正态分布下任意秩有限总体中的Minimax预测

对于任意秩有限总体,在二次损失下,有关文献已给出了线性可预测变量在齐次线性预测类中的唯一线性Minimax预测．本文在正态假设下,证明了这个线性Minimax预测也是线性可预测变量在一切预测类中的唯一Minimax预测．     

Interaction between the end groups and the main chain of conjugated polymers by time-resolved EPR and fluorescence spectroscopy

ABSTRACT

Interaction between a zinc porphyrin (ZnPor) as the end-group and poly(9,9-di-n-octylfluorene-2,7-vinylene) (PFV) as the main chain in a porphyrin end-modified fluorescent conjugated polymer, ZnPFV, was studied by time-resolved electron paramagnetic resonance (EPR) and fluorescence spectroscopy. While fluorescence from the PFV part of ZnPFV showed a spectral profile almost identical to that of a PFV oligomer without end-modification, the emission spectrum of the ZnPor part exhibited a much broader profile compared to that of the reference zinc porphyrin monomer. Based on the analysis of lifetimes and quantum yields, it was found that radiative rate constant of the ZnPor part was enhanced by nearly three times. The observed unusual enhancement in the radiative rate constant was rationalised in terms of a partial π-conjugation between the end group and the main chain, as a result of co-planarisation in fluid solution. On the other hand, the time-resolved EPR spectrum of ZnPFV at 100?K basically showed a similar spectral pattern to that of the reference zinc porphyrin, but with significant differences in zero-field spitting parameters and initial population ratios. The π-system of the excited triplet state is deduced to deviate from D_4h symmetry in the end zinc porphyrin groups. The obtained results show that interaction of the porphyrin end group with the main chain of the polymer significantly influences the excited singlet state properties of the porphyrin, while its triplet state properties were affected to a lesser extent.     

矩阵损失下一般Gauss-Markov模型线性预测的可容许性

本文研究了一般Gauss-Markov模型中线性可预测变量的线性预测的可容许性.在给出线性预测可容许性定义的基础上,通过构造一个特殊的常量矩阵D0,分别得到了齐次和非齐次线性预测类中可容许的充要条件.     

自反B空间中集值增过程的对偶投影

假定Ａ是以自反Ｂａｎａｃｈ空间中弱紧凸集为值的集值增过程，本文研究了非负有界可测过程关于Ａ的积分以及Ａ在乘积可测空间上生成的集值测度，证明了每个可积集值增过程存在唯一对偶可选（可料）投影．     

On the Theory of (Dual) Projection for Fuzzy Stochastic Processes

Abstract

In a theory similar to one of real-valued stochastic processes, in this paper, we investigate the projection and dual projection for fuzzy stochastic processes. First, the related concepts of fuzzy stochastic processes are introduced, such as adaption, measurability, optionality, predictability, etc. Subsequently, we study fuzzy stochastic integral and fuzzy measure generated by increasing fuzzy stochastic processes. Moreover, (dual) projection w.r.t. (increasing) fuzzy stochastic processes are discussed. We prove the existence and uniqueness of (dual) optional (predictable) projection for (increasing) fuzzy stochastic processes.     

Anionic Polymerization of New Dual-Functionalized Styrene and α-Methylstyrene Derivatives Having Styrene or α-Methylstyrene Moieties

Anionic polymerizations of four new dual-functionalized styrene and α-methylstyrene derivatives, 3-(4-(4-isopropenylphenoxy)butyl)styrene ( 4 ), 3-(4-(2-isopropenylphenoxy)butyl)-α-methylstyrene ( 5 ), 4-(4-(4-isopropenylphenoxy)butyl)-α-methylstyrene ( 6 ), and 4-(4-(2-vinylphenoxy)butyl)styrene ( 7 ), were carried out in THF at -78 °C with sec-BuLi as an initiator. Both 4 and 5 underwent anionic polymerization in a living manner to quantitatively afford functionalized polystyrenes and poly(α-methylstyrene)s having α-methylstyrene moiety in each monomer unit and precisely controlled chain lengths. On the other hand, insoluble polymers were obtained by the anionic polymerization of 6 and 7 under the same conditions. The positional effect of substituent on anionic polymerization was discussed.     

Filtrations for the two parameter jump process

A process which has just one jump, and whose time parameter is the positive quadrant [0, ∞] × [0, ∞], is considered. Following Merzbach, related stopping lines are introduced, and the filtration {$\text{F}$_t1,t2³} considered in this paper is such that, modulo completion, the σ-field $\text{F}$_t1,t2³ is the Borel field on the region

$\text{L}{}_{\mathrm{t1,t2}}\text{={(s}{}_1\text{,s}{}_2\text{); 0?s}{}_1\text{?t}{}_1\text{or}\text{0?s}{}_2\text{?t}{}_2\text{}}$

, together with the atom which is the complement in Ω = [0, ∞]² of L_t1,t2. Optional and predictable projections of related processes are defined, together with their dual projections, and an integral representation for martingales is obtained.     

Doob-meyer decomposition for set-indexed submartingales

Set-indexed martingales and submartingales are defined and studied. The admissible function of a submartingale is defined and some class (D) conditions are given which allow the extension of the function to a -additive measure on the predictable -algebra. Then, we prove a Doob-Meyer decomposition: A set-indexed submartingale can be decomposed into the sum of a weak martingale and an increasing process. A hypothesis of predictability ensures the uniqueness of this decomposition. An explicit construction of the increasing process associated with a submartingale is given. Finally, some remarks, about quasimartingales are discussed.Research supported by a grant from the Natural Sciences and Engineering Research Council of Canada. Dept. of Math. University of Ottawa, Ottawa, Ontario, Canada, K1N 6N5.The third author wishes to thank Professor Ivanoff and Dr. Dozzi for their kind hospitality. Dept. of Math. & Comp. Sci. Bar-Ilan University, Ramat-Gan 52900, Israel.     

两指标局部鞅的停止变换及Wiener过程的鞅刻划

本文主要讨论两指标局部平方可积鞅的停止变换问题及Ｗｉｅｎｅｒ过程的鞅刻划和停止问题。