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.     

Defect of the five-thirds law using the Wiener-Hermite expansion

Application of the refined Wiener-Hermite expansion with moderate to high Reynolds numbers Re to homogeneous, isotropic turbulence is presented. The results show a defect to Kolmogorov's five-thirds law, increase in the absolute value of the exponent comparable with many theoretical predictions. Midrange spectra up to fluctuation Reynolds numbers of 10⁸ show little, if any, dependence of the defect on Re, as long as the initial spectra do not deviate too far from their equilibrium states. The renormalization scheme has also been proven to have no effect on the final shape of the spectrum.     

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.     

Synthesis and photoinduced memory effect of poly[2-N-carbazolylethyl acrylate-co-2-(3,5-dinitrobenzoyloxy) ethyl methacrylate]

Copolymers containing an intramolecular electron donor-acceptor (EDA) complex were synthesized by free radical copolymerization of 2-N-carbazolylethyl acrylate and 2-(3,5-dinitrobenzoyloxy)ethyl methacrylate. Glass transition temperatures show a positive deviation from the weight-average values of copolymers, indicating the presence of the specific EDA interaction in copolymers in the solid state. Photoinduced “memory effect,” which is defined as the percentage of the difference of the surface potential given by corona charging before and after irradiation of light on polymer films, was 30% for the copolymer with 5 mol% of acceptor content. Memory effect increased to 70% for a 8 μm film by doping with 2 wt% of trichloroacetic acid (TCAA), and leveled off at 5 wt% of TCAA content. Memory effect was also enhanced by increasing the thickness of polymer films and irradiation time. The largest value of memory effect (85%) was obtained from the film of the copolymer with 5 mol% acceptor content doped with 1 wt% TCAA and with thickness larger than 14 μm.     

Synthesis of oxychelerythrine using lithiated toluamide-benzonitrile cycloaddition

Oxychelerythrine, benzo[c]phenanthridine alkaloid, was synthesized from easily available starting toluamide 5 and benzonitrile 6 using toluamide-benzonitrile cycloaddition reaction in 6 steps.