Determinations of combustion and formation enthalpies of C60 and C70

By using a micro-bomb calorimeter, the standard enthalpies of combustion of C₆₀ and C₇₀ have been determined to be - (25 947.1±8.5) and - (29 956.1 ± 8.9) kJ/mol respectively. A g. 1. c. analysis indicated that the amounts of residual organic solvents in the samples were very small, and their effects on the final results were negligible. The energy of combustion ofC60 determined in this work is in agreement in the uncertainty interval with that determined by means of traditional calorimeter using macro amount of sample. The enthalpies of formation of these two substances have been derived. The strain energies in the molecules of C₆₀ and C₇₀ were estimated by a bond energy scheme and by using corannulene as the model compound, the results estimated from different methods are very close. Project supported by the National Natural Science Foundation of China (Grant No. 29473143)     

Structural evolution of (Ca0.35Sr0.65)TiO3 perovskite at high pressures

Lattice parameters of a synthetic powder sample of Ca_0.35Sr_0.65TiO₃ perovskite have been determined by the method of Le Bail refinement, using synchrotron X-ray diffraction patterns collected at pressures up to 15.5 GPa with a membrane-driven diamond anvil cell. At ambient conditions, diffraction data were consistent with the I4/mcm structure reported previously in the literature for the same composition. Diffraction data collected at high pressures were consistent with tetragonal (or, at least, pseudo-tetragonal) lattice geometry, and no evidence was found for the development of any of the orthorhombic structures identified in other studies of (Ca, Sr)TiO₃ perovskites. Additional weak reflections, which could not be accounted for by the normal I4/mcm perovskite structure, were detected in diffraction patterns collected at pressures of 0.9-2.5 GPa, and above ∼13.5 GPa, however. Small anomalies in the evolution of unit cell volume and tetragonal strain were observed near 3 GPa, coinciding approximately with breaks in slope with increasing pressure of bulk and shear moduli for a sample with the same composition which had previously been reported. The anomalies could be due either to new tetragonal↔tetragonal/pseudo-tetragonal phase transitions or to subtle changes in compression mechanism of the tetragonal perovskite structure.     

导数振荡与应变能极小的平面分段三次参数Hermite插值

由于分段三次参数Hermite插值的切矢往往被作为变量,故可对其进行优化以使得构造的插值曲线满足特定的要求.为了构造兼具保形性与光顺性的平面分段三次参数Hermite插值曲线,给出了一种通过同时极小化导数振荡和应变能来确定切矢的方法.首先以导数振荡函数和应变能函数为双目标建立了切矢满足的方程系统;然后证明了方程系统存在唯一解,并给出了解的具体表达式;最后给出了误差分析,并通过数值算例表明方法的有效性.结果表明,相对于导数振荡极小化方法和应变能极小化方法,所提出的导数振荡和应变能极小化方法同时兼顾了平面分段三次参数Hermite插值曲线的保形性和光顺性.     

带有随机初值的复值Ginzburg-Landau方程的弱平均动力学*

本文研究了无界域上的带有随机初值的复值Ginzburg-Landau方程.首先, 基于解过程的全局适定性, 建立了带有随机初值的Ginzburg-Landau方程的平均随机动力系统.然后, 证明了弱拉回平均随机吸引子的存在唯一性以及随机吸引子的周期性,并将其进一步推广到加权空间L²(?, L²_σ(R)).     

Low Mach number limit of inviscid Hookean elastodynamics

The low Mach number limit of inviscid Hookean elastodynamic equations is rigorously proved in bounded domain, whole space and periodic domain, respectively. The uniform existence of smooth solutions and convergence results as the Mach number tends to zero are obtained in three different domains.     

Dynamic complexity of optimal paths and discount factors for strongly concave problems

We study the relationship between the dynamical complexity of optimal paths and the discount factor in general infinite-horizon discrete-time concave problems. Given a dynamic systemx _t+1=h(x _t ), defined on the state space, we find two discount factors 0 < ^{* **} < 1 having the following properties. For any fixed discount factor 0 < < ^*, the dynamic system is the solution to some concave problem. For any discount factor ^** < < 1, the dynamic system is not the solution to any strongly concave problem. We prove that the upper bound ^** is a decreasing function of the topological entropy of the dynamic system. Different upper bounds are also discussed.This research was partially supported by MURST, National Group on Nonlinear dynamics in Economics and Social Sciences. The author would like to thank two anonymous referees for helpful comments and suggestions.     

Initial data truncation for multivariate output of discrete-event simulations using the Kalman filter

Data truncation is a commonly accepted method of dealing with initialization bias in discrete-event simulation. An algorithm for determining the appropriate initial-data truncation point for multivariate output is proposed. The technique entails averaging across independent replications and estimating a steady-state output model in a state-space framework. A Bayesian technique called Multiple Model Adaptive Estimation (MMAE) is applied to compute a time varying estimate of the output's steady-state mean vector. This MMAE implementation features the use, in paralle, of a bank of Kalman filters. Each filter is constructed under a different assumption concerning the output's steady-state mean vector. One of the filters assumes that the steady-state mean vector is accurately reflected by an estimate, called the assumed steady-state mean vector, taken from the last half of the simulation data. As the filters process the output through the effective transient, this particular filter becomes more likely (in a Bayesian sense) to be the best filter to represent the data and the MMAE mean estimator is influenced increasingly towards the assumed steady-state mean vector. The estimated truncation point is selected when a norm of the MMAE mean vector estimate is within a small tolerance of the assumed steady-state mean vector. A Monte Carlo analysis using data from simulations of open and closed queueing models is used to evaluate the technique. The evaluation criteria include the ability to construct accurate and reliable confidence regions for the mean response vector based on the truncated sequences.     

Theoretical study of structure and stability of fullerene derivative: C50O

A total of eight possible isomers of C₅₀O, an oxide of fullerene C₅₀ (D_5h), have been investigated by B3LYP/3‐21G calculations. The isomer, which has an annulene‐like structure with oxygen bridging across a [5,6] type C? C bond at the site between the pole and the equatorial belt, is found being the ground state of C₅₀O. Four isomers are relatively more stable and the energy differences between them are not large. This result indicates that more than one C₅₀O isomer will coexist once C₅₀O is synthesized. The relative stabilities of the C₅₀O isomers may be determined mainly by the strain release and by the formation of the cyclic phenylene substructure at the equatorial belt of the cage. The calculated nucleus independent chemical shifts (NICS) of the C₅₀O isomers will be useful because from them one can expect outstanding NMR properties that can lead to their identification and characterization. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Norvancomycin-capped silver nanoparticles: Synthesis and antibacterial activities against E. coli

The synthesis of norvancomycin (NVan)-capped silver nanoparticles (Ag@NVan) and their notable in vitro antibacterial activities against E. coli, a Gram-negative bacterial strain (GNB), are reported here. Mercaptoacetic acid-stabilized spherical silver nanoparticles with a diameter of 16±4 nm are prepared by a simple chemical reaction. The formation process of the silver nanoparticles is investigated by UV-visible (UV-vis) spectroscopy and transmission electron microscopy (TEM). NVan is then grafted to the terminal carboxyl of the mercaptoacetic acid in the presence of N-(3-Dimethylaminopropyl)-N′-ethylcarbodiimide hydrochloride (EDAC). The TEM images of single bacteria treated with Ag@NVan show that plenty of Ag@NVan aggregate in the cell wall of E. coli. A possible antibacterial mechanism is proposed that silver nanoparticles may help destroy the stability of the outer membrane of E. coli, which makes NVan easier to bind to the nether part of the peptidoglycan structure. The antibacterial activities of silver nanoparticles on their own, together with the rigid polyvalent interaction between Ag@NVan and cell wall, enables Ag@NVan to be an effective inhibitor of GNB. This kind of bionanocomposites might be used as novel bactericidal materials and we also provide an effective synthesis method for preparing functional bioconjugated nanoparticles here. Supported by the National Natural Science Foundation of China (Grant No. 50373036) and Fok Ying Tung Education Foundation (Grant No. J20040212)     

Dislocation Analysis for Large-sized Sapphire Single Crystal Grown by SAPMAC Method

In this paper,large-sized sapphire (230×210 mm,27.5 kg) was grown by SAPMAC method (sapphire growth technique with micro-pulling and shoulder-expanding at the cooled center). Dislocation peculiarity in large sapphire boule (0001) basal plane was investigated by chemical etching,scanning electron microscopy and X-ray topography method. The triangular dislocation etch pit measured is 7.6×101～8.0×102 cm-2,in which relative high-density dislocations were generated at both initial and final stages of crystal growth. The analysis of single-crystal X-ray topography shows that there are no apparent sub-grain boundaries; the dislocation lines are isolated and straight. Finally,the origins of low-density dislocation in sapphire crystal are discussed by numerical analysis method.