多维正态分布均值向量的多重比较

一维正态模型均值的多重比较问题已有较多讨论.本文讨论多维正态分布均值向量的多重比较问题.在一维情形,所谓多重比较即为构造一族参数比较函数的同时置信区间,其中Γ为指标集,μ_j 为均值.多维情形的多重比较也就是构造与上同样的一族{φ_γ}的同时置信域,只是μ_j 现为向量,从而{φ_γ}为一族向量参数.本文通过构造同时置信椭球来解决多维总体的多重比较问题,得到两种方法.第一种方法适用于Γ势为无穷的情形,而对Γ有限的情形通常第二种方法更好一些.在导出第二种方法时我们证明并应用了 Sidák 不等式的一个推广.     

氢气在碳纳米管内吸附的密度泛函理论研究

本文应用密度泛函理论研究纯流体氢气在单壁碳纳米管内吸附过程,采用硬球状态方程改进的基本测量理论表征硬球的斥力作用,离子吸引项的贡献则用微扰理论描述.在温度为300k,氢气本体对比密度范围为0.2～0.7条件下,计算了三种不同尺寸的碳纳米管氢气吸附的密度分布,其密度泛函计算结果与计算机分子模拟数据完全一致.     

Bifurcation analysis and control of periodic solutions changing into invariant tori in Langford system

Bifurcation characteristics of the Langford system in a general form are systematically analysed, and nonlinear controls of periodic solutions changing into invariant tori in this system are achieved. Analytical relationship between control gain and bifurcation parameter is obtained. Bifurcation diagrams are drawn, showing the results of control for secondary Hopf bifurcation and sequences of bifurcations route to chaos. Numerical simulations of quasi-periodic tori validate analytic predictions.     

Low-Dimensional Forest-Like and Desert-Like Fractal Patterns Formed in a DDAN Molecular System

Two kinds of forest-like and desert-like patterns are formed by thermal evaporation of 4-dicyanovinyl-N, Ndimethylamino-1-naphthalene （DDAN） onto SiO2 substrates. Based on thermal kinetics of the molecules on the substrate the transformation between the forest and desert patterns is due to two factors. The first one is the diffusion length, which is related to the deposition rate, the diffusion potential energy barrier and the substrate temperature. The second one is the strong interaction between the two polarity chemical groups of the molecules, which is beneficial to the formation of branches. Totally different patterns are also found on mica substrates, and are attributed to the anisotropic diffusion and the stronger interaction between DDAN molecules and the mica surface.     

抑制型离子色谱快速测定I^—,SCN^—,S2O^2—3

本用抑制型离子色谱，薄壳强碱性阴离子交换树脂为分离柱，柱温为３０±１℃，在常规淋洗液ＮａＨＣＯ３－Ｎａ２ＣＯ３中加入对－硝基苯酚作为有机改进剂，测定了Ｉ＾－、ＳＣＮ＾－、Ｓ２Ｏ＾２－３离子。它们有良好的线性关系，三种离子浓度在５．０～３０．０ｍｇ／Ｌ范围内其相关系数分别为：ｒＩ＾－０．９９９４、ｒｓｃｎ＾－０．９９０６、ｒｓ２ｏ＾２－３０．９９８５，检测限分别为：Ｉ＾－０．１７ｍｇ／Ｌ、ＳＣＮ＾     

稀土催聚的顺-1,4-聚丁二烯的表征

本文研究了镧系稀土元素催化聚合的顺-1,4-聚丁二烯(Ln-PB),其顺式含量不小于97％,最近测得达99.8％,比过渡元素(如Ti,Co,Ni等)催聚为高,并可与铀催聚的U-PB相比拟.对Ln-PB的表征,文中考察了它与Ni等经典催聚的异同,结果认为稀土催化聚合的高顺-1,4-聚丁二烯的大分子以线性良好,不易缠结为其分子结构特征,导致稀溶液性质、结晶行为、本体粘度、应力松弛、屈服强度等性能与支化的Ni-PB相区别。     

定量SEC法同时测定短链共聚物的组成和分子量

由于端基对整体高分子链光学性质的贡献，短链高分子的折光指数增量有明显的分子量依赖性．从整体高分子链折光指数增量依从各结构组成单元折光指数增量的重量分数加和律，指示同一高分子链改变端基后，如分别测定它们的折光指数增量。由其差值可以同时获得链干的分子量和折光指数增量，对共聚物言，从链干的折光指数增量又可进而估定共聚物的组成．这一原则特别适用于具有显著端基效应的短链高分子．本工作用定量尺寸排除色谱方法测量具有不同端基的环氧乙烷－环氧丙烷共聚物苯溶液的折光指数增量，以考验此原则，获得了满意结果．     

新的Cauchy-Schwarz距离函数与多模态医学图像配准

信息论测度,特别是Shannon互信息是多模态图像配准的一种重要方法,但除了互信息之外,仍然存在其它的函数来实现这一任务。对互信息、Kullback-Leibler距离和Shannon不等式之间相互关系作了分析,根据这些关系和不等式理论,提出了新的Cauchy-Schwarz距离,并将这一距离测度用于多模态医学图像的配准处理。从计算速度、噪声容忍性、测度函数图形的特点和图像窗口大小影响等几个方面,通过MR和PET医学图像的实验分析,对新的Cauchy-Schwarz距离测度和典型的Shannon信息论测度进行了分析比较。实验结果表明,新的Cauchy-Schwarz距离测度函数同样可以用于多模态图像配准,而且有着更强的噪声容忍性和更为节省的计算量。     

Solution and transcritical bifurcation of Burgers equation

Burgers equation is reduced into a first-order ordinary differential equation by using travelling wave transformation and it has typical bifurcation characteristics.We can obtain many exact solutions of the Burgers equation,discuss its transcritical bifurcation and control dynamical behaviours by extending the stable region.The transcritical bifurcation exists in the (2 + 1)-dimensional Burgers equation.     

Hopf bifurcation control of a Pan-like chaotic system

This paper is concerned with the Hopf bifurcation control of a modified Pan-like chaotic system. Based on the Routh-Hurwtiz theory and high-dimensional Hopf bifurcation theory, the existence and stability of the Hopf bifurcation depending on selected values of the system parameters are studied. The region of the stability for the Hopf bifurcation is investigated.By the hybrid control method, a nonlinear controller is designed for changing the Hopf bifurcation point and expanding the range of the stability. Discussions show that with the change of parameters of the controller, the Hopf bifurcation emerges at an expected location with predicted properties and the range of the Hopf bifurcation stability is expanded. Finally,numerical simulation is provided to confirm the analytic results.