Chaotic polynomials on Banach spaces

We show the existence of chaotic (in the sense of Devaney) polynomials on Banach spaces of q-summable sequences. Such polynomials P consist of composition of the backward shift with a certain fixed polynomial p of one complex variable on each coordinate. In general we also prove that P is chaotic in the sense of Auslander and Yorke if and only if 0 belongs to the Julia set of p.     

Pooled marginal slicing approach via SIR<Subscript><Emphasis Type="Italic">α</Emphasis></Subscript> with discrete covariables

In this paper, we consider a semiparametric regression model involving both p-dimensional quantitative covariable X and categorical predictor Z, and including a dimension reduction of X via K indices X′β _k . The dependent variable Y can be real or q-dimensional. We propose an approach based on SIR _α and pooled marginal slicing methods in order to estimate the space spanned by the β _k ’s. We establish -consistency of the proposed estimator. Simulation studies show the numerical qualities of our estimator.     

子结构Ritz向量综合法

讨论了在动态子结构法中应用静态Ｒｉｔｚ向量替代模态向量时所应考虑的基本问题，即如何合理地定义荷载空间分布向量｛ｆ（ｓ）｝，以避免在子结构中出现低阶模态不连续分布的情况。文中给出了在自由子结构和约束子结构内进行Ｒｉｔｚ变换的一般形式及修正公式。算例表明：应用子结构Ｒｉｔｚ向量综合技术能有效地提高线性结构模态分析的计算效率     

Mesoporous Silica Nanoparticles Decorated with Carbosilane Dendrons as New Non‐viral Oligonucleotide Delivery Carriers

A novel nanosystem based on mesoporous silica nanoparticles covered with carbosilane dendrons grafted on the external surface of the nanoparticles is reported. This system is able to transport single‐stranded oligonucleotide into cells, avoiding an electrostatic repulsion between the cell membrane and the negatively charged nucleic acids thanks to the cationic charge provided by the dendron coating under physiological conditions. Moreover, the presence of the highly ordered pore network inside the silica matrix would make possible to allocate other therapeutic agents within the mesopores with the aim of achieving a double delivery. First, carbosilane dendrons of second and third generation possessing ammonium or tertiary amine groups as peripheral functional groups were prepared. Hence, different strategies were tested in order to obtain their suitable grafting on the outer surface of the nanoparticles. As nucleic acid model, a single‐stranded DNA oligonucleotide tagged with a fluorescent Cy3 moiety was used to evaluate the DNA adsorption capacity. The hybrid material functionalised with the third generation of a neutral dendron showed excellent DNA binding properties. Finally, the cytotoxicity as well as the capability to deliver DNA into cells, was tested in vitro by using a human osteoblast‐like cell line, achieving good levels of internalisation of the vector DNA/carbosilane dendron‐functionalised material without affecting the cellular viability.     

On stationary Markov processes with polynomial conditional moments

We study a class of stationary Markov processes with marginal distributions identifiable by moments such that every conditional moment of degree say m is a polynomial of degree at most m. We show that then under some additional, natural technical assumption there exists a family of orthogonal polynomial martingales. More precisely we show that such a family of processes is completely characterized by the sequence {(α_n, p_n)}_{n ? 0} where α′_ns are some positive reals while p′_ns are some monic orthogonal polynomials. Bakry and Mazet (Séminaire de Probabilit?s, vol. 37, 2003) showed that under some additional mild technical conditions each such sequence generates some stationary Markov process with polynomial regression.

We single out two important subclasses of the considered class of Markov processes. The class of harnesses that we characterize completely. The second one constitutes of the processes that have independent regression property and are stationary. Processes with independent regression property so to say generalize ordinary Ornstein–Uhlenbeck (OU) processes or can also be understood as time scale transformations of Lévy processes. We list several properties of these processes. In particular we show that if these process are time scale transforms of Lévy processes then they are not stationary unless we deal with classical OU process. Conversely, time scale transformations of stationary processes with independent regression property are not Lévy unless we deal with classical OU process.     

Relationships between the canonical ascending and descending central series of ideals of an associative algebra

We consider the canonical descending and ascending central series of ideals of an associative algebra. In particular, we prove that some ideal in the descending central series is finite-dimensional if and only if some ideal in the ascending central series is finite-codimensional. This result is the associative algebra analogue of results due to Reinhold Baer and Philip Hall in group theory and Ian Stewart in Lie algebra. We also prove various related results.     

Bilayer matrix composed of polycation/DNA complex and sodium alginate gel as a tumor cell catcher

A bilayer matrix consisting of TABP-SS/DNA complexes and sodium alginate gel is formed via electrostatic interaction. In vitro cell adhesion, proliferation and transfection of the bilayer matrix are investigated in HepG2, HeLa and COS7 cells. Results show that this matrix can only promote tumor cell attachment and growth. Compared with normal cells, the bilayer matrix exhibits significantly higher transfection efficacy in tumor cells. Cell co-culture competitive transfection assay shows that the cell uptake of TABP-SS/DNA complexes is significantly enhanced in tumor cells rather than normal cells under the co-culture competitive condition, which confirms that TABP-SS/DNA complexes have strong tumor cell selectivity and tumor targeting transfection ability.     

Dual disjoint hypercyclic operators

Let E be a separable Fréchet space. The operators T₁,…,Tm are disjoint hypercyclic if there exists x∈E such that the orbit of (x,…,x) under (T₁,…,Tm) is dense in E×?×E. We show that every separable Banach space E admits an m-tuple of bounded linear operators which are disjoint hypercyclic. If, in addition, its dual E^∗ is separable, then they can be constructed such that are also disjoint hypercyclic.     

矩阵广义对角化的探讨

利用子空间关于矩阵的最小多项式研究了矩阵可广义对角化的充要条件,给出了矩阵可广义对角化的一种算法.     

图书采购流程中资金分配模型研究

本应用现代经济理论的择优分配原理，在图书产出效益函数的性质探讨的基础上，将效益函数的约束条件转化为对资金变量的约束条件，从而简化了资金分配方案的求解。提出了资金在各类别图书中的分配模型，指导图书馆图书采购工作。