dN离子在三角场中的基矢及有关矩阵元

通过选用合适的单电子基矢, 使按群链[(O?D_3?C_3)×SU(2)]~N构成的多电子基矢, 成为dN体系D_3?C_3旋量群不可约表示的基矢或其两个一维不可约表示直和的基矢。讨论了有关矩阵元和顺磁参数的计算。     

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.     

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.     

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.     

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.     

Construction of multiwavelets with high approximation order and symmetry

In this paper, based on existing symmetric multiwavelets, we give an explicit algorithm for constructing multiwavelets with high approximation order and symmetry. Concretely, suppose Φ(x) := (φ1(x), . . . , φr(x))T is a symmetric refinable function vectors with approximation order m. For an arbitrary nonnegative integer n, a new symmetric refinable function vector Φnew(x) := (φn1 ew(x), . . . , φrn ew(x))T with approximation order m + n can be constructed through the algorithm mentioned above. Additionally,...     

Novel cationic polyaspartamide with covalently linked carboxypropyl-trimethyl ammonium chloride as a candidate vector for gene delivery

The non-viral gene vector properties of a protein-like polymer, the α,β-poly(N-2-hydroxyethyl)-d,l-aspartamide (PHEA) were investigated after its derivatization with 3-(carboxypropyl)trimethyl-ammonium chloride (CPTA) as molecule bearing cationic groups, in order to obtain stable polycations able to condense DNA. PHEA was firstly functionalized with hydrazide pendant groups by reaction with hydrazine monohydrate (HYD), obtaining the polyhydrazide α,β-poly(N-2-hydroxyethyl/carbazate)-d,l-aspartamide (PHEA-HYD). In this paper we reported that polymer functionalization degree can be easily modulated by varying reaction conditions, so allowing us to produce two PHEA derivatives at different molar percentage of hydrazide groups. Subsequently, condensation reaction of PHEA-HYD copolymers with CPTA yielded α,β-poly(N-2-hydroxyethyl)-N-carbazate[N′-(3-trimethylammonium chloride)propylhydrazide]-d,l-aspartamide (PHEA-HYD-CPTA) polycation derivatives. In vitro studies were carried out to evaluate polycations ability to complex DNA and to protect it from nuclease degradation. Obtained results demonstrated the good efficiency of our new PHEA-polycations derivatives, PHEA-HYD-CPTA, to complex and condense genomic material even at very low polycation/DNA weight ratio.     

Remarks on common hypercyclic vectors

We treat the question of existence of common hypercyclic vectors for families of continuous linear operators. It is shown that for any continuous linear operator T on a complex Fréchet space X and a set Λ⊆R₊×C which is not of zero three-dimensional Lebesgue measure, the family has no common hypercyclic vectors. This allows to answer negatively questions raised by Godefroy and Shapiro and by Aron. We also prove a sufficient condition for a family of scalar multiples of a given operator on a complex Fréchet space to have a common hypercyclic vector. It allows to show that if and φ∈H^∞(D) is non-constant, then the family has a common hypercyclic vector, where Mφ:H²(D)→H²(D), Mφf=φf, and , providing an affirmative answer to a question by Bayart and Grivaux. Finally, extending a result of Costakis and Sambarino, we prove that the family has a common hypercyclic vector, where Tbf(z)=f(z−b) acts on the Fréchet space H(C) of entire functions on one complex variable.     

Divergences without probability vectors and their applications

In general, divergences and measures of information are defined for probability vectors. However, in some cases, divergences are ‘informally’ used to measure the discrepancy between vectors, which are not necessarily probability vectors. In this paper we examine whether divergences with nonprobability vectors in their arguments share the properties of probabilistic or information theoretic divergences. The results indicate that divergences with nonprobability vectors share, under some conditions, some of the properties of probabilistic or information theoretic divergences and therefore can be considered and used as information measures. We then use these divergences in the problem of actuarial graduation of mortality rates. Copyright © 2009 John Wiley & Sons, Ltd.     

乘法运算和虚数单位的几何定义

对于自然数,乘法是加法一种简明的表达式;但由自然数系扩展为整数系时,乘法却需要补充的几何定义,以加深对运算律的理解。为此,任何有向线段a与(-1)的乘积定义为有向线段a绕其起点逆时针旋转π角所生成的有向线段;任何有向线段a与j的乘积定义为有向线段a绕其起点逆时针旋转π/2角所生成的有向线段,由此可推导出j即是虚数单位,j=i=(-1)～(1/2)。eiθ既是单位向量,又是平面向量的乘法旋转算子。文中还阐明了复数的指数形式为平面向量的最佳表达式,以及平面向量三种乘法的对应关系。