Mixed crystals in the system Cu2MnGexSn1−xS4: Phase analytical investigations and inspection of tetrahedra volumes

Cu₂MnGeS₄ crystallizes orthorhombic in a wurtzite superstructure type while Cu₂MnSnS₄ crystallizes in a tetragonal sphalerite superstructure type. Lattice constants and thermal analyses of the solid solution series Cu₂MnGe_xSn_1−xS₄ are presented. A two-phase region is found from Cu₂MnGe_0.3Sn_0.7S₄ to Cu₂MnGe_0.5Sn_0.5S₄. The cell volume of the mixed crystals increases with increasing Sn content. The melting points increase smoothly with increasing Ge content to x=0.5 and then steeply for higher Ge contents. The single crystal X-ray structure analysis of Cu₂MnGe_0.55Sn_0.45S₄ is presented. The refinement converges to R=0.0270 and wR₂=0.0586, Z is 2. The volumes of the tetrahedra [MS₄] (M=Cu, Mn, Ge, Sn) are calculated. From these volumes the differences in size of the tetrahedra are derived and compared with the corresponding differences in the end members of the solid solution series. It turns out that the resulting structure type in these materials depends on the volume differences of the constituting tetrahedra [MS₄].     

Schrödinger Equation Solutions for the Central Field Power Potential Energy I. V(r) = V 0(r/a 0)2ν−2, ν ≥ 1

The solution of a generalized non-relativistic Schrödinger equation with radial potential energy V(r)=V ₀(r/a ₀)^2–2 is presented. After reviewing the general properties of the radial ordinary differential equation, power series solutions are developed. The Green's function is constructed, its trace and the trace of its first iteration are calculated, and the ability of the traces to provide upper and lower bounds for the ground eigenvalue is examined. In addition, WKB-like solutions for the eigenvalues and eigenfunctions are derived. The approximation method yields valid eigenvalues for large quantum numbers (Rydberg states).     

铁系元素冠醚配合物的研究——V.三氯化铁与4′-溴苯并-15-冠-5固态配合物的合成和性质

本文报导了三氯化铁(水合物)与4′-溴苯并-15-冠-5(L)固态配合物的合成,对合成的新配合物,进行了元素定量分析及摩尔电导测定,并作了红外光谱、紫外光谱,热重和差热以及X-射线粉末衍射分析的性质表征。从而证明,该配合物中FeCl₃与配体L比为1:1,是溶化剂,含有结晶水的固态配合物。     

Quantitative characterization of the global electrophilicity pattern of some reagents involved in 1,3-dipolar cycloaddition reactions

The global electrophilicity power, ω, of a series of dipoles and dipolarophiles commonly used in 1,3-dipolar cycloadditions may be conveniently classified within a unique relative scale. The effects of chemical substitution on the electrophilicity of molecules have been evaluated using a representative set of electron-withdrawing and electron-releasing groups for a series of dipoles including nitrone, nitrile oxide and azide derivatives. The absolute scale of electrophilicity is used to rationalize the chemical reactivity of these species as compared to the static reactivity pattern of the reagents involved in the Diels-Alder reactions.     

Simultaneous determination of radionuclides separable into natural decay series by use of time-interval analysis

A delayed coincidence method, time-interval analysis (TIA), has been applied to successive – decay events on the millisecond time-scale. Such decay events are part of the ²²⁰Rn²¹⁶Po (T_1/2 145 ms) (Th-series) and ²¹⁹Rn²¹⁵Po (T_1/2 1.78 ms) (Ac-series). By using TIA in addition to measurement of ²²⁶Ra (U-series) from -spectrometry by liquid scintillation counting (LSC), two natural decay series could be identified and separated. The TIA detection efficiency was improved by using the pulse-shape discrimination technique (PSD) to reject -pulses, by solvent extraction of Ra combined with simple chemical separation, and by purging the scintillation solution with dry N₂ gas. The U- and Th-series together with the Ac-series were determined, respectively, from alpha spectra and TIA carried out immediately after Ra-extraction. Using the ²²¹Fr²¹⁷At (T_1/2 32.3 ms) decay process as a tracer, overall yields were estimated from application of TIA to the ²²⁵Ra (Np-decay series) at the time of maximum growth. The present method has proven useful for simultaneous determination of three radioactive decay series in environmental samples.     

STUDY ON 1-HEXENE POLYMERIZATION BASED ON ZIEGLER-NATTA CATALYSTS WITH DOPED SUPPORT

A series of Ti/Mg supported catalysts are prepared by using ball-milled mixtures of MgCl2-ethanol adducts and NaCl as supports, and 1-hexene polymerizations catalyzed by the novel catalysts are studied. It is found that the molecular weight distribution of poly(1-hexene) becomes apparently narrower when catalysts with doped supports are used, indicating that changing the structure of the support is an effective way to regulate the active center distribution of heterogeneous Ziegler-Natta catalyst.     

Approximation of enthalpy of formation by Fourier series

A possible approximation of the enthalpy of formation of C,H,N,O-containing compounds by trigonometric Fourier series has been shown.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1389–1390, August, 1994.     

Robustly complete synthesis of sampled-data control for continuous-time nonlinear systems with reach-and-stay objectives

Formal methods are becoming favorable for control and verification of safety-critical systems because of the rigorous model-based computation. Relying on an over-approximated model of the original system behaviors, formal control synthesis algorithms are not often complete, which means that a controller cannot necessarily be synthesized even if there exists one. The main result of this paper shows that, for continuous-time nonlinear systems, a sample-and-hold control strategy for a reach-and-stay specification can be synthesized whenever such a strategy exists for the same system with its dynamics perturbed by small disturbances. Control synthesis is carried out by a fixed-point algorithm that adaptively partitions the system state space into a finite number of cells. In each iteration, the reachable set from each cell after one sampling time is over-approximated within a precision determined by the bound of the disturbances. To meet such a requirement, we integrate validated high-order Taylor expansion of the system solution over one sampling period into every fixed-point iteration and provide a criterion for choosing the Taylor order and the partition precision. Two nonlinear system examples are given to illustrate the effectiveness of the proposed method.     

Products and transforms of white-noise functionals (in general setting)

Some sharp results about Weiner and Wick products of whitenoise functionals are obtained. Using the inequality of Wick products we show to what extent scaling transformations, translations, and Sobolev differentiations can be performed on white-noise functionals.This work was supported by the National Natural Science Foundation of China. This paper is an enlargement and revised version of the paper entitled Products and Transforms of White-Noise Functionals (preprint, 1990).     

Exact results for the asymmetric simple exclusion process with a blockage

We present new results for the current as a function of transmission rate in the one-dimensional totally asymmetric simple exclusion process (TASEP) with a blockage that lowers the jump rate at one site from one tor<1. Exact finitevolume results serve to bound the allowed values for the current in the infinite system. This proves the existence of a nonequilibrium phase transition, corresponding to an immiscibility gap in the allowed values of the asymptotic densities which the infinite system can have in a stationary state. A series expansion inr, derived from the finite systems, is proven to be asymptotic for all sufficiently large systems. Padé approximants based on this series, which make specific assumptions about the nature of the singularity atr=1, match numerical data for the infinite system to 1 part in 10⁴.