气相二氧化硅填充极性低聚物的界面与流变

气相二氧化硅(FS)/低聚物纳米复合材料应用广泛于涂料、胶黏剂、锂离子电池、液体防弹衣等诸多领域.然而,极性低聚物与FS表面相互作用复杂,FS/低聚物复合材料(ONCs)的流变响应多种多样.如何实现ONCs流变行为调控,是长期困扰工业界的难题.本文详细总结了FS在ONCs领域的应用,将FS粒子间相互作用与ONCs流变性质相关联,综述ONCs界面层结构的表征、调控手段及界面层与流变行为的关系.结合本课题组对FS/极性低聚物体系界面及流变行为的研究成果,提出未来ONCs领域的2个重要方向,即研究界面结构与粒子-极性低聚物相互作用间的关系,并通过界面设计实现对纳米粒子/极性低聚物复合材料的流变行为的精确调控.     

Suberitane sesterterpenoids from the Antarctic sponge Phorbas areolatus (Thiele, 1905)

Following ecological and chemical screenings, the Antarctic sponge Phorbas areolatus was chemically investigated for the first time. Three new suberitane derivatives named isosuberitenone B, 19-episuberitenone B, and isoxaspirosuberitenone were identified together with the known compounds suberitenones A and B, and oxaspirosuberitenone after a thorough inspection of their NMR data. These compounds were found to exhibit moderate cytotoxic activity and their presence in this sponge rules out their use as a chemotaxonomic marker for Suberites sponges.     

On an Inequality of Pual Turan Concerning Polynomials-Ⅱ

Let P(z) be a polynomial of degree n and for any complex number α, let D_αP(z) = nP(z)+(α- z) P′(z) denote the polar derivative of the polynomial P(z) with respect to α. In this paper, we obtain inequalities for the polar derivative of a polynomial having all zeros inside a circle. Our results shall generalize and sharpen some well-known results of Turan, Govil, Dewan et al. and others.     

Generalized Polar Decompositions on Lie Groups with Involutive Automorphisms

The polar decomposition, a well-known algorithm for decomposing real matrices as the product of a positive semidefinite matrix and an orthogonal matrix, is intimately related to involutive automorphisms of Lie groups and the subspace decomposition they induce. Such generalized polar decompositions, depending on the choice of the involutive automorphism σ , always exist near the identity although frequently they can be extended to larger portions of the underlying group. In this paper, first of all we provide an alternative proof to the local existence and uniqueness result of the generalized polar decomposition. What is new in our approach is that we derive differential equations obeyed by the two factors and solve them analytically, thereby providing explicit Lie-algebra recurrence relations for the coefficients of the series expansion. Second, we discuss additional properties of the two factors. In particular, when σ is a Cartan involution, we prove that the subgroup factor obeys similar optimality properties to the orthogonal polar factor in the classical matrix setting both locally and globally, under suitable assumptions on the Lie group G . September 12, 2000. Final version received: April 16, 2001.     

Potential theory of infinite dimensional Lévy processes

We study the potential theory of a large class of infinite dimensional Lévy processes, including Brownian motion on abstract Wiener spaces. The key result is the construction of compact Lyapunov functions, i.e., excessive functions with compact level sets. Then many techniques from classical potential theory carry over to this infinite dimensional setting. Thus a number of potential theoretic properties and principles can be proved, answering long standing open problems even for the Brownian motion on abstract Wiener space, as, e.g., formulated by R. Carmona in 1980. In particular, we prove the analog of the known result, that the Cameron-Martin space is polar, in the Lévy case and apply the technique of controlled convergence to solve the Dirichlet problem with general (not necessarily continuous) boundary data.     

A characterization of duality through section/projection correspondence in the finite dimensional setting

In this paper, we show that the well-known duality operation in the context of convex bodies in Rn is completely characterized by its property of interchanging sections with projections. Our results are compared to results by Böröczky-Schneider and Artstein-Milman, who showed that in many cases, the property of order reversing is sufficient to determine a duality operation, up to obvious linear modifications. In fact, we provide another result that recovers a known characterization of duality by the property of order reversing, and up to a mild condition, also a characterization of duality by interchanging sections by projections.     

FURTHER APPLICATIONS OF POLAR COORDINATES IN Cn

Simplify the proof on the domain of convergence of multiple power series and consider the case where some of z1, · · · , zn are contained only in a finite number of terms of the series. Obtain some results on holomorphic functions in Cn.     

Conditional limit results for type I polar distributions

Let (S ₁,S ₂) = (R cos(Θ), R sin(Θ)) be a bivariate random vector with associated random radius R which has distribution function F being further independent of the random angle Θ. In this paper we investigate the asymptotic behaviour of the conditional survivor probability when u approaches the upper endpoint of F. On the density function of Θ we impose a certain local asymptotic behaviour at 0, whereas for F we require that it belongs to the Gumbel max-domain of attraction. The main result of this contribution is an asymptotic expansion of , which is then utilised to construct two estimators for the conditional distribution function . Furthermore, we allow Θ to depend on u.      

Polaroid operators and Weyl's theorem

``Polaroid elements" represent an attempt to abstract part of the condition, ``Weyl's theorem holds" for operators.