Functional Central Limit Theorems for Triangular Arrays of Function-Indexed Processes under Uniformly Integrable Entropy Conditions

Functional central limit theorems for triangular arrays of rowwise independent stochastic processes are established by a method replacing tail probabilities by expectations throughout. The main tool is a maximal inequality based on a preliminary version proved by P. Gaenssler and Th. Schlumprecht. Its essential refinement used here is achieved by an additional inequality due to M. Ledoux and M. Talagrand. The entropy condition emerging in our theorems was introduced by K. S. Alexander, whose functional central limit theorem for so-calledmeasure-like processeswill be also regained. Applications concern, in particular, so-calledrandom measure processeswhich include function-indexed empirical processes and partial-sum processes (with random or fixed locations). In this context, we obtain generalizations of results due to K. S. Alexander, M. A. Arcones, P. Gaenssler, and K. Ziegler. Further examples include nonparametric regression and intensity estimation for spatial Poisson processes.     

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.     

Dimerization of some substituted benzoic acids in aqueous solution from conductance measurements

Precision molar conductances of benzoic, o-toluic, 2,6-dimethylbenzoic, 2,3,6-trimethylbenzoic, and, o-fluorobenzoic acids have been determined in aqueous solution as a function of temperature and of concentration up to near saturation (<0.035 M). At the higher concentrations molar conductances are found to be less than anticipated for the simple dissociation of a 1-1 electrolyte. Although the deviations are only 1% or less they have been interpreted to show that these acids are dimerized in solution. The interpretation includes an assumption that the dimer ionizes to produce a triple ion. Increasing numbers of methyl groups lead to increasing dimerization. For those acids with two ortho groups the dimerization increases with increasing temperature while the other three show decreasing dimerization with increasing temperature. Temperature functions have been determined for the dimerization constants and from these functions standard changes in enthalpy, entropy, and heat capacity have been determined. Comparisons are made with dimerization studies in non-aqueous solvents. From these as well as the behavior of benzene in water it is concluded that a major factor driving the dimerization is hydrophobic interaction. To provide a limiting conductance of the triple ion needed in the dimerization calculations a conductance study was also made for o-Phenylbenzoic acid on the assumption that its anion provides an approximate model of the triple ion.     

Microheterogeneity in aqueous-organic solutions: Heat capacities,volumes and expansibilities of some alcohols,aminoalcohol and tertiary amines in water

The heat capacities per unit volume and the densities of aqueous solutions of 2-propanol, neopentanol, tert-amylalcohol, 2-amino-2-methylpropanol, triethylamine and diethylmethylamine were measured, in many cases as a function of temperature, over the whole mole fraction or solubility range. Apparent and partial molal heat capacities, volumes and expansibilities were derived. The concentration dependence of these functions suggest the existence of transitions in some of these systems, in the water-rich region, qualitatively similar to micellization. The large relaxation contribution observed with some of the thermodynamic functions of hydrophobic alcohols and amines suggests a reinforcement of hydrophobic hydration due to strong hydrogen-bonding interactions of the polar groups with water.     

Thermodynamic properties of organic compounds in aqueous solution. II. Apparent molal heat capacities of piperidines,morpholines, and piperazines

Apparent molal heat capacities of some piperidine, morpholine, and piperazine derivatives in aqueous solution have been determined by adiabatic calorimetry in the temperature range 20–55°C and in the molality range 0.2–1m. Comparison of experimental values with those calculated through group contributions, found for monofunctional compounds, indicates strong interactions between the hydrophilic centers. An interpretation is given of the possible mechanism of this interaction. Also, values of ΔC _p for the addition reaction of proton to nitrogen centers of mono- and bifunctional organic compounds are examined.     

配合物Zn(Phe)(NO3)2·H2O(s)的低温热容和标准摩尔生成焓

利用精密自动绝热热量计直接测定了配合物Zn(Phe)(NO3)2·H2O(s) (Phe:苯丙氨酸)在78-370 K温区的摩尔热容. 通过热容曲线的解析得到该配合物的起始脱水温度为, T0=(324.27±0.37) K. 将该温区的摩尔热容实验值用最小二乘法拟合得到摩尔热容(Cp, m)对温度(T)的多项式方程, 并且在此基础上计算出了它的舒平热容值和各种热力学函数值. 依据Hess定律, 通过设计热化学循环, 选择体积为100 mL浓度为2 mol·L-1 的盐酸作为量热溶剂, 利用等温环境溶解-反应热量计分别测定混合物{ZnSO4·7H2O(s)+2NaNO3(s)+L-Phe(s)}和{Zn(Phe)(NO3)2·H2O(s)+Na2SO4(s)}的溶解焓为, ⊿dH0m,1 =(69.42±0.05) kJ·mol-1, ⊿dH0 m,2 =(48.14±0.04) kJ·mol-1, 进而计算出该配合物的标准摩尔生成焓为, ⊿fH0m =-(1363.10±3.52) kJ·mol-1. 另外, 利用紫外-可见(UV-Vis)光谱和折光指数(refractiveindex)的测量结果检验了所设计的热化学循环的可靠性.     

Product or sum: comparative tests of Voigt,and product or sum of Gaussian and Lorentzian functions in the fitting of synthetic Voigt‐based X‐ray photoelectron spectra

A comparative study for the fitting of X‐ray photoelectron spectra (XPS) using different model functions is presented. Synthetically generated test spectra using Gaussian/Lorentzian convolution and a real measured spectrum are fitted with the three commonly used models: product, sum and Gaussian/Lorentzian convolution functions. In these limited tests, it was found that the sum function is superior to the product function, particularly for low‐noise spectra. Copyright © 2007 John Wiley & Sons, Ltd.     

New generalized computations of quasi-planar waveguides characteristics

An efficient hybrid field solution to the general multilayer substrates transmission line problems with full shielded and half open cross-sectional geometry is presented by using the waveguide modes coupling and decoupling procedure in the spectral domain. Modal transverse transmission lines corresponding to the LSE and LSM modes are taken into account so that the Green's elements for the edge conditions can be derived by a simple iterative method. In this paper, we analyze not only the propagation constants and characteristic impedances but also the available transmission power capacity and power distribution of most commonly used structures. Normalized eigenmode power levels characterizing the propagation features are computed.     

The thermodynamics of proton dissociation of adenine

The thermodynamic quantities associated with ionization of the N₁ and N₉ protons of adenine have been calorimetrically determined as a function of temperature. The H values for proton dissociation of these groups, with pK values of 4.19 and 9.92, were found to be 5.1 and 9.1 kcal/mole, respectively, at 25°C, =0.025. The C _p values for proton dissociation of these groups were estimated to be –11 and –17 cal/mole-deg. These results indicate that the large heat capacity changes observed during conformational transitions of polynucleotides are not the result of ionization of the bases.