Struktur‐ und magnetochemische Untersuchungen an KCuGaF6

Structural and Magnetochemical Studies on KCuGaF₆ The crystal structure of KCuGaF₆ was determined on the base of X‐ray single crystal data (wR₂ = 0.084 for 2476 independent reflections). The compound crystallizes with a = 728.56(4), b = 989.51(6), c = 676.27(3) pm, β = 93.120(5)°, Z = 4 in space group P2₁/c of the pyrochlore related KCuCrF₆ type. The octahedral coordinations [GaF₆] and [CuF₆] are slightly resp. strongly distorted (mean values Ga‐F: 188.2 pm resp. Cu‐F: 188.2/200.1/227.6 pm). The longest distances Ga‐F and the shortest ones Cu‐F are found within octahedral chains of these two kinds of atoms, running along [100] and [001], resp., and being mutually bridged as well (M‐F‐M in between 114 and 145°). The magnetic mole susceptibilities measured at powders and at a single crystal follow the isotropic Heisenberg model for S = ¹/₂, if effects of chain disrupture are considered in the form of some paramagnetic portion. No indication of threedimensional magnetic order is observed down to T = 2 K and low magnetic fields H < 100 G. KCuGaF₆ (J/k = —71 K for the powder) is distinguished this way from the chain structure compounds KCuAlF₆ und Na₂CuScF₇ (J/k = —76 resp. —59 K) which were also magnetically studied and yield similar antiferromagnetic exchange constants J/k.     

Gold catalysis contra platinum catalysis in hydroarylation contra phenol synthesis

Three silylated γ-alkynylfurans were prepared and subjected to both gold and platinum catalysts. The TMS- and the TBDMS-substituted furans reacted. With AuCl₃ and the binuclear [(Ph₃PAu)₂Cl][BF₄] catalyst a hydroarylation of the alkyne was observed. Na[AuCl₄] gave phenols as the product, but these were formed only after in situ desilylation of the starting material by the gold catalyst and thus the wrong isomer dominated. Only with PtCl₂(MeCN)₂ phenols with a silyl group were formed. The TBDPS-substituted furan failed to react. Two alkynylsilanes were synthesized, but they also failed to react.     

氢气对氯硅烷功能化非共轭α,ω-双烯烃和丙烯共聚物链结构的影响

基于Ziegler-Natta催化剂的氯硅烷功能化非共轭α,ω-双烯烃与丙烯共聚,在水的引发下脱水缩合可有效地形成长支链结构的聚丙烯树脂.而氢气常作为丙烯聚合中的链转移剂,调控聚丙烯的分子量,基于此,研究了氢气对氯硅烷功能化非共轭α,ω-双烯烃与丙烯共聚物链结构的影响.核磁共振氢谱(~1H-NMR)测试结果表明,氢气抑制了氯硅烷功能化非共轭α,ω-双烯烃的插入,随着氢气用量的增加,共聚物分子链中端基乙烯基含量由0.12 mol%降低到0.05 mol%.熔体流变行为测试结果显示,聚合物熔体的储能模量、损耗模量和零剪切黏度均随着氢气用量增加而降低,这主要是由于相对分子质量减小和长支链密度的减少.     

有限型的首次返回例外集的测度和维数北大核心CSCD

设M=(m_(ij))是一个b×b阶矩阵且m_(ij)∈{0,1},∑_(M)是矩阵M=(m_(ij))诱导产生的有限型,σ是其上左推移算子.本文主要研究的是有限型动力系统(∑_(M),σ)上的首次返回速度问题.令τ_(k)(x)是点x∈∑_(M)首次返回到包含x的k阶柱集时间,且E_(α,β)={x∈∑_(M):lim inf_(k→∞)(logτ_(k)(x))/k=α,lim sup_(k→∞)(logτ_(k)(x))/k=β}.我们证明了:当M是不可约矩阵时,对任意0≤α≤β≤+∞,集合E_(α,β)的Markov测度要么等于0要么等于1并且具有满的Hausdorff维数.     

Infinite lexicographic products

We generalize the lexicographic product of first-order structures by presenting a framework for constructions which, in a sense, mimic iterating the lexicographic product infinitely and not necessarily countably many times. We then define dense substructures in infinite products and show that any countable product of countable transitive homogeneous structures has a unique countable dense substructure, up to isomorphism. Furthermore, this dense substructure is transitive, homogeneous and elementarily embeds into the product. This result is then utilized to construct a rigid elementarily indivisible structure.     

Set controllability of Markov jump switching Boolean control networks and its applications

In this article, a novel method is proposed for investigating the set controllability of Markov jump switching Boolean control networks (MJSBCNs). Specifically, the switching signal is described as a discrete-time homogeneous Markov chain. By resorting to the expectation and switching indicator function, an expectation system is constructed. Based on the expectation system, a novel verifiable condition is established for solving the set reachability of MJSBCNs. With the newly obtained results on set reachability, a necessary and sufficient condition is further derived for the set controllability of MJSBCNs. The obtained results are applied to Boolean control networks with Markov jump time delays. Examples are demonstrated to justify the theoretical results.     

The nearest neighbor random walk on subspaces of a vector space and rate of convergence

LetX be the collection ofk-dimensional subspaces of ann-dimensional vector spaceV _n overGF(q). A metric may be defined onX by letting

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.     

On two--block--factor sequences and one--dependence

The distributions of two--block--factors arising from i.i.d. sequences are observed to coincide with the distributions of the superdiagonals of jointly exchangeable and dissociated arrays . An inequality for superdiagonal probabilities of the arrays is presented. It provides, together with the observation, a simple proof of the fact that a special one--dependent Markov sequence of Aaronson, Gilat and Keane (1992) is not a two--block factor.

     

The matched queueing network PH/M/c→oPH/PH/1

We consider a matched queueing network PH/M/coPH/PH/1, where the output of the first subsystem PH/M/c is regarded as one of the inputs of the second subsystem and matched with another input of PH-renewal process, and they are served by a single server with PH-service-distribution. The stationary state probabilities, the distribution of the virtual waiting times in the two subsystems, and the distribution of the total virtual waiting time are derived.The work was supported by the Max-Planck-Gesellschaft, Germany, and the Chinese Academy ofSciences.