小角X射线散射应用研究若干进展

文章从小角X射线散射（small-ande X-ray scattering，SAXS）的理论分析出发，结合国内外SAXS理论和应用研究的最新动态，总结了文章作者所在的研究小组近年来在SAXS技术用于材料微结构表征方面的研究成果。主要包括以下三个方面的内容：（1）有机／无机杂化材料中电子密度波动的研究；（2）弦长度分布函数材料的周期结构的研究；（3）纳米粉末晶化过程的研究。     

复杂通信网络的结构分解法及其在可靠性分析中的应用

对复杂通信网络拓扑结构的恰当描述与刻画是研究其可靠性及确定信号流在其中有效的传输方式的前提。通过引进适当的数据结构并采用递归分解的技巧，本给出了将任意复杂通信网络分解为环、弦、链等基本网络结构的某种组合与连接的结构分解法，并由此得到了研究网络可靠性的新的两阶段法，即先分析各基本结构的可靠性，再由此给出原网络可靠性的估计。     

Relationships between distributions of chord lengths and distributions of bubble sizes including their statistical parameters

The performance of fluidized beds is strongly influenced by bubble behavior. Among various hydrodynamic properties, bubble size distributions are of prime concern, but in practice, bubble size is not readily measured. When a probe is used to determine bubble size, it intersects a bubble with a chord length other than the largest vertical dimension. The relationships between the size distribution of bubbles in the bed, the size distribution of bubbles touching the probe and the distribution of chord lengths must be resolved for correct interpretation of probe signals. A method for translating statistical parameters, namely mean and standard deviation of chord lengths to mean and standard deviation of bubble sizes, and an approach to infer the size distribution of bubbles touching the probe and the size distribution of bubbles in the bed system by using the distribution of chord lengths measured by a probe in closed form are proposed for the first time.     

凸域的外平行集的包含测度

本文研究了凸域内定长线段的包含测度问题,利用广义支持函数和限弦函数,得到了一类特殊凸域的包含测度.     

Groups with small Dehn functions and bipartite chord diagrams

We introduce a new invariant of bipartite chord diagrams and use it to construct the first examples of groups with Dehn function n²log n. Some of these groups have undecidable conjugacy problem. Our groups are multiple HNN extensions of free groups. We show that n²log n is the smallest Dehn function of a multiple HNN extension of a free group with undecidable conjugacy problem. Both authors were supported in part by the NSF grants DMS 0245600 and DMS 0455881. In addition, the research of the first author was supported in part by the Russian Fund for Basic Research 05-01-00895, the research of the second author was supported in part by the NSF grant DMS 9978802 and the US-Israeli BSF grant 1999298. Received: February 2005; Revision: September 2005; Accepted: September 2005     

Standardization of distributions of the chord length and distance within oval domains

The distributions of the chord length and distance within oval domains are expressed in terms of the distributions of these values in a circle and of some parameters of oval domains. Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 4, pp. 469–474, October–December, 1999. Translated by E. Gečiauskas     

旋转抛物面的新定义及其性质

从点的轨迹的角度,将R<'3>中的旋转抛物面定义为:R<'3>中到一定点与到一定平面(点不在平面上)距离相等的点的轨迹.同时引入旋转抛物面的焦点、准平面、准线等概念,并在此基础上证明关于旋转抛物面的焦点弦、准平面、顶点、对称轴、切平面之间的若干重要性质.     

Orlicz Sylvester Busemann型函数的极值研究

研究了两个Orlicz Busemann型函数A(K;φ)和I(K;φ;m),建立了A(K_t;φ)和I(K_t;φ;m)的最小值.特别地,在二维平面的情况下,给出了它们的最大值.     

Ageing of spherulites of an industrial relevant aromatic amine derivative

Polycrystalline spherulites of an aromatic amine derivative have been precipitated in a batch process by pH‐shift with hydrochloric acid from stirred aqueous solutions. The time dependent behaviour of the spherulites has been studied during crystallization in the temperature range from 5 °C to 60 °C. Cake resistance values have been obtained from batch filtration tests performed at 2 bar pressure difference at different stages of the crystallization process. The FBRM mean chord length of the crystals decreases with time as a result of crystal ageing into plate‐like crystals. The rate of the ageing process increases with temperature. XRD‐studies show no significant differences in the crystal structure during the ageing process, and the mechanism of the transformation was not established. The filterability of aromatic amine crystals deteriorates as the crystallization progresses. The decrease in the filterability is attributed to the appearance of small plate‐like crystals and a change in the interaction between the crystal surface and the solution, during the ageing of the particles. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)