Excess Molar Volumes of Binary Mixtures of 1-Heptanol or 1-Nonanol with n-Polyethers at 25°C

Excess molar volumes V ^E _m at 25°C and atmospheric pressure over the entirecomposition range for binary mixtures of 1-heptanol with 2,5-dioxahexane, 2,5,8-trioxanonane,5,8,11-trioxapentadecane, 2,5,8,11-tetraoxadodecane,or 2,5,8,11,14-pentaoxapentadecane, and mixtures of 1-nonanol with 2,5-dioxahexane,3,6-dioxaoctane, 2,5,8-trioxanonane, 3,6,9-trioxaundecane, 5,8,11-trioxapentadecane,2,5,8,11-tetraoxadodecane, or 2,5,8,11,14-pentaoxapentadecane are reportedfrom densities measured with a vibrating-tube densimeter.V ^E _m curves are nearlysymmetrical at about 0.5 mole fraction. Excess molar volumes are usually positive,indicating predominance of positive contributions to V ^E _m from the disruption ofH bonds of alcohols and from physical interactions. When chain lengths ofboth components of the mixture are increased, the contribution from interstitialaccommodation appears to be sufficiently negative, such that V ^E _m becomes negative(e.g., l-nonanol + 5,8,11-tetraoxapentadecane).     

Electronic absorption spectra of L-ascorbic acid in nonaqueous media

An Electronic spectroscopic study of the self-association of Vitamin C in the nonaqueous phase is reported, pre-sumably for the first time. The oxidation of ascorbic acid in 1,4-dioxane has been studied by UV spectroscopy. The dramatic role of the environment in the stability and identification of the possible intermediates formed in the oxidation of ascorbic acid is shown. Published in Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 2, pp. 263–265, March–April, 2006.     

两两NQD序列部分和的强大数定律

By using the moment inequality, maximal inequality and the truncated method of random variables, we establish the strong law of large numbers of partial sums for pairwise NQD sequences, which extends the corresponding result of pairwise NQD random variables.     

NA列与两两NQD列的L^p收敛性

设{Xn,n≥1）是NA列或两两NQD列,{ank;1≤k≤n,n∈N）是实数阵列．利用矩不等式和截尾方法,研究了∑k=1^n ankXk的L^p收敛性,所获结论推广和改进了前人的相应结果．     

有限个互素因子链上幂GCD矩阵与幂LCM矩阵的行列式的整除性

设S={x1,x2,...,xn}是由n个不同的正整数组成的集合,并设a为正整数.如果一个n阶矩阵的第i行j列元素是S中元素xi和xj的最大公因子的a次幂(xi,xj)a,则称该矩阵为定义在S上的a次幂最大公因子(GCD)矩阵,用(Sa)表示;类似定义a次幂LCM矩阵[Sa].如果存在{1,2,...,n}上的一个置换σ使得xσ(1)|xσ(2)|···|xσ(n),则称S为一个因子链.如果存在正整数k,使得S=S1∪S2∪···∪Sk,其中每一个Si(1ik)均为一个因子链,并且对所有的1i=jk,Si中的每个元素与Sj中的每个元素互素,则称S由有限个互素因子链构成.本文中,设S由有限个互素的因子链构成,并且1∈S.我们首先给出幂GCD矩阵与幂LCM矩阵的行列式的公式,然后证明:如果a|b,则det(Sa)|det(Sb),det[Sa]|det[Sb],det(Sa)|det[Sb].最后我们指出:如果构成S的有限个因子链不互素,则此结论一般不成立.     

Cesàro α-Integrability and Laws of Large Numbers I

For a sequence of integrable random variables, we introduce a new set of conditions called Cesàro -Integrability and Strong Cesàro -Integrability and show that, for <1/2, these conditions that are strictly weaker than Cesàro Uniform Integrability and Strong Cesàro Uniform Integrability respectively, are sufficient for WLLN and SLLN to hold for a sequence of pairwise independent random variables. For some special kinds of dependent sequences of random variables also, Cesàro -integrability for appropriate is shown to be sufficient for WLLN to hold.     

Thermodynamics of Organic Mixtures Containing Amines. II. Excess Molar Volumes at 25°C for Methylbutylamine + Alkane Systems and Eras Characterization of Linear Secondary Amine + Alkane Mixtures

Excess molar volumes, at 25°C and atmospheric pressure for methylbutyl amine + n-hexane; + cyclohexane; + n-octane; n-decane; + n-dodecane; + n-tetradecane, or + n-hexadecane systems are reported from densities measured with a vibrating-tube densimeter. The excess functions, molar enthalpy, and volume, for linear secondary amine + n-alkane systems are discussed in terms of interactional and structural effects. In addition, these solutions, which include amines from dimethyl to dioctylamine, are studied in the framework of the ERAS model. The corresponding ERAS parameters are reported. The agreement between experimental data and ERAS results is good for excess enthalpies, excess Gibbs energies, and excess molar volumes. The larger discrepancies are found for the excess volumes when strong free-volume effects are present in the investigated mixtures. The variation with temperature of the thermodynamic properties is well described by ERAS.     

Thermodynamics of mixtures of amines with n-alkanes and 1-alkanols

The LFAS (Lattice-Fluid Associated Solution) model, which has been applied to alkanol + alkane and to alkanol + alkanol mixtures is now extended to mixtures consisting of one self-associated and one active or weakly self-associated component. The types of association complexes considered are A_nB_m and A_nB with a single A-B bond each. The model is subsequently applied to binary alkanol + amine mixtures with an emphasis on vapor-liquid equilibria. Self-association constants for n-alkyl amines and dialkyl amines are presented along with the pure component lattice-fluid scaling constants. These parameters are used for correlating pure component data on vapor pressures, heats of vaporization, and orthobaric densities as well as mixing properties of amine + alkane mixtures.Communicated at the Festsymposium celebrating Dr. Henry V. Kehiaian's 60^th birthday, Clermont-Ferrand, France, 17–18 May 1990.     

Formation of regular clusters through self-association of intramolecularly hypercrosslinked polystyrene-type nanosponges

Atactic polystyrene of M = 330,000 Da and M_w/M_n = 1.04 was subjected to chloromethylation. By the heating of chloromethylpolystyrene with SnCl₄ in a very dilute solution in ethylene dichloride, the polymeric coils were converted into intramolecularly hypercrosslinked macromolecules, nanosponges, of molecular weight of about 370,000 Da and a diameter of about 17 nm. When in solution, the nanosponges tend to reversibly self-assemble into regular clusters. Size exclusion chromatography and sedimentation analysis corroborate the suggestion that the clusters consist of 13 spherical subunits and thus acquire a molecular weight of about 5.0 × 10⁶ Da and a diameter of about 45 nm. © John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 3847–3852, 1997