一般投影线性群PGL(2,q)和4-(q+1,5,λ)设计

本文主要考虑了一般投影线性群PGL(2,q)区传递作用下的4-(q+1,5,λ)设计的存在性问题。经讨论知λ的可能值是4。     

Absolutely convergent Fourier series and function classes

We study the smoothness property of a function f with absolutely convergent Fourier series, and give best possible sufficient conditions in terms of its Fourier coefficients to ensure that f belongs either to one of the Lipschitz classes Lip(α) and lip(α) for some 0<α?1, or to one of the Zygmund classes Λ_∗(1) and λ_∗(1). Our theorems generalize some of those by Boas [R.P. Boas Jr., Fourier series with positive coefficients, J. Math. Anal. Appl. 17 (1967) 463-483] and one by Németh [J. Németh, Fourier series with positive coefficients and generalized Lipschitz classes, Acta Sci. Math. (Szeged) 54 (1990) 291-304]. We also prove a localized version of a theorem by Paley [R.E.A.C. Paley, On Fourier series with positive coefficients, J. London Math. Soc. 7 (1932) 205-208] on the existence and continuity of the derivative of f.     

某类解析函数的性质

引入了解析函数类H的子类H(λ,α,A,B),通过利用Briot-Bouquet微分从属的方法,研究了它的从属关系、包含关系、属于H(λ,α,A,B),或属于其子类的充要条件.     

λ-Shaped azomesogens with polar chloro- and nitro-substituents

A new homologous series of λ-shaped mesogenic azo esters with polar chloro- and nitro- substituents has been synthesised by attaching a rigid 2-chloro-4-nitrophenylazo group to a resorcinol moiety by a central azo linkage. Both phenolic hydroxyl groups are esterified by 4-n-alkoxybenzoyl groups. All the compounds synthesised have been characterised using a combination of elemental analysis and standard spectroscopic methods. The mesomorphic properties of the compounds have been determined by polarising optical microscopy and differential scanning calorimetry. The lower members of the series are non-mesogenic, the middle members exhibit a nematic mesophase, and higher members exhibit a smectic A mesophase. The effect of polar chloro-, nitro-, and long lateral aromatic substituents, on mesomorphism is discussed.     

Radial Operators on the Weighted Bergman Spaces over the Polydisk

In this paper, we study radial operators in Toeplitz algebra on the weighted Bergman spaces over the polydisk by the(m, λ)-Berezin transform and find that a radial operator can be approximated in norm by Toeplitz operators without any conditions. We prove that the compactness of a radial operator is equivalent to the property of vanishing of its(0, λ)-Berezin transform on the boundary. In addition, we show that an operator S is radial if and only if its(m, λ)-Berezin transform is a separately radial function.     

Selective Functional Transformation of 1,2-Diols Via Organophosphorus Reagents

A new synthesis of 1,3,2λ⁵-dioxaphospholanes was realized by direct reaction of dibromotriphenylphosphorane with 1,2-diols. Ring opening studies were performed with or without electrophilic activation (Lewis acids or hydrogen bonding) in order to substitute selectively one of the hydroxy function.     

Mono and Bisphosphonates from Perfluoro Olefins and Polyfunctional Fluoro Ketones. Syntheses,Molecular Structure and Derivatives

Perfluoroalkenyl phosphonates were formed along with Me₃SiF using CF₃CF=CF₂, CF₃CH=CF₂, F₅SCF=CF₂ or F₅SCH=CF₂ and silylated phosphites, (R¹O)₂POSiMe₃ (R¹=Et, SiMe₃). This straightforward method could be extended to perfluorobutadienes CF₂=C(R^F)C(R^F)=CF₂ (R^F F=F, CF₃). The formation of CF₃C(=O)P(=O)(OSiMe₃)₂ and further reactions to yield bisphosphonates will be described. Acetylphosphonates, R²C(=O)P(=O)(OSiMe₃)₂ (R²=CH₃, CF₃) reacted with the ketimine, CH₃C(=NiPr)Ph to give α-hydroxy-γ-imino phosphonates. Trifluoroacetylphenol and 2,6-bis(trifluoracetyl)-4-methyl-phenol have been proven to be versatile precursors for α-and γ-hydroxy phosphonates. Intermediates in these reactions were found to be cyclic λ⁵σ⁵P species.     

Synthesis and Study of the Thermal Epimerization of r -2-Ethoxy- cis -4- cis -5-Dimethyl-1,3,2-λ 3 -Dioxaphospholane Using 31 P NMR

The exclusive synthesis of r -2-ethoxy- cis -4- cis -5-dimethyl-1,3,2- u 3 -dioxaphospholane ( cis - 1 ) is reported. The kinetic measurements of the epimerization of cis - 1 to trans - 1 were performed by 31 P NMR from 50 to 80;C in toluene. The energy of activation (E a ) of the epimerization process was calculated from Arrhenius plot. The thermodynamic parameters of the transition state led us to conclude that the activation barrier of the inversion at phosphorus is driven by the enthalpy and by a large and negative entropy of activation.     

一类复杂时滞系统的λ实用稳定性

主要研究了一类具有多时滞的复杂微分系统的λ实用稳定性问题,通过对Lyapunov函数方法以及比较原理的运用,建立一般形式的实用稳定性直接判据.在此基础上给出讨论这类多时滞复杂微分系统实用稳定性的新方法.