A molecular theory of inhomogeneous broadening,including the correlation between different transitions,in liquids and glasses

Summary We present a molecular theory of the energy distributions for the internal quantum states of a solute in a liquid or glassy solvent. We show that the energy distributions for different states are correlated in a way that depends on the solute-solvent interactions. We show how the theory can be modified easily to describe the transition-energy distributions for different pairs of states, which are of course related to inhomogeneously broadened absorption spectra. We also show that the distributions for different transitions are correlated, and describe how this correlation is measured by nonresonant fluorescence- and phosphorescence-line-narrowing and hole-burning experiments. The theory provides a microscopic framework within which to interpret different phenomenological models. For the case of a Lennard-Jones solute in a Lennard-Jones liquid solvent, we compare our theory to Monte Carlo simulation.     

Synthesis and Crystal Structur of (4,4''-H2bipy)[CdBr4]·H2O

The title compound (4,4'-H2bipy)[CdBr4]·H2O 1 has been synthesized via hydrothermal reaction and characterized by X-ray diffraction. The crystal belongs to monoelinic,space group P21/c with a=8.260(3), b=23.926(7), c=9.774(2) (A), β=106.777(9)°,C10H12Br4CdN2O, Mr=608.26, V=1849.4(9)(A)3, Z=4, Dc=2.185 g/cm3, S=1.005, μ(MoKα)=9.814 mm-1, F(000)=1128, R=0.0646 and wR=0.0989. The crystal structure analysis of 1reveals that the title compound features an isolated structure, based on discrete 4,4'-H2bipy moieties and lattice water molecules which are linked by hydrogen bonds together with tetrahedral cadmium atoms terminally coordinated by four bromine atoms.     

Analysis of long-term distributions of calibration parameters and calibration intervals for an atomic absorption spectrophotometer

 A combination of "black box" and "calendar-time" methods for the determination of calibration intervals of an analytical measuring instrument is discussed. Since the methods require information on the distributions of the calibration parameters, such information is described for an atomic absorption spectrophotometer, as an example. The hypotheses on the normal distribution of the calibration parameters are tested using the ω²-criterion and accepted at 0.90–0.95 levels of confidence. Corresponding control charts are designed for indication of warning and action limits of the calibration parameters, and diagnoses of outliers in further calibrations. Control charts indicate also when the calibration should be done according to the full program of the equipment manufacturer. Received: 15 April 2000 / Accepted: 24 July 2000     

Pore size distributions in microporous membranes. A critical analysis of the bubble point extended method

An extended bubble point method has been used to examine the porous morphology of several track-etched microporous polycarbonate membranes with nominal pore sizes ranging from 0.1 to 5.0 μm. The technique has been carefully analyzed and corrected to take into account the diverse non-ideal factors in flow along with the prevalence of Knudsen flow over the Hagen-Poiseuille one in the smaller pores.     

A coupled electron diffraction and rigid unit mode (RUM) study of the crystal chemistry of some zeotypic AlPO4 compounds

Electron diffraction and lattice dynamical calculations are used to investigate the unit cells, space group symmetries and inherent displacive flexibility of the room-temperature average structures of AlPO₄-8, AlPO₄-16 and AlPO₄-tridymite. The zero-frequency rigid unit modes (RUMs) of the idealized high-symmetry polymorphs thereof are also investigated along with their relationship to the lower-temperature polymorphism of these zeotypic aluminophosphates. The clear presence of satellite reflections in addition to the Bragg reflections (G) of the underlying Cmc2₁ parent structure in the case of AlPO₄-8 shows that the true unit cell of the room-temperature polymorph has a doubled c-axis due to a condensed RUM mode. Structured diffuse scattering is also observed which can be related to the thermal excitation of RUM modes. In the case of AlPO₄-tridymite, a complex F1 triclinic polymorph is observed and related to soft RUM modes while, in the case of AlPO₄-16, a soft q=0 RUM mode is shown to be responsible for an observed phase transition in the case of the all SiO₂ analogue of AlPO₄-16. A large number of additional zero-frequency RUM modes also exist in the case of AlPO₄-16.     

A modified steepest descent method with applications to maximizing likelihood functions

In maximizing a non-linear function G(), it is well known that the steepest descent method has a slow convergence rate. Here we propose a systematic procedure to obtain a 1–1 transformation on the variables , so that in the space of the transformed variables, the steepest descent method produces the solution faster. The final solution in the original space is obtained by taking the inverse transformation. We apply the procedure in maximizing the likelihood functions of some generalized distributions which are widely used in modeling count data. It was shown that for these distributions, the steepest descent method via transformations produced the solutions very fast. It is also observed that the proposed procedure can be used to expedite the convergence rate of the first derivative based algorithms, such as Polak-Ribiere, Fletcher and Reeves conjugate gradient methods as well.     

Rates of convergence of α-stable random motions

The rate-of-convergence problem in the central limit theorem is considered for -stable distributions on the noncommutative group of motions in ^d. The method used here is based on the theory of probability metrics.     

Supercritical Propanol-Water Synthesis and Comprehensive Size Characterisation of Highly Crystalline anatase TiO2 Nanoparticles

Highly crystalline anatase TiO₂ nanoparticles have been synthesised in less than 1 min in a supercritical propanol-water mixture using a continuous flow reactor. The synthesis parameter space (T, P, concentration) has been explored and the average particle size can be accurately controlled within 10-18 nm with narrow size distributions (2-3 nm). At subcritical conditions amorphous products are obtained, whereas a broad range of T and P in the supercritical regime gives 11-14 nm particles. At high temperature and pressure, the particles size increase to 18 nm. The nanoparticles have been extensively characterised with powder X-ray diffraction (PXRD), transmission electron microscopy (TEM) and small-angle X-ray scattering (SAXS) with excellent agreement on size and size distribution parameters. The SAXS analysis suggests disk-shaped particles with diameters that are approximately double the height. For comparison, a series of conventional autoclave sol-gel syntheses have been carried out. These also produce phase-pure anatase nanoparticles, but with much broader size distributions and at much longer synthesis times (hours). The study demonstrates that synthesis in supercritical fluids is a very promising method for manipulating the size and size distribution of nanoparticles, thus removing one of the key limitations in many applications of nanomaterials.     

同分布NA列Jamison型加权和强稳定的充要条件

本文将Ｊａｍｉｓｏｎ等（１９６５）关于ｉｉｄ列加权和强稳定的充分性结果推广到ＮＡ列的场合并且得到了ＮＡ列Ｊａｍｉｓｏｎ型加权和强稳定的必要性结果。