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].     

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。     

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.     

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.     

Series representation for semistable laws and their domains of semistable attraction

If the centered and normalized partial sums of an i.i.d. sequence of random variables converge in distribution to a nondegenerate limit then we say that this sequence belongs to the domain of attraction of the necessarily stable limit. If we consider only the partial sums which terminate atk _n wherek _n+1 ck _n then the sequence belongs to the domain of semistable attraction of the necessarily semistable limit. In this paper, we consider the case where the limiting distribution is nonnormal. We obtain a series representation for the partial sums which converges almost surely. This representation is based on the order statistics, and utilizes the Poisson process. Almost sure convergence is a useful technical device, as we illustrate with a number of applications.This research was supported by a research scholarship from the Deutsche Forschungsgemeinschaft (DFG).     

Fractional Power Series and Pairings on Drinfeld Modules

Let be an algebraically closed field containing which is complete with respect to an absolute value . We prove that under suitable constraints on the coefficients, the series converges to a surjective, open, continuous -linear homomorphism whose kernel is locally compact. We characterize the locally compact sub--vector spaces of which occur as kernels of such series, and describe the extent to which determines the series. We develop a theory of Newton polygons for these series which lets us compute the Haar measure of the set of zeros of of a given valuation, given the valuations of the coefficients. The ``adjoint' series converges everywhere if and only if does, and in this case there is a natural bilinear pairing

which exhibits as the Pontryagin dual of . Many of these results extend to non-linear fractional power series. We apply these results to construct a Drinfeld module analogue of the Weil pairing, and to describe the topological module structure of the kernel of the adjoint exponential of a Drinfeld module.

     

On pasting -weights

Theorem 3 gives a condition when two -weights can be ``pasted' together to yield another -weight. It is subsequently used in Example 6 to give an example that shows that a necessary condition by Gohberg, Krupnik, and Spitkovsky is not sufficient.

     

Critical behavior of self-avoiding walks on fractals

Using a new graph counting technique suitable for self-similar fractals, exact 18th-order series expansions for SAWs on some Sierpinski carpets are generated. From them, the critical fugacityx _c and critical exponents _SAW and _SAW are obtained. The results show a linear dependence of the critical fugacity with the average number of bonds per site of the lattices studied. We find for some carpets with low lacunarity that _SAW<0.75, thus violating the relation _SAW(fractal) > _SAW (d) for SAWs on the fractals which are embedded in ad-dimensional Euclidean space.