Coulomb pair density matrix I

The Coulomb pair density matrixG (r, r) for attractive and repulsive potentials is not only interesting for determining the two-particle effective potentials, but it is also essential in numerical studies of quantum systems. A high-temperature approximation is obtained for logG (r, r), in the form of simple integrals or series expansions; large-distance expansions are also given.     

Coupling of the GB set property for ergodic averages

Let (Y,,,T) be an ergodic dynamical system. LetA be an nonempty subset ofL ²() such that , whereA=sup{||sȒt||₂ ,s, tA} andN(A, u) is the smallest number ofL ²()-open balls of radiusu, centered inA, enough to coverA. Let . We prove as a consequence of a more general result, thatC(A) is aGB subset ofL ²().     

Optimality of a Threshold Policy in theM/M/ queue with repeated vacations

Consider anM/M/1 queueing system with server vacations where the server is turned off as soon as the queue gets empty. We assume that the vacation durations form a sequence of i.i.d. random variables with exponential distribution. At the end of a vacation period, the server may either be turned on if the queue is non empty or take another vacation. The following costs are incurred: a holding cost ofh per unit of time and per customer in the system and a fixed cost of each time the server is turned on. We show that there exists a threshold policy that minimizes the long-run average cost criterion. The approach we use was first proposed in Blanc et al. (1990) and enables us to determine explicitly the optimal threshold and the optimal long-run average cost in terms of the model parameters.     

Chemical diffusion of oxygen in tin dioxide: Effects of dopants and oxygen partial pressure

Tin dioxide SnO_2−δ is a pronounced n-type electron conductor due to its oxygen deficiency. This study investigates the rate of chemical diffusion of oxygen in SnO_2−δ single crystals, which is a crucial step in the overall stoichiometry change of the material. The chemical diffusion coefficient D^δ was determined from conductivity- and EPR-relaxation methods. The temperature dependence was found to be . The dependence on crystal orientation, dopant content and oxygen partial pressure was below experimental error. The latter observation leads to the conclusion that the chemical diffusion coefficient is close to the diffusion coefficient of oxygen vacancies. Along with the relaxation process resulting from the chemical diffusion of oxygen, additional processes were observed. One of these was attributed to complications in the defect chemistry of the material. The relevance of the results for the kinetics of drift processes of Taguchi sensors is discussed.     

Stationary queues with one autonomous server

Given a stationary stochastic continuous demand of service σ(θ_tω) dt with ∫ σ(ω)P(dω) < 1, we construct real stationary point processes $\text{(T}{}_{\mathrm{n}}\text{, n ∈}\text{Z}\text{)[T}{}_{\mathrm{n}}\text{< T}{}_{\mathrm{n}}\text{+1, lim}{}_{\mathrm{\pm \infty }}\text{T}{}_{\mathrm{n}}\text{= ±∞]}$ such that

for a given constant D \2>0. These point processes correspond to a service discipline for which a single server services during the time intervals [T_n, T_n+1[ the demand of service accumulated during the proceding intervals [T_n?1, T_n[ and take a rest of fixed duration D.     

Photophysical processes and photochemical reactions involved in poly(N-vinylcarbazole) and in copolymers with carbazole units

This paper is devoted to the analysis of the photochemical behaviour of copolymers with carbazole units exposed to long-wavelength radiation. These copolymers are constituted of two types of carbazolylethyl methacrylate units (CEM) with octyl methacrylate moieties (OMA). The exposure of copolymers and PVK to UV light results in dramatic modifications of the physical and photophysical properties of the polymer. These modifications can be correlated with modifications of the chemical structure of the matrix. The photoageing of copolymers and PVK has been analysed by fluorescence, ESR, UV-vis and infrared spectroscopies. The effects of crosslinking and chain scissions were determined by gel fraction measurements and size exclusion chromatography.     

Shortcut method for evaluation and design of a hybrid process for enantioseparations

Hybrid processes for enantioseparations have a considerable potential for reducing investment and operational costs. An example is the combination of simulated moving bed (SMB) chromatography and selective crystallisation. However, the design of integrated processes is a difficult task. A shortcut method is presented that can serve as a tool for design and estimation of the potential of such processes. The approach requires only limited experimental data and thus allows for systematic parameter studies. The method is based on the determination of the purity-performance characteristic of the SMB process and rigorous application of mass balances. The use of relative mass fluxes allows derivation of simple algebraic expressions for essential process parameters. The significant potential of combining SMB and crystallisation is demonstrated for the example of the separation of mandelic acid enantiomers.     

The application of the concept of reaction layer to the study of electrode processes coupled with the second-order chemical reactions at microelectrodes under steady-state conditions

Under steady-state conditions, the current equations of the second-order EC, ECE and DISPI reactions at microdisk, microspherical and microring electrodes are derived with the aid of the concept of the reaction layer. The conditions under which these equations would be valid are also discussed. Using these equations, methods to determine the kinetic parameters for the second-order EC, ECE and DISPI reactions are presented. The reduction of 2,6-diphenyl-pyrylium cation and oxidation of triphenylamine were investigated as examples of the second-order EC and ECE reactions.     

Characterization of Autocatalytic Reactions in Modified Cellulose/NMMO Solutions by Thermal Analysis and UV/VIS Spectroscopy

The thermal stability of cellulose/N-methylmorpholine-N-oxide (NMMO) solutions were investigated using UV/VIS spectrometry with a temperature programming cuvette and caloric measurements by means of the Systag calorimeter RADEX (mini-autoclave). Both analytical methods allow to characterize the influences of stabilizers and additives. With the temporal course of the optical density, temperature and pressure thermal runaway reactions with gas evolution and accumulation of chromophoric degradation products were recognized. Kinetic model calculations compared with UV/VIS measurements demonstrate the existence of autocatalytic reactions in cellulose/NMMO solutions. Varying the heating rate autocatalysis can be proved by dynamic caloric measurements as well.     

手性试剂TMPEA用于手性酮对映体纯度测定的研究

β-三氟甲基-β甲氧基β-苯基乙胺（TMPEA）是含氨基功能团的手性试剂[1]．由于胺可将按酸转变成酸胺，该试剂已成功地用于手性有机酸对映体的纯度测定[2]．考虑到胺同样可将醛酮转变成亚胺，本文进一步探讨了TMPEA用于手性醒酮对映体纯度测定的可行性．用R－（－）－TMPEA及dl－TMPAE分别与下列4种手性酮反应，制备相应的非对映异构亚胶：比较光活亚胺及相应的非对映异构体混合物亚腔的NMR谱，可确定各组非对映异构亚胺‘HNMR位移差（以OCH为探针基团）和’‘FNMR的位移差（以CF为探针基团）（表1）．TablelCheffiicalshif…