Nanosized starlike molecules. Synthesis and optical properties of tris- and tetrakis[oligo(disilanylenebithienylene)dimethylsilyl]benzene

The syntheses of two types of starlike molecules with the arms that extend to three and four directions have been reported. The molecules with the arms consisting of a regular alternating arrangement of a silicon-silicon bond and bithienylene unit that extend to three directions were synthesized by the reactions of 1,3,5-tris(chlorodimethylsilyl)benzene, which was chosen as a core, with the lithio[oligo(disilanylenebithienylene)] derivatives. The starlike molecules with extended arms to four directions were prepared by the reaction of 1,2,4,5-tetrakis(fluorodimethylsilyl)benzene used as a core, with lithio[oligo(disilanylenebithienylene)]s. UV-Vis absorption and fluorescence properties of these starlike molecules have been investigated in a dioxane solution. The present molecules showed absorption maxima in a range of 321-337 nm, and revealed higher fluorescence quantum yields than that of the corresponding linear polymer, poly[(tetraethyldisilanylene)bithiophene].     

On a condition for α-starlikeness

In this paper we give a sufficient condition for function to be α-starlike function and some of its applications. We use the techniques of convolution and differential subordinations.     

The generalization of the generalized Al-Oboudi differential operator

In this paper, firstly we define the generalization of the generalized Al-Oboudi differential operator. Then we also define new classes of analytic and p-valently starlike and convex functions with complex order by means of this new general differential operator. Our main purpose is to determine coefficient bounds for functions in certain subclasses of this classes, which are introduced here by means of a family of nonhomogeneous Cauchy-Euler differential equations. Relevant connections of some of the results obtained with those in earlier works are also provided.     

单位球上星形映射在极值点处的偏差定理

利用多复变数的边界型Schwarz引理,建立了C~n中单位球上正规化双全纯星形映射在极值点处的行列式型偏差定理和矩阵型偏差定理.     

Extension Operators Preserving Biholomorphic Mappings on Hartogs Domains*

In this paper, the authors extend the Roper-Suffridge operator on the generalized Hartogs domains. They mainly research the properties of the extended operator.By the characteristics of Hartogs domains and the geometric properties of subclasses of spirallike mappings, they obtain the extended Roper-Suffridge operator preserving almost starlikeness of complex order λ, almost spirallikeness of type β and order α, parabolic spirallikeness of type β and order ρ on the Hartogs domains in different co...     

Majorization for certain classes of analytic functions defined by fractional derivatives

Here we investigate a majorization problem involving starlike function of complex order belonging to a certain class defined by means of fractional derivatives. Relevant connections of the main results obtained in this paper with those given by earlier workers on the subject are also pointed out.     

有界凸圆型域上的准凸映照

本文研究星形映照的一类子族——有界凸圆型城上的准凸映照,并讨论了它与星形映照及凸映照的关系,建立其与凸映照同形的增长定理和掩盖定理．     

On classes of analytic functions defined by convolution with incomplete beta functions

Carlson and Shaffer [SIAM J. Math. Anal. 15 (1984) 737-745] defined a convolution operator L(a,c) on the class A of analytic functions involving an incomplete beta function ?(a,c;z) as L(a,c)f=?(a,c)?f. We use this operator to introduce certain classes of analytic functions in the unit disk and study their properties including some inclusion results, coefficient and radius problems. It is shown that these classes are closed under convolution with convex functions.     

Convolution properties for certain classes of multivalent functions

Recently N.E. Cho, O.S. Kwon and H.M. Srivastava [Nak Eun Cho, Oh Sang Kwon, H.M. Srivastava, Inclusion relationships and argument properties for certain subclasses of multivalent functions associated with a family of linear operators, J. Math. Anal. Appl. 292 (2004) 470-483] have introduced the class of multivalent analytic functions and have given a number of results. This class has been defined by means of a special linear operator associated with the Gaussian hypergeometric function. In this paper we have extended some of the previous results and have given other properties of this class. We have made use of differential subordinations and properties of convolution in geometric function theory.     

Region of variability of two subclasses of univalent functions

Let F₁ (F₂ respectively) denote the class of analytic functions f in the unit disk |z|<1 with f(0)=0=f^′(0)−1 satisfying the condition RePf(z)<3/2 (RePf(z)>−1/2 respectively) in |z|<1, where Pf(z)=1+zf^″(z)/f^′(z). For any fixed z₀ in the unit disk and λ∈[0,1), we shall determine the region of variability for logf^′(z₀) when f ranges over the class and , respectively.