Nitrido-Sodalithe. I Synthese,Struktur und Eigenschaften von Zn7–xH2x[P12N24]Cl2 mit 0 ⩽ x ⩽ 3

Nitrido Sodalites. I Synthesis, Crystal Structure, and Properties of Zn_7–xH_2x [P₁₂N₂₄]Cl₂ with 0 ? x ? 3 The nitrido sodalites Zn_7–xH_2x[P₁₂N₂₄]Cl₂ with 0 ? x ? 3 are obtained by heterogeneous pressure-ammonolysis of P₃N₅ at presence of ZnCl₂ (T = 650°C). These compounds are available too by reaction of ZnCl₂, (PNCl₂)₃, and NH₄Cl at 700°C. The crystal structures of four representatives of the above mentioned compounds have been refined by the Rietveld full-profile technique using X-ray powder diffractometer data (I4 3m, a = 821.61(4) to 824.21(1) pm, Z = 1). In the solid a three-dimensional framework of corner-sharing PN₄-tetrahedra occurs (P? N: 163.6 pm, P? N? P: 125.6°, mean values) which is isosteric with the sodalite type of structure. In the center of the β-cages Cl^? ions have been found, which are tetrahedrally coordinated by Zn²⁺ ions. The Zn²⁺ ions are statistically disordered. According to the phase-width observed (0 ? x ? 3) the Zn²⁺ ions may be partially replaced each by two hydrogen atoms which on the other hand are covalently bonded to nitrogen atoms of the P? N framework. The IR-spectra of these compounds show characteristic vibrations.     

Products of regular-closed spaces

Conditions under which a product space will be regular-closed or minimal regular are studied. It is shown that a product of regular-closed spaces need not be regular-closed and that a product of minimal regular spaces need not be minimal regular.     

Attainable rates of convergence of maxima

Any exponential rate of convergence can be obtained for maxima of i.i.d. random variables, while faster than exponential convergence implies that the variables have an extreme value distribution.     

Electronic properties of free and supported metal clusters studied by photoelectron spectroscopy

The electronic properties of free and supported metal clusters are studied by photoelectron spectroscopy. Experimental as well as theoretical results clearly demonstrate a dramatic dependence of the level structure on the cluster size. By this an interesting way might be opened to modify the electronic, optical and chemical properties of surfaces.     

关于Fuzzy矩阵的广义逆

本文分别给出了Fuzzy矩阵存在广义{1,3}-逆、广义{1,4}-逆以及Moore-Penrose广义逆Fuzzy矩阵的一些充要条件。又得到求上述广义逆Fuzzy矩阵的一些公式。主要的结果有: 1.Fuzzy矩阵A的广义{1,3}-逆A~((1.3))(广义{1,4}-逆A~((1.4))存在的充要条件是Fuzzy关系方程有解。2.Fuzzy矩阵A的Moore-Penrose广义逆A~T存在的充要条件是Fuzzy关系方程均有解。3.如果B、C分别为Fuzzy关系方程的一个解,那么。     

Laser photoelectron microspectroscopy for imaging impurity ions,color centers,and small-size irregularities in dielectric media

New photoelectron microscopy application fields are considered for imaging the arrangement of color centers, small-size defects, and impurity ions in dielectric matrices. The techniques proposed are based on the first experimental results obtained in studying the possibilities of observing stepwise laser photoelectric effect in ZrO₂:Nd³⁺, where photoelectron emission results from the stepwise absorption of light by the impurity ions Nd³⁺. In that case, the electrons being emitted originate in immediate proximity to the impurity ions, which offers possibilities to image the above structures by photoelectron microscopy techniques.     

Precise Asymptotics in Spitzer's Law of Large Numbers

Let <i>Xi>, <i>Xi> ₁, <i>Xi> ₂,... be a sequence of i.i.d. random variables such that <i>EXi>=0, assume the distribution of <i>Xi> is attracted to a stable distribution with exponent <img src="/content/V1T57711557G6852/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0"><1, and set <i>Si> _n=<i>Xi> ₁+ &middot;&middot;&middot; +<i>Xi> _n. We prove that idth="100%">

Bounds for the Concentration of Asymptotically Normal Statistics

Let X₁,..., X _<i>ni> be independent, not necessarily identically distributed random variables. An optimal bound is derived for the concentration function of an arbitrary real-valued statistic T = T (<i>Xi> ₁,...,<i>Xi> _<i>ni> ) for which ET² < <img src="/content/t613378l2804hlr4/xxlarge8734.gif" alt="infin" align="MIDDLE" BORDER="0">. Applications are given for Wilcoxon"s rank-sum statistic, U-statistics, Student"s statistic, the two-sample Student statistic and linear regression.     

Sufficient and necessary conditions for limit laws on lag sums of I. I. D. R. V. S

Let {<i>X, Xi> _<i>ni> ;<i>ni>>-1} be a sequence of i.i.d.r.v.s with<i>EXi>=0 and<i>EXi> ²=σ²(0 < σ < ∞). <img src="/content/Q7W5G38169P30426/10114_2007_Article_BF02563891_TeX2GIFIE1.gif" alt=" $$S_n = \sum\limits_{i = 1}^n {X_i } $$ " align="middle" border="0"> we obtain some sufficient and necessary conditions foridth="100%">