Gaussian estimates and L p -boundedness of Riesz means

We show that suitable upper estimates of the heat kernel are sufficient to imply the L ^p boundedness of several families of operators associated with the Schr?dinger group in various situations. This generalizes results by Sj?strand and others in the Euclidean case, and by Alexopoulos in the case of Lie groups and Riemannian manifolds. RID="*" ID="*"Research partially supported by the European Commission (European TMR Network "Harmonic Analysis" 1998-2001, Contract ERBFMRX-CT97-0159).     

Structure of 9,10-di(9,9-dioctylfluorenyl)anthracene in the solid and in solution

A new example of magnetic nonequivalence of chemically equivalent atoms is identified from the proton and carbon resonance spectra of 9,10-di(9,9-dioctylfluorenyl)anthracene with the aid of its conformation in the crystalline state. Molecular modeling suggests that it has a similar conformation in solution.     

Bisphenol-A polycarbonate–poly(butylene terephthalate) transesterification. II. Structure analysis of the reaction products by IR and 1H and 13C NMR

The structure of the four-component copolyester resulting from the exchange reaction between molten bisphenol-A polycarbonate and poly(butylene terephthalate) is analyzed as a function of the reaction time by infrared and nuclear magnetic resonance spectroscopy. By applying a statistical method developed earlier, the mean chain length of the various sequences as well as the degree of randomness is computed. The exchange reaction leads initially to the formation of a block copolyester with reduced solubility. As the reaction proceeds, a soluble random copolycondensate is progressively formed.     

A model for the oxidation of Mg(0001) based upon LEED,AES, ELS and work function measurements

The Mg(0001) face is subjected to oxygen adsorption from 0 to 10³ L. Three characteristic stages of oxygen adsorption are detected from 0 to 10 L. The AES signal of clean Mg decays exponentially against exposure with slopes α _ai such that α_A2 (0.75 → 3 L) >α_A1 (0 → 0.75 L)>α_A3 (3 → 10 L). For increasing exposures, they correspond to: (1) a clear (1 × 1)-Mg(0001), (2) a diffuse (1 × 1)-Mg(0001) and (3) a (1 × 1) with a weaker (1 × 1)-R30°-MgO(111) LEED patterns, respectively. At the end of the third stage, a supplementary ($\text{7}\text{×}\text{7}\text{2}\text{)?R19°?MgO(111)}$ pattern is observed. In ELS, a very fast intensity decrease of energy loss peaks due to surface and bulk plasmon excitations of the clean metal is recorded during the first stage. The energy loss peak due to the oxidized surface plasmon excitation reaches a maximum intensity at the end of the second stage. Energy loss peaks to be attributed to excitations in bulk MgO appear during the third stage. The work function of the sample decreases and shows a minimum around 6 L, and then slowly increases. Beyond 10 L, a logarithmic relation between oxide thickness and exposure seems to exist. These results are interpreted by the following sequential processes: stage 1: random oxygen chemisorption followed by oxygen incorporation (α_A1); stage 2: assembling into islands and lateral island growth (α_A2); stage 3: oxide formation (α_A3) and stage 4: oxide thickening. Lattice models describing these processes are proposed and discussed. The influence of surface roughness on the results is emphasized.     

Etude comparative des proprietes magnetiques des oxydes lamellaires ACrO2 (A = Li,Na, K)—I: Etude par effet Mössbauer de LiCrO2 dope par le fer

A Mössbauer study of the dimensionality of magnetic interactions in the layer oxide LiCr_0.99Fe_0.01O₂ shows a 2-D behaviour.     

Reduction of β-ketosulfoxides : a highly efficient asymmetric synthesis of both enantiomers of methyl carbinols from the corresponding esters

It is shown that reductions of β-ketosulfoxides of identical chirality (R) at sulfur, lead to reduction products of opposite stereochemistry according to the reducing agent used. The high enantiomeric excesses obtained (80 to 100%) provide a general route to both enantiomers of methylcarbinols from the corresponding esters.     

Symetries isometriques applications a la dualite des espaces reticules

We show that ifE is a non-reflexive Banach lattice, there exists for everyn a dual of finite even order ofE which contins isometicallyl _n ^/l . We show that itE is a Banach lattice which is isometric to the dual of a Banach spaceX, then the order intervals are σ (E, X)-compact. We prove then that under various conditions, a Banach lattice which is a dual as a Banach space, is a dual as a Banach lattice. In particular, this is true when the predual ofE is unique.      

Finite-amplitude disturbances in self-gravitating media. II

This paper deals with finite-amplitude axisymmetric disturbances in a self-gravitating fluid column of finite radius R. It is shown that the cutoff wavelength λ_nl above which gravitational breakup occurs now depends on the relative amplitude $\text{?}\text{R}$ of the initial perturbation. Actually, for small-but finite-amplitude disturbances, $\text{λ}{}_{\mathrm{nl}}\text{=}\text{λ}{}_{\mathrm{l}}\text{(1 ? 0.34368}\text{?}{}^2\text{R}{}^2\text{)}$, where λ_l ( = 5.8898R) designates the cutoff wavelength predicted in the linear approximation.     

Use of Induced Circularly Polarized Luminescence (CPL) from Racemic D3 Lanthanide Complexes to Determine the Absolute Configuration of Amino Acids

The perturbation of the racemic equilibrium of luminescent D₃ lanthanide(III) complexes by added chiral agents, such as amino acids, may be a useful technique for determining the absolute configuration of the added species. It is shown in this work, however, that simple interpretation of the equilibrium shift of racemic tris-terdentate complexes of Tb(III) with 2,6-pyridine-dicarboxylate by amino acids, as measured by the sign of the resultant circularly polarized luminescence (CPL) in terms of specific structural characteristics is not possible. CPL results for a number of derivatized amino acids are also presented, and some insights into the nature of the chiral discriminatory forces that might be exploited in this kind of study are discussed.