Small random perturbations of finite- and infinite-dimensional dynamical systems: Unpredictability of exit times

We apply previous results on the pathwise exponential loss of memory of the initial condition for stochastic differential equations with small diffusion to the problem of the asymptotic distribution of the first exit times from an attracted domain. We show under general hypotheses that the suitably rescaled exit time converges in the zero-noise limit to an exponential random variable. Then we extend the results to an infinite-dimensional case obtained by adding a small random perturbation to a nonlinear heat equation.     

新的酰胺型开链冠醚的合成与性质

Simon在70年代开发了一类酰胺型开链冠醚,能选择性配位碱土金属离子并可作为中性载体制备离子选择性电极.由于酰胺型开链冠醚易于制备,因此受到人们广泛地重视.Vgtle等提出的“末端基”概念为开链冠醚的合成、设计起了重要的指导作用.前文报道2-甲氧基-1-氨甲基萘与三甘醇二碘化物在无水碳酸钠存在下于乙腈中反应得到双手臂的套索冠醚与碘化钠的配合物.X射线衍射晶体结构分析表明萘环上的甲氧基中的氧原子参加了与钠离子的配位,生成了扭曲的六边形双锥结构配合物.因此2-甲氧基-1-氨基萘可以作为开链冠醚的“末端基”.开链冠醚的合成路线是:     

Thermal coefficient of linear expansion of non-crystalline chalcogenides in the As-S-Se-Te-I system

The object of the paper is an investigation of the glasses of the (As₂S₃)_x(AsSe_0.5Te_0.5I)_100-x. type for 65≤;x≤;95, using methods of thermomechanical analysis. Values of the thermal coefficients of linear expansion in solid and visco-plastic phase were determined. it was shown that introducing arsenic-sulfide in glass-matrix AsChI, i.e. (AsSe_0.5Te_0.5I), leads to an increasing stability of these glasses. The characteristic temperatures of softening Tg and the temperature of the beginning of deformation t_w increase by increasing content of As₂S₃. The analytical forms of dependence of four significant physical values α_g, α_l, Tg, Tw, as a function of As₂S₃ content in the structure of glasses were fitted. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

WS2 超细粉体的固相法合成

WS2 超细粉体的固相法合成;WS2;固相反应;过硫系数;高能球磨;粒度     

Freezing temperatures and densities of solutions of some hydrocarbons and sodium oleate inN-methylacetamide. Evidence for a solvophobic interaction

The freezing temperatures and densities (at 31°C) of solutions of octane, nonane, decane, 3,3-diethylpentane, and sodium oleate inN-methylacetamide (NMA) have been measured. The molality of the freezing solution was calculated from the density. The solubilities of octane, nonane, and decane inN-methylacetamide are also reported. Apparent molal volumes calculated from the densities are close to the values in the pure hydrocarbons and are not strong functions of the concentration. This indicates the absence of any unusual packing effect. The calculated free energies of transfer of the hydrocarbons from pure hydrocarbon to NMA solution are much less negative than the corresponding values for water, showing that the bulk solvophobic interaction inN-methylacetamide is smaller than in water. This is consistent with the freezing temperatures of sodium oleate which show that micelles do not form below 0.1 mole-kg^–1. The osmotic coefficients of the hydrocarbons calculated from the freezing temperatures showed negative deviations from ideality that were larger for the hydrocarbons with the higher molecular weights. Two estimates of the pairwise solvophobic interaction inN-methylacetamide indicate that it is also smaller than in water. The solvophobic effect in this solvent does not include the large entropy and enthalpy effects found in aqueous solutions.     

Diffusion in organic solvents: Interdiffusion coefficient of 1,1,2,2-tetrabromoethane

Interdiffusion coefficient have been measured for 1,1,2,2-tetrabromoethane in 21 organic solvents in order to ascertain the influence of shape, size, viscosity, nature and degree of branching, of the solvent molecules on transport properties. None of the existing correlations for diffusion in binary liquid systems appear to fit all the experimental data. Steric effects due to the solvent molecules are shown to be very important in the interpretation of the diffusion process.     

Convergence of optimal stochastic bin packing

Consider independent identically distributed random variables (X_i) valued in [0,1]. Let B(n) be the optimal (minimum) number of unit size bins needed to pack n items of size X₁, X₂,…,X_n. We prove that there exists a numerical constant C such that for t > 0,

$\text{Pr(∣B(n)?E(B(n))∣>t}\text{n}\text{)≤ C exp(? t).}$

The constant C does not depend on the distribution of X.     

Averaged molecular weight of complex mixtures as determined by rapid measurements of diffusion

Summary The concept of a diffusion-averaged molecular weight, M_d is presented, and M_d is defined for polydisperse samples. It is shown via oligostyrene mixtures that M_d can be determined in 20 minutes with common chromatographic equipment. If M_d is measured and M_n or M_w is known, the polydispersity can be obtained.