Hopf π-代数与π-子代数

主要讨论局部有限维的Hopf π-代数的π-子代数与Hopf π-子代数,分别得到了Hopf π-代数的π-子代数和Hopf π-子代数的一些充分必要条件.     

Hopf π-子模

设H为有限型Hopfπ-代数,研究Hopfπ-代数H上的Hopfπ-模与Hopf π-余代数H *上的Hopfπ-余模之间的对偶关系,得出了Hopfπ-子模与Hopfπ-子 余模之间的充分必要条件,推广了Hopf代数中的相关结论.     

纳米金的绿色合成与CTAB对金纳米聚集体的解聚集作用

室温下利用鞣酸(TA)既作还原剂又作保护剂,通过绿色还原方法制备了鞣酸包裹的金纳米粒子,并通过紫外可见光谱(UV-Vis)、透射电镜(TEM)、X射线衍射(XRD)、红外光谱(FTIR)等分别进行了表征和分析。结果表明,随着nTA/nHAuCl4比率的增加,紫外可见光谱显示鞣酸稳定的金溶胶最大吸收波长明显增大且吸收带变宽,而最大吸光率逐渐减小。TEM观察证实增加鞣酸用量会导致溶胶体系中花状金纳米聚集体的形成。实验发现,阳离子型表面活性剂十六烷基三甲基溴化铵(CTAB)对鞣酸保护的金纳米聚集体具有强烈的解聚集作用,在剧烈搅拌的条件下CTAB能使金纳米聚集体成功解聚为单分散状态的金纳米粒子,提高体系温度可明显促进CTAB对金纳米聚集体的解聚集作用。     

Ultrasonicated Condensation of Indene and 2-Nitrofluorene with Aromatic Aldehydes Catalyzed by bis-(pMethoxyphenyl)telluroxide (BMPTO)

The condensation of indene or 2-nitrofluorene with aromatic aldehydes catalyzed by bis-(p-methoxyphenyl)telluroxide (BMPTO) under ultrasonic wave irradiation gave corresponding fulvenes in fair to good yield.     

Solubility of Genistin in Ethanol/Acetone + Water and Daidzein in Ethanol + Water Co-solvent Mixtures Revisited: IBKI Preferential Solvation Method

The preferential solvation parameters (δx_1,3) of genistin in ethanol/acetone (1) + water (2) and daidzein in ethanol (1) + water (2) co-solvent mixtures at elevated temperatures were derived from available solubility data using the inverse Kirkwood–Buff integral method. The values of δx_1,3 varied non-linearly with the co-solvent (1) proportion in all the aqueous mixtures. For the three co-solvent mixtures, the values of δx_1,3 were negative in water-rich mixtures, which indicated that daidzein or genistin was preferentially solvated by water and can act as Lewis bases to establish hydrogen bonds with the proton-donor functional groups of water (1). The same behavior was also observed for daidzein in ethanol (1) + water (2) and acetone (1) + water (2) mixtures with co-solvent-rich composition. For daidzein in ethanol (1) + water (2) mixtures with composition 0.24 < x₁ < 1, and genistin in ethanol (1) + water (2) and acetone (1) + water (2) mixtures with intermediate compositions, the local mole fractions of ethanol or acetone were higher than those of the mixtures and therefore the δx_1,3 values were positive, which indicated that genistin and daidzein were preferentially solvated by the co-solvent. In these regions, daidzein and genistin were acting as a Lewis acid with ethanol or acetone molecules.     

拓扑系统的紧性和分离性

考察拓扑系统的两种紧性——空间式紧和locale式紧,给出紧性的若干刻画,讨论了两种紧性的相互关系,证明了拓扑系统的两种紧性都是拓扑空间紧性的良好推广,说明了紧拓扑系统的闭子拓扑系统、有限和系统以及积系统仍是紧拓扑系统。最后在拓扑系统中考察了紧性加强分离性的问题,得到了紧,(强)T2拓扑系统为(强)T3,(强)T4拓扑系统等结论,并用理想收敛刻画了拓扑系统的强T2分离性。     

On an inequality related to the splitting of a convex body by a plane

This paper gives an improved version of an inequality due to J. Bokowski, which estimates the product of the volumes of the two parts into which a convex body is divided by a hyperplane through its interior.This work was done in 1991 when the author was visiting the Auburn University of Alabama.     

On the isoperimetric deficit of a simplex and of a polygon

This paper gives inequalities which estimate the isoperimetric deficit of a simplex and of a polygon and some consequences thereof.     

Excellent扩张和弱维数

在这篇文章里，我们证明了，当环Ｓ是Ｒ的ｅｘｃｅｌｌｅｎｔ扩张，Ｍ是Ｓ－模时，Ｍ做为Ｓ－模的弱维数与Ｍ做为Ｒ－模的弱维数相等。