Constrained Kantorovich inequalities and relative efficiency of least squares

This paper establishes a type of Kantorovich inequality subject to some constraints and obtains some lower bounds for the relative efficiency of the least squares. These lower bounds can be much sharper than that obtained by using the unconstrained Kantorovich inequality. Multivariate extensions of the results are also obtained. Some interesting examples are presented.     

Synthesis and thermal behavior of phenylethynyl‐terminated linear and hyperbranched polyphenylquinoxalines

A phenylquinoxaline (PQ) AB monomer mixture was treated with monofunctional and difunctional end‐capping agents and with and without a coupling agent to afford phenylethynyl‐terminated linear PQ oligomers. The resulting PQ oligomers were soluble in common organic solvents and had intrinsic viscosities (IVs) of 0.21–0.30 dL/g. The glass‐transition temperature (T_g) of the diphenylethynyl‐end‐capped PQ oligomer on both sides increased the most, from 215 °C (before curing) to 251 °C (after curing). The PQ AB₂ monomer, which acted as both a coupling agent and a monomer for the hyperbranched polymer, was treated with an AB monomer and end‐capping agents to afford phenylethynyl‐terminated hyperbranched polyphenylquinoxalines (PPQs). They were also soluble in common organic solvents, had IVs of 1.00–1.65 dL/g and T_g's of 251–253 °C, and underwent exothermic cure with maxima around 412–442 °C. The T_g's of the cured hyperbranched PPQs ranged from 258 to 261 °C, depending on the number of phenylethynyl groups on the surface. After further curing, they displayed a T_g of 316 °C in one sample and turned into a fully crosslinked network. The dynamic melt viscosities of a linear oligomer (IV = 0.21 dL/g), a hyperbranched sample (IV = 1.00 dL/g), and a linear reference PPQ (IV = 1.29 dL/g) were compared with respect to the processing temperature. The PQ oligomer and hyperbranched PPQ had low melt viscosities. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 6318–6330, 2004     

相空间中二阶线性非完整系统的形式不变性

研究相空间中二阶线性非完整系统的形式不变性.给出相空间中二阶线性非完整系统形式不变性的定义和判据，得到形式不变性的结构方程和守恒量的形式，并举例说明结果的应用. 关键词： 相空间 二阶线性非完整系统 形式不变性 守恒量     

对部分线性模型用惩罚最小二乘估计时最优光滑化的注记

部分线性模型也就是响应变量关于一个或者多个协变量是线性的, 但对于其他的协变量是非线性的关系\bd 对于部分线性模型中的参数和非参数部分的估计方法, 惩罚最小二乘估计是重要的估计方法之一\bd 对于这种估计方法, 广义交叉验证法提供了一种确定光滑参数的方法\bd 但是, 在部分线性模型中, 用广义交叉验证法确定光滑参数的最优性还没有被证明\bd 本文证明了利用惩罚最小二乘估计对于部分线性模型估计时, 用广义交叉验证法选择光滑参数的最优性\bd 通过模拟验证了本文中所提出的用广义交叉验证法选择光滑参数具有很好的效果, 同时, 本文在模拟部分比较了广义交叉验证和最小二乘交叉验证的优劣.     

关于随机共轭空间的各种定义及随机线性泛函各种有界性的某些评论

中心目的是详细廉政论在随机共轭空间理论形成过程中所经历的三个阶段的工作，尤其指出了这三个阶段工作之间的联系及本质差别；给出了强有界、拓扑有界及几乎处处有界随机线性泛函之间的关系；亦指出了在概率赋范空间上线性算子理论研究中目前存在的不足．     

THE ZERO AND ORDER OF SOME SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS WITH TRANSCENDENTAL MEROMORPHIC COEFFICIENTS

ＴＨＥＺＥＲＯＡＮＤＯＲＤＥＲＯＦＳＯＭＥＳＥＣＯＮＤＯＲＤＥＲＬＩＮＥＡＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＷＩＴＨＴＲＡＮＳＣＥＮＤＥＮＴＡＬＭＥＲＯＭＯＲＰＨＩＣＣＯＥＦＦＩＣＩＥＮＴＳＣＨＥＮＺＯＮＧＸＵＡＮＡｂｓｔｒａｃｔ：Ｉｎｔｈ...     

A simpler GMRES

The generalized minimal residual (GMRES) method is widely used for solving very large, nonsymmetric linear systems, particularly those that arise through discretization of continuous mathematical models in science and engineering. By shifting the Arnoldi process to begin with Ar₀ instead of r₀, we obtain simpler Gram–Schmidt and Householder implementations of the GMRES method that do not require upper Hessenberg factorization. The Gram–Schmidt implementation also maintains the residual vector at each iteration, which allows cheaper restarts of GMRES(m) and may otherwise be useful.     

The influence of aliphatic sulfides on the photoinduced polymerization of butanediol-1,4 dimethacrylate

The photoinduced polymerization of butanediol-1,4 dimethacrylate was investigated in the presence of various linear sulfides and cyclic dithioacetals. Benzophenone was used as a sensitizer. It was found that the addition of small amounts of sulfides to the polymerization mixture causes, depending on the sulfide structure and concentration, reduction or full elimination of an induction period as well as an increase in the reaction rate and yield both in air and argon-saturated systems. The explanation of the obtained results is based on the propensity of sulfides to act as hydrogen donors, chain-transfer agents, and highly oxidizable compounds.     

Geometry of optimal value functions with applications to redundancy in linear programming

In 1967, Wets and Witzgall (Ref. 1) made, in passing, a connection between frames of polyhedral cones and redundancy in linear programming. The present work elaborates and formalizes the theoretical details needed to establish this relation. We study the properties of optimal value functions in order to derive the correspondence between problems in redundancy and the frame of a polyhedral cone. The insights obtained lead to schemes to improve the efficiency of procedures to detect redundancy in the areas of linear programming, stochastic programming, and computational geometry.The author is indebted to G. Dewan for his review and discussions.     

一个分析不等式的反向

本文建立了作者在１９９０年证明的一个分析不等式的反向形式；作为其直接推论，我们得到了Ｊａｎｏｕｓ－Ｋｌａｍｋｉｎ猜想（１９９２年）等一系列有意义的结果。