Cross -sections of star bodies and dual mixed volumes

In this paper, we establish an extension of Funk's section theorem. Our result has the following corollary: If is a star body in whose central -slices have the same volume (with appropriate dimension) as the central -slices of a centered body , then the dual quermassintegrals satisfy , for any , with equality if and only if . The case that is a centered body implies Funk's section theorem.

     

Uniform designs for mixture-amount experiments and for mixture experiments under order restrictions

With order statistics of the uniform distribution on [0, l], exponential and beta distributions, a stochastic representation is obtained for the uniform distribution over various domains, where A-type domains are closely associated with reliability growth analysis, order restricted statistical inference and isotonic regression theory, V-type domains are connected with the mixture-amount experiments, and T-type domains are well related to mixture experiments. With these stochastic representations, the corresponding uniform distribution and number-theoretic nets can be generated. This approach seems to be new and is called order statistics method. Some examples on reliability growth analysis and experimental design are presented. This work was partially supported by a Hong Kong UGC-RGC grant, the Statistics Research and Consultancy Centre of HK-BU, and the Chinese Academy of Sciences.     

非线形嵌段共聚物的合成

主要介绍了非线形嵌段共聚物,如星型嵌段共聚物、杂臂星型共聚物、梳型聚合物等的合成方法,包括多官能团引发剂法、大分子引发剂法等。各种活性聚合方法,如阳离子开环聚合、原子转移自由基聚合(ATRP)和氮氧稳定自由基聚合等都可以用于合成非线形嵌段共聚物。     

Topology Controlled All-(Meth)acrylic Thermoplastic Elastomers by Multi-Functional Lewis Pairs-Mediated Polymerization

It remains challenging to synthesize all-(meth)acrylic triblock thermoplastic elastomers (TPEs), due to the drastically different reactivities between the acrylates and methacrylates and inevitable occurrence of side reactions during polymerization of acrylates. By taking advantage of the easy structural modulation features of N-heterocyclic olefins (NHOs), we design and synthesize strong nucleophilic tetraphenylethylene-based NHOs varying in the number (i.e. mono-, dual- and tetra−) of initiating functional groups. Its combination with bulky organoaluminum [ⁱBuAl(BHT)₂] (BHT=bis(2,6-di-^tBu-4-methylphenoxy)) constructs Lewis pair (LP) to realize the living polymerization of both acrylates and methacrylates, furnishing polyacrylates with ultrahigh molecular weight (M_n up to 2174 kg ⋅ mol⁻¹) within 4 min. Moreover, these NHO-based LPs enable us to not only realize the control over the polymers’ topology (i.e. linear and star), but also achieve triblock star copolymers in one-step manner. Mechanical studies reveal that the star triblock TPEs exhibit better mechanical properties (elongation at break up to 1863 % and tensile strength up to 19.1 MPa) in comparison with the linear analogs. Moreover, the presence of tetraphenylethylene group in the NHOs entitled the triblock TPEs with excellent AIE properties in both solution and solid state.     

基于DMD光谱可调的星模拟器光源光学系统设计

为满足在各种谱线分布下对星敏感器探测能力的高准确度标定,提出了一种基于数字微镜器件的光谱可调星模拟器光源光学系统设计方法,以解决星模拟器与星敏感器观星色温不匹配对星敏感器光信号定标准确度产生的问题.首先,根据设计指标选取Czerny-Turner型光学系统为光源光学系统,对Czerny-Turner型光学系统的彗差和象散进行分析,选取消彗差的Czerny-Turner结构;其次利用MATLAB程序求解Czerny-Turner型光学系统初始结构并应用ZEMAX对其进行优化;最后对光学系统进行公差分析.公差分析结果表明,在400~1 100nm的工作谱段范围内,光学系统的光谱分辨率小于2nm,设计结果满足要求,有效降低了光谱不匹配带来的定标误差.     

热光效应对星敏感器测量准确度的影响

运用"热-结构-光"耦合分析方法,计算典型星敏感器光学系统(6透镜光具组,f=56 mm,相对孔径1/1.3)恒星像斑理想质心位移和亚像元内插质心偏移量,研究温度分布对星敏感器测量准确度的影响.以20℃为光学系统标定温度,计算光学系统均匀温度分布、轴向温差分布和上下侧温差分布三种条件下,星敏感器测量误差.均匀分布温度变化20℃时,星敏感器测量误差约0.07″;轴向温差10℃和20℃时,测量误差分别约为0.17″和0.31″;上下侧温差仅2℃时,测量误差就高达1.46″.计算结果表明,上下侧温差分布对星敏感器准确度影响最大,均匀温度分布影响最小.     

基于Tikhonov正则参量后验选择策略的PCS颗粒粒度反演方法

采用基于Morozov偏差原理的后验策略来选择最优正则参量,并采用此方法对单峰和多峰分布颗粒系的模拟电场自相关函数进行了反演,结果表明,对于单峰颗粒体系,当电场自相关函数的扰动误差小于0.05时,反演得到的峰值准确,当电场自相关函数的扰动误差大于0.05时,反演得到的峰值偏离所模拟的颗粒粒径.正则参量初始值在0.000 02～2范围内,在反演所得的峰值准确的基础上,正则参量初始值越小,反演得到的分布宽度越窄.收敛误差在0.000 05～50范围内,在保持反演结果稳定的基础上,收敛误差取值越大,反演得到的分布宽度越窄.对于多峰颗粒体系,当颗粒系中的颗粒粒径差别较小时,峰值向平均值偏移,当颗粒系中的颗粒粒径差别较大时,小颗粒粒径分布以噪音的形式出现.     

宽视场大相对孔径星敏感器光学系统设计

介绍了一种用于卫星姿态控制的星敏感器光学系统,该光学系统焦距为51 mm,相对孔径为1/1.1,视场角为21°×21°（圆视场2ω＝30°）,光谱范围为0.5～0.85 μm,采用了复杂化双高斯结构.与普通成像系统不同的是,该系统要求对不同光谱的恒星所采集到的点像能量中心是一致的,且星像点像的弥散圆须控制在一定的范围内.具有倍率色差小、轴上和轴外能量分布比较一致的特点.     

四臂星型聚苯乙烯-聚4-乙烯基吡啶嵌段共聚物纤维状胶束及负载金纳米粒子的研究

通过两步原子转移自由基聚合,制备了4种不同嵌段长度的四臂星型嵌段共聚物苯乙烯-聚4-乙烯基吡啶嵌段共聚物(PS-b-P4VP)4.在选择性溶剂甲苯中,随着嵌段长度的变化,自组装胶束的形态从球型到短棒状和纤维状的转变,其中(PS25-b-P4VP90)4自组装形成的以P4VP为核,以PS为花瓣型壳的纤维状胶束.以这种纤维状胶束作为模板,制备了金纳米粒子均匀分布的一维纳米材料     

Improved prediction for a multivariate normal distribution with unknown mean and variance

The prediction problem for a multivariate normal distribution is considered where both mean and variance are unknown. When the Kullback–Leibler loss is used, the Bayesian predictive density based on the right invariant prior, which turns out to be a density of a multivariate t-distribution, is the best invariant and minimax predictive density. In this paper, we introduce an improper shrinkage prior and show that the Bayesian predictive density against the shrinkage prior improves upon the best invariant predictive density when the dimension is greater than or equal to three.