Zur Reaktion eines Bis(amino)germylens mit Germaniumaziden: Abfangreaktionen von instabilen Germa-Iminen

Reaction of a Cyclic Bis(amino)germylene with Germaniumazides: Trapping-Reactions of Unstable Germa-Imines . The cyclic bis(amino)germylene 1 reacts with different germaniumazides of the type Me₂Si(NtBu)₂Ge(R)N₃ (R = Me ( 2 ), tBu ( 3 ), N(SiMe₃)₂ ( 4 ), R = N₃ ( 5 )). With the exception of 4 all azides lose dinitrogen when treated with 1 and the Ge^II center coordinates the α-nitrogen of the azide group. It seems to be reasonable to assume a transient germaimine (nitride) which is trapped by further reaction with the azide molecules 2 and 5 or by reaction with the solvent pyridine ( 3 ). In the case of 2 the germatetrazole [Me₂Si(NtBu)₂]GeN₄[Ge(NtBu)₂SiMe₂]₂ ( 6 ) is formed, the tetrazole nitrogens being exclusively substituted by germanium atoms (point symmetry of the molecule C_s(m)). When 1 is treated with 5 a tris(germa)amine [Me₂Si(NtBu)₂Ge(N₃)]₃N ( 8 ) is formed, which has an azide group attached to each Ge-atom. X-ray analysis reveals that the nine nitrogen atoms of the azide groups are coplanar with the trigonal planar Ge₃N moiety (crystallographic symmetry: 3/m). The reaction of 1 with 3 is very surprising: the pyridine in the product Me₂Si(NtBu)₂Ge(C₅H₄N)? N(H)Ge(tBu)(NtBu)₂SiMe₂ ( 7 ) is bonded via an α-carbon atom while the remaining hydrogen has added to the nitride-nitrogen. 6 crystallizes in the monoclinic system space group C2/m, a = 24.306(9), b = 10.933(6), c = 19.420(9) Å, β = 91.81(2)° and Z = 4. 7 crystallizes in the hexagonal system space group P6₃/m with a = b = 16.73(1), c = 11.006(8) Å, γ = 120° and Z = 2, and 8 crystallizes in the monoclinic system space group P2₁/n, a = 11.341(6), b = 26.086(9), c = 13.244(7) Å, β = 98. I2(2)° mit Z = 4.     

Butler groups with a single τ-adic relation

It is proved that a τ-adic relation characterizing a Butler group is piecewise rational. Translated fromMatematicheskie Zametki, Vol. 60, No. 6, pp. 882–887, December, 1996.     

四峰映射四倍周期分岔度量普适性的重正化群分析

 对四峰映射四倍周期分岔进行重正化群分析,获得了相应的重正化群方程组,并求出其普适函数和度量普适常数的数值解.     

上海青少年女性消费者研究及服装品牌企划

通过AIOV分析法对上海青少年女性消费者的研究,得到了该市场消费群的总体特征。根据对此目标市场的分析,制定了服装品牌“Cacao”的企划案。这里明确提出了一种应对服饰消费感性化需求创设个性化品牌的预测提案型策略。     

Limit distributions and one-parameter groups of linear operators on Banach spaces

Let = {U_t: t > 0} be a strongly continuous one-parameter group of operators on a Banach space X and Q be any subset of a set (X) of all probability measures on X. By (Q; ) we denote the class of all limit measures of {U_tn(μ₁ * μ₂*…*μ_n)*δ_xn}, where {μ_n}Q, {x_n}X and measures U_tnμ_j (j=1, 2,…, n; N=1, 2,…) form an infinitesimal triangular array. We define classes L_m( ) as follows: L₀( )= ( (X); ), L_m( )= (L_m−1( ); ) for m=1, 2,… and L_∞( )=_m=0^∞L_m( ). These classes are analogous to those defined earlier by Urbanik on the real line. Probability distributions from L_m( ), m=0, 1, 2,…, ∞, are described in terms of their characteristic functionals and their generalized Poisson exponents and Gaussian covariance operators.     

Successive Proportional Additive Numeration Using Fuzzy Linguistic Labels (Fuzzy Linguistic SPAN)

The SPAN (Successive Proportional Additive Numeration or Social Participatory Allocation Network) is a procedure that converts individual judgments into a group decision. The procedure is based on a voting design by which individual experts allocate their votes iteratively between their preferred options and other experts. The process ends when all the votes are allocated to options, and the one with the highest number of votes is selected. The method requires the experts to specify an exact allocation of votes to both options and other experts. The Fuzzy Linguistic SPAN allows experts to allocate their votes using linguistic labels such as “most of” or “a few”, and determine the preferred option. This method is demonstrated using the Max–Min aggregation function used to develop a proportional representation of the option and member voting schemes. The method is also demonstrated using the LOWA aggregation function. The Fuzzy Linguistic SPAN method is beneficial since the linguistic voting process is easier for the experts and significantly reduces the computational process compared to the traditional SPAN. The paper presents the method and two examples with comparisons to the numerical SPAN method.     

Evolution of Orbits and Quantum Correlation Functions by Quadratic Hamiltonians

Quantum systems with quadratic Hamiltonians are considered. Some results about the time evolution of homogeneous polynomials and of quantum correlation functions are given. The image of arbitrary orbit of Weyl–Heisenberg group under this time evolution is shown to be again an orbit of this group. For quantum free particle it is shown that its time evolution intersects arbitrary such orbit at most once. A result about existence of more orbits having the same dispersion of some quantum position is presented.PACS: 02.20.Qs, 02.30.Sa     

Free field realization of the level-2 elliptic algebra Ux,p ([^(\mathfraks\mathfrakl)]2 )*)U_{x,p} (\widehat{\mathfrak{s}\mathfrak{l}}_2 )*)

We give a level-2 representation of the elliptic algebra in terms of one free boson and one free fermion. We show that -modules have a natural direct sum decomposition into the irreducible (deformed) super-Virasoro modules associated with the coset . Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

<Emphasis Type="Italic">p</Emphasis>-Nuclearity in a New Perspective

In this Letter we try to settle some confused points concerning the use of the notion of p-nuclearity in the mathematical and physical literature, pointing out that the nuclearity index in the physicists’ sense vanishes for any p> 1. Our discussion of these issues suggests a new perspective, in terms of ε-entropy and operator spaces, which might permit connections to be drawn between phase space criteria and quantum energy inequalities.Mathematics Subject Classification (2000): 81T05, 47B10, 47L25.