L1-optimal estimates for a regression type function in R

Let X₁, X₂, …, X_n be random vectors that take values in a compact set in R^d, d ≥ 1. Let Y₁, Y₂, …, Y_n be random variables (“the responses”) which conditionally on X₁ = x₁, …, X_n = x_n are independent with densities f(y | x_i, θ(x_i)), i = 1, …, n. Assuming that θ lives in a sup-norm compact space Θ_q,d of real valued functions, an optimal L₁-consistent estimator of θ is constructed via empirical measures. The rate of convergence of the estimator to the true parameter θ depends on Kolmogorov's entropy of Θ_q,d.     

m阶多时滞中立型微分方程的2T周期解

研究m阶常系数线性多时滞中立型方程的周期解，讨论了2T周期解的存在性和唯一性，得到了2T周期解存在唯一若干新的充分必要条件。所得主要结果适用性更广。它包括了许多相关献的结果为其特例，推广、改进了这些献的主要结果。可对所研究的中立型方程周期解存在的大量情形作出判断，而这些情形用其他献的结果是无法判断的。换言之，对方程（1），主要结果是最一般化的，用同样的方法已不可能得到更好的结果。     

在对称群Sm中解循环方程组

本文研究了在对称群S_m中解循环方程组:x_mX_(m+1)…x_(ω+k-1)σ_m,其中σ_m∈S_m,ω=1,2,…,s,确定了这个循环方程组有解的充分必要条件和解的个数,而且给出了求解过程。     

关于(QU)型模糊拓扑群的直积

研究(QU)型模糊拓扑群族直积,证明了任意(QU)型模糊拓扑群族的直积仍是(QU)型模糊拓扑群;研究了(QU)型模糊拓扑群族直积的模糊单位元之重域基的结构,得到了(QU)型模糊拓扑群族直积的一些重要性质.     

Synthesis and characterization of norbornene–ethylene–styrene terpolymers with a substituted ansa‐fluorenylamidodimethyltitanium‐based catalyst

This article reports a synthetic method for a norbornene–ethylene–styrene (N‐E‐S) terpolymer, which has not been well investigated so far, via incorporation of styrene (S) into vinyl‐type norbornene–ethylene (N‐E) copolymers catalyzed by a substituted ansa‐fluorenylamidodimethyltitanium [Me₂Si(3,6‐tBu₂Flu)(tBuN)]TiMe₂ catalyst ( I ) activated with a [Ph₃C][B(C₆F₅)₄]/Al(iBu)₃ cocatalyst at room temperature in toluene. The resulting terpolymerization product contained the targeted N‐E‐S terpolymer and the contaminated homopolymers, which were then able to be completely removed by solvent fractionation techniques. While homopolystyrene was easily extracted by fractionation with methylethylketone as a soluble part, homopolyethylene and a trace amount of homopolynorbornene could be perfectly separated by fractionation with chloroform as insoluble parts. The detail characterizations of a chloroform‐soluble polymer with gel permeation chromatography, nuclear magnetic resonance, and differential scanning calorimetry analyses proved that it contained a true N‐E‐S terpolymer with long N‐E sequences incorporated with isolated or short styrene sequences. The homogeneity of the morphology together with a single glass transition temperature that proportionally decreased with the increase of the styrene contents indicated that the N‐E‐S terpolymer obtained in this work is a random polymer with an amorphous structure. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2765–2773, 2007     

The Classification of Exponential Paths in Sp(2)

众所周知，四阶以上辛群中指数型道路的Ｍａｓｌｏｖ指标可以取任意整数．本文给出了二阶辛群中指数型道路的分类及其Ｍａｓｌｏｖ指标的取值范围，指出了与高阶情形的不同之处．     

A New Derivation of the Inner Product Formula for the Macdonald Symmetric Polynomials

We give a short proof of the inner product conjecture for the symmetric Macdonald polynomials of type A_n-1. As a special case, the corresponding constant term conjecture is also proved.     

一类时变需求且存货影响销售率的EOQ模型

从实际背景出发,在R AM P型需求和存货影响销售率条件下,讨论了一类以缺货开始的变质性物品的EOQ模型.给出了模型的求解方案及单位时间内平均利润最大化的两个充分条件,并用数值算例进行了验证.     

一类具无穷时滞泛函微分方程的周期解

讨论具有无穷时滞中立型泛函微分方程$ \frac{\rm d}{{\rm d}t}\left(x(t)-\int_{-\infty}^{0}g(s,x(t+s)){\rm d}s\right) =A(t,x(t))x(t)+f(t,x_t)$的周期解问题,利用重合度理论中的延拓定理得到了周期解的存在性和唯一性条件;特别地,当$g(s,x)\equiv 0, A(t,x)=A(t)$时, 给出了存在唯一稳定周期解的条件.     

Effect of the pore surface modification of an inorganic substrate on the plasma‐grafting behavior of pore‐filling‐type organic/inorganic composite membranes

We have investigated the effect of the surface state and surface treatment of the pores of an inorganic substrate on the plasma‐grafting behavior of pore‐filling‐type organic/inorganic composite membranes. Shirasu porous glass (SPG) was used as the inorganic substrate, and methyl acrylate was used as the grafting monomer. The grafting rate increased as the density of silanol on the SPG substrate increased. This result suggests that radicals are generated mainly at the silanol groups on the pore surface by plasma irradiation. The SPG substrates were treated with silane coupling agents used to control the mass of organic material bonded to the pore surface. The thickness of the grafted layer became thinner as the mass of organic material bonded to the pore surface of SPG increased. This decrease in the thickness of the grafted layer could be explained by the decrease in the penetration depth of vacuum ultraviolet rays contained in plasma having a wavelength of less than 160 nm that generated radicals in the pores of the substrate. The thickness of the grafted layer inside the SPG substrates could be controlled through the control of the mass of organic material bonded to the pore surface of the SPG substrate. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 846–856, 2006