Sur une conjecture de M. Kac

Summary We consider the following heat conduction problem. Let K be a compact set in Euclidean space ³. Suppose that K is held at the temperature 1, while the surrounding medium is at the temperature 0 at time 0. Following Spitzer we investigate the asymptotic behaviour of the integral E _K (t) which represents the total energy flow in time t from the set K to the surrounding medium ³–K. An asymptotic expansion is given for E _K (t) which refines a theorem due to Spitzer. This expansion also verifies and improves a formal calculation of Kac. Similar results are proved in higher dimensions. Up to the constant m(K), the quantity E _K (t) can be interpreted as the expected value of the volume of the Wiener sausage associated with K and a d-dimensional Brownian motion. This point of view both plays a major role in the proofs and leads to a probabilistic interpretation of the different terms of the expansion.     

LiCoO2中锂离子固相扩散系数随循环次数的变化

The solid diffusion coefficient of lithium-ion in LiCoO₂ cathode material has been investigated by the capacity intermittent titration technique (CITT) at different voltages and at different charge/discharge cycles. By SEM, XRD and FTIR techniques, the structure of LiCoO₂ was studied before and after charge-discharge cycles, and the relationship between solid diffusion coefficient and crystal structure was further discussed. CITT results show that the value of Li⁺ solid diffusion coefficient of LiCoO₂ is about 10^-12 cm²·s^-1. During the whole charge-discharge cycles, the Li⁺ solid diffusion coefficient decreased within the voltage of 4.0～4.3 V, which is attributed to the change of the structure of LiCoO₂.     

Nouveaux thiochlorures de molybdène(II): Mo6Cl10Y (Y = S,Se, Te): Structure et propriétés magnétiques et électriques

The thiochlorides Mo₆Cl₁₀Y (Y = S, Se, Te) have been prepared; they are isostructural with Nb₆I₁₁, space group Pccn, and have four formula units per unit cell. The X-ray structure of Mo₆Cl₁₀Se has been determined from three-dimensional single-crystal counter data and refined to a final R value of 0.053 for 3350 independent reflections. The most important result concerning this structure is a statistical distribution of the Se atom on the unit (Mo₆X′₈) with $\text{X′ ?}\text{7}\text{8}\text{Cl}\text{+}\text{1}\text{8}\text{Se}$: so the compound Mo₆Cl₁₀Se must be formulated $\text{(Mo}{}_6\text{Cl}{}_7\text{Se)Cl}{}_{\mathrm{<mtext>4</mtext><mtext>2</mtext>}}\text{Cl}{}_{\mathrm{<mtext>2</mtext><mtext>2</mtext>}}$. The diamagnetic and dielectric behavior of these new thiochlorides is discussed.     

Study of the State of Water and Oil in Frozen Emulsions Using Time Domain NMR

Here T(1) and T(2)(*) relaxation time measurements by low-field NMR have been used to quantify the state of oil and water in frozen emulsions. Water-in-oil and oil-in-water emulsions have been studied. A discrete method (NLREG program) and a continuous method (CONTIN program) have been used to analyze the FID and inversion-recovery relaxation curves. The FID signal (T(2)(*)) analysis allowed us to calculate the global solid-intermediate-liquid ratio, and the state of the solid and liquid phases was determined by the T(1) values. Thus we have been able to show that the major part of water ( approximately 99%) is in a solid state in such emulsions (average droplet diameter of about 1.5 &mgr;m). This result was confirmed by the study of a solid paraffin-Span 80-water emulsion and a heavy water-caseinate-triolein emulsion. These first results have shown the interest of this new method for the study of the state of water and oil in frozen emulsions. Copyright 2000 Academic Press.     

Reactions de photoaddition de benzo[b]selenophenes avec l'acetylene dicarboxylate de methyle et avec le dichloro-1,2 ethylene

Photoirradiated in presence of acetophenone, benzo[b]selenophene and its 3-methyl derivative add to dimethyl acetylenedicarboxylate. In each ease, the primary reaction product is unstable and has not been isolated. Photoexeited in its triplet state (the energy of which is in the neighbourhood of 69 $\text{kcal}\text{mole}$) benzo[b]selenophene and its 2- and 3-methyl, 2,3 dimethyl, 3 acetoxy and 2-methyl-3-acetoxy derivatives add to 1,2 dichloroethylene leading to cyclobutanes. Neither cyclo-addition occurs in absence of photosensitiser. Single-crystal X-ray analysis gave the structures of the two adducts of 3-acetoxybenzo[b]selenophene with trans-1,2-dichloroethylene. In both compounds the chlorine atoms are trans.     

Determination of Organochlorine Pesticides in Sediments from Authie Bay Using Microwave Assisted Solvent Extraction

The aim of this study was to develop an analytical method to determine the organochlorine concentrations in sediments. Combination of Microwave assisted Solvent Extraction (MASE) and capillary gas chromatography with specific detection (electron capture detector) was a viable approach for the determination of pesticides in solid matrixes. In this study, MASE development was focused on the selection of a suitable extraction solvent for all the target analytes. MASE procedure was validated by comparison with conventional methods such as Soxhlet and sonication extraction. The proposed method was then applied to determine the organochlorine insecticides concentrations in samples from Authie Bay (France). Environmental water samples were analysed and five target analytes were detected in concentrations from 0.03 to 0.56 ng/g of dry sediment. These investigations showed the accumulation and the persistency of these products in sediments in spite of the fact they were banned a few decades ago.     

New labdane-type diterpenoids from Leonurus heterophyllus SW

Five new natural labdane-type diterpenoids (5-9), designated leoheteronins A-E, together with four known diterpenoids (1-4), two phytosterols as a mixture of beta-sitosterol and stigmasterol, and the flavone genkwanin (10) were isolated from the aerial parts of Leonurus heterophyllus SW. (Lamiaceae) collected in northern Vietnam. Compound 1 was isolated for the first time from a Leonurus species, and 10 is considered to be a chemotaxonomic marker of the Leonurus genus. Their structures were determined using spectroscopic analyses.