Metal Vector Manipulated Molecular Self-Assembly from Werner System to Cotton System

A definition of metal vector was given to coordinatively unsaturated metals or asymmetrically coordinated metal complexes in which the metal center is partly blocked by inert chelating ligand(s), thus possess specific reactivity and directionality, such as cis-coordinated square Pd(Ⅱ) or Pt(Ⅱ) complexes. Metal vectors have been extensively used in coordination catalysis and molecular assembly. In 1990, Fujita [ 1 ] first demonstrated the utility of cis-coordinated square Pd(Ⅱ)or Pt(Ⅱ) complexes as a right angular 2D metal vector in the formation of molecular square, a cyclic tetramer with nano-cavity and unique molecular recognition. So far, much attention has been paid to the use of the mononuclear coordination centers (Werner-type metal vectors) in molecular assembly.As late as 1999, Cotton et al. [2] reported the use of cis-coordinated metal-metal bonded dimetal units (Cotton-type metal vectors) to direct assembly of molecular squares.This presentation includes two parts: 1) Werner-type metal vector directed molecular assembly; [3]2) Cotton-type metal vector directed molecular assembly.[4]Firstly, the Werner-type metal vector, cis-coordinated Pd(Ⅱ) nitrate, was used to direct a 6-component self-assembly. This leads to the formation of a molecular bowl or crown with syn,syn,syn conformation. These structures are analogues of calix[3]arenes and can function as anion receptors. Interestingly, an nitrate is found to distort from a trigonal plane into a trigonal pyramid when binding to the bottom of the molecular bowl.Secondly, the Cotton-type metal vector, cis-diRh(Ⅱ, Ⅱ), was used to assemble di- or poly-carboxylate anions into neutral supermolecules. Most interestingly, a calixarene-based carceplex with four cis-diRh(Ⅱ, Ⅱ) fastners was obtained[5].All self-assembling entities were studied by both X-ray crystallographic analysis and solution NMR spectra, which are consistent with the presence of assembling structures even in solution.     

On the optimal mapping of distributions

We consider the problem of mappingXY, whereX andY have given distributions, so as to minimize the expected value of X–Y². This is equivalent to finding the joint distribution of the random variable (X, Y), with specified marginal distributions forX andY, such that the expected value of X–Y² is minimized. We give a sufficient condition for the minimizing joint distribution and supply numerical results for two special cases.     

Construction of a yeast plasmid cloning vector with high stability inSaccharomyces cerevisiae strains deficient in 2 µmDNA

PlasmidpCP1 was constructed from cloned 2 µmDNA ofSaccharomyces cerevisiae and from plasmidpJDB207. VectorpCP1 contains the completeB form of 2 µmDNA interrupted in theFLP gene, together withDNA derived from theEscherichia coli plasmidpAT153 and a low expression variant of theS. cerevisiae LEU2 gene. The new vector is lost at a low frequency from yeastcir ⁺ orcir ⁰ strains under non-selective growth conditions and is stable against rearrangements incir ⁰ strains. Its usefulness for curingcir ⁺ strains from endogenous 2 µmDNA and for their conversion tocir ⁰ strains was demonstrated.Dedicated to Professor Dr.Karl Schlögl on the occasion of his 60th birthday.     

Mode selection in a caricature of eutectic solidification

We have studied the problem of mode selection, specifically, selection of the lamellar spacing, in eutectic solidification, by constructing a caricature of a thin-film eutectic solidifying at constant velocity in the presence of a finite temperature gradient and in a slightly noisy environment. Our model incorporates mechanisms which allow termination of substable lamellae and creation of new lamellae by the splitting of lamellae larger than a spacing _max. We have studied this model both by a simple analytic approximation and by computer simulation. We find that both the steady state spacing and the regularity of the pattern are sensitively dependent on the ratio _max/_min, where _min is the minimum spacing required for steady state stability. An additional result to emerge from our investigation is that when _max becomes less than a critical value, the system apparently undergoes a transition into a chaotic state.For a review of the eutectic problem see Ref. 2.     

Triplet superconductivity in a 1D itinerant electron system with transverse spin anisotropy

In this paper we study the ground state phase diagram of a one-dimensional t-J-U model away from half-filling. In the large-bandwidth limit and for ferromagnetic exchange with easy-plane anisotropy a phase with gapless charge and massive spin excitations, characterized by the coexistence of triplet superconducting and spin density wave instabilities is realized in the ground state. With increasing ferromagnetic exchange transitions into a ferrometallic and then a spin gapped triplet superconducting phase take place.     

Statistical Estimation of the Shannon Entropy

The behavior of the Kozachenko–Leonenko estimates for the(differential) Shannon entropy is studied when the number of i.i.d. vector-valued observations tends to infinity. The asymptotic unbiasedness and L~2-consistency of the estimates are established. The conditions employed involve the analogues of the Hardy–Littlewood maximal function. It is shown that the results are valid in particular for the entropy estimation of any nondegenerate Gaussian vector.     

Antiferromagnetism and the node structure of the superconducting order parameter of UPd Al

The node structure of the superconducting order parameter of the heavy-fermion system is analyzed within the weak-coupling theory. A pairing interaction induced by the exchange of antiferromagnetic spin excitations is assumed as suggested by recent inelastic neutron scattering experiments and tunneling spectroscopy. The multi-sheeted Fermi surface is taken into account. Based on a model susceptibility for the simple antiferromagnetic structure of , line nodes result at the rim of the magnetic Brillouin zone. Received 29 July 1999     

2013 unit vectors in the plane

Given a norm in the plane and 2013 unit vectors in this norm, there is a signed sum of these vectors whose norm is at most one.     

Well-behaved asymptotical convex-concave functions

Recently Auslender & Crouzeix introduced a well-behaved asymptotical notion for convex functions. The aim of this work is to extend this notion to the saddle case     

我国农民消费问题的分省面板协整模型分析

依据现代消费理论,在符合中国经济现实假设条件下,建立了我国农民消费问题的数理函数。使用1980-2006年的宏观消费数据,通过协整模型分析表明我国农民的边际消费倾向约为0.69;基于Hausman检验的固定效应模型的面板单位根和面板协整对我国30个省份分析结果表明边际消费倾向为0.7;变截距变斜率面板模型表明各省的长期自主消费和长期边际消费倾向差异显著,上海、江苏呈现双高特征,吉林、海南和西藏则呈现双低特征,其他省份则表现为自主消费和边际消费倾向两者此高彼低的特点。差异产生的原因在于消费习惯不同以及收入差异导致的"主动、被动"消费造成的结果,提出了为西部增收以促进消费良性循环的合理的政策建议。