimes are used in this context: the intensity and the amplitude average lifetime. In this paper the different average parameters are carefully analyzed and their "best" combinations are derived. These average parameters are analyzed in the context of external and internal dynamic and static quenching, Föster energy transfer and the calculation of the radiative rate constant. The use of the amplitude average lifetime for the analysis of multiple fluorophore-containing systems and the detection of interactions is discussed.     

The search for formal electrostatic effects on molecular conformation and crystal packing: crystal structure of 2,2′′‐disubstituted (H versus PPh2) 1,1′‐(1,2‐phenylene)bis(3‐methyl‐1H‐imidazol‐3‐ium) bis(trifluoromethanesulfonate)

Electrostatic interactions between localized integral charges make the stability and structure of highly charged small and rigid organics intriguing. Can σ/π‐electron delocalization compensate reduced conformational freedom by lowering the repulsion between identical charges? The crystal structure of the title salt, C₁₄H₁₆N₄²⁺·2CF₃SO₃⁻, (2), is described and compared with that of the 2,2′′‐bis(diphenylphosphanyl) derivative, (4). The conformations of the dications and their interactions with neighbouring trifluoromethanesulfonate anions are first analyzed from the standpoint of formal electrostatic effects. Neither cation exhibits any geometrical strain induced by the intrinsic repulsion between the positive charges. In contrast, the relative orientation of the imidazolium rings [i.e. anti for (2) and syn for (4)] is controlled by different configurations of the interactions with the closest trifluoromethanesulfonate anions. The long‐range arrangement is also found to be specific: beyond the formal electrostatic packing, C—H…O and C—H…F contacts have no definite `hydrogen‐bond' character but allow the delineation of layers, which are either pleated or flat in the packing of (2) or (4), respectively.     

Highly Selective Artificial Cholesteryl Crown Ether K+‐Channels

The bacterial KcsA channel conducts K⁺ cations at high rates while excluding Na⁺ cations. Herein, we report an artificial ion‐channel formed by H‐bonded stacks of crown‐ethers, where K⁺ cation conduction is highly preferred to Na⁺ cations. The macrocycles aligned along the central pore surround the K⁺ cations in a similar manner to the water around the hydrated cation, compensating for the energetic cost of their dehydration. In contrast, the Na⁺ cation does not fit the macrocyclic binding sites, so its dehydration is not completely compensated. The present highly K⁺‐selective macrocyclic channel may be regarded as a biomimetic of the KcsA channel.     

One Pot Synthesis of Bisphosphonate Esters: A Way to Synthesize Tetraphosphonate Esters

Abstract

Several methods for the preparation of symmetrical bisphosphonates of general type (RO)₂P(O)(R′OH)P(O)(OR)₂, have been developed, and investigated for their pharmacological. Pharmacological screening of these bisphosphonates have shown that these compounds have potent cardiovascular activity and are. potentialy useful in the treatment of hypertension. In this work we described of new method “one pot” for the synthesis of hydroxy bis and tetra phosphonates (I, II, III and IV).     

Preparation of 1,3-Dithiol-2-ones from 1,2-Bis-triisopropylsilanylsulfanyl Alkenes Under Mild Acidic Conditions

1,2-Bis-triisopropylsilanylsulfanyl alkenes are readily converted to 1,3-dithiol-2-ones with phosgene under very mild acidic conditions at room temperature.