On a Generalized Cochrane Sum and Its Hybrid Mean Value Formula

The main purpose of this paper is to use a mean value theorem of Dirichlet L-functions to study the asymptotic property of a hybrid mean value of a generalized Cochrane sum, and give an interesting mean value formula.2000 Mathematics Subject Classification: Primary—11F20; Secondary—11F99     

A new property of Bernstein-Kantorovi? operators

In the present paper, we prove that the Bernstein-Kantorovič operators have the ability of preserving translation property in both C and L^p norms. Supported (in part) by the NSFC(10471130,10371024) of PRC and the Natural Science Foundation (Y604003) of Zhejiang Province.     

Spaces on which every pointwise convergent series of continuous functions converges pseudo-normally

A topological space is a -space provided that, for every sequence of continuous functions from to , if the series converges pointwise, then it converges pseudo-normally. We show that every regular Lindelöf -space has the Rothberger property. We also construct, under the continuum hypothesis, a -subset of of cardinality continuum.

     

Wecken property for roots

We show that maps from a compact space into a topological manifold which have geometric Nielsen root number zero satisfy the Wecken property, i.e., such that .

     

Cardinal restrictions on some homogeneous compacta

We give restrictions on the cardinality of compact Hausdorff homogeneous spaces that do not use other cardinal invariants, but rather covering and separation properties. In particular, we show that it is consistent that every hereditarily normal homogeneous compactum is of cardinality . We introduce property wD(), intermediate between the properties of being weakly -collectionwise Hausdorff and strongly -collectionwise Hausdorff, and show that if is a compact Hausdorff homogeneous space in which every subspace has property wD( ), then is countably tight and hence of cardinality . As a corollary, it is consistent that such a space is first countable and hence of cardinality . A number of related results are shown and open problems presented.

     

Totally hereditarily normaloid operators and Weyl's theorem for an elementary operator

A Hilbert space operator T∈B(H) is hereditarily normaloid (notation: T∈HN) if every part of T is normaloid. An operator T∈HN is totally hereditarily normaloid (notation: T∈THN) if every invertible part of T is normaloid. We prove that THN-operators with Bishop's property (β), also THN-contractions with a compact defect operator such that and non-zero isolated eigenvalues of T are normal, are not supercyclic. Take A and B in THN and let dAB denote either of the elementary operators in B(B(H)): ΔAB and δAB, where ΔAB(X)=AXB−X and δAB(X)=AX−XB. We prove that if non-zero isolated eigenvalues of A and B are normal and , then dAB is an isoloid operator such that the quasi-nilpotent part H₀(dAB−λ) of dAB−λ equals ⁻¹(dAB−λ)(0) for every complex number λ which is isolated in σ(dAB). If, additionally, dAB has the single-valued extension property at all points not in the Weyl spectrum of dAB, then dAB, and the conjugate operator , satisfy Weyl's theorem.     

磁流变液体的流变力学特性试验和建模

从唯象角度讨论磁流变液体的流变力学特性。基于对磁流变液体的试验 ,讨论了磁感强度、温度和剪切应变速率等对磁流变液剪切应力的影响 ;建立了描述磁流变液剪切应力的 Bingham模型、广义 Bingham模型和非线性模型。     

老化反应对高碱度烷基水杨酸钙胶体结构及抗磨性的影响

采用冷冻蚀刻电镜（ＦＥ－ＥＭ）,傅立叶红外光谱（ＦＴ－ＩＲ）及钙分布测定等研究了高碱度烷基水杨酸钙的老化过程,并探讨了老化机理,老化反应高碱度烷基水杨酸钙胶体粒子变小,胶体中氢氧化钙的相对含量增加,粘度降低,总碱值（ＴＢＮ）升高;老化后样品的清净性及抗磨性明显提高;水、甲醇及氢氧化钙等影响老化效果。     

炼铝工业固体废料(赤泥)的物质组成与工程特性及其防治利用研究

据保守估算 ,我国每年排放的铝工业固体废料赤泥至少在 5 0 0万 t以上。由于赤泥对生态环境的严重危害 ,赤泥坝、赤泥库的安全已成为令人关注的环境问题。各类固体废弃物 (包括生活垃圾 )储存、处理和利用的研究不仅是当代环境科学的重要任务 ,亦是当代环境工程地质学、环境岩土工程学最重要、最迫切的研究任务之一。本文利用工程岩土学的有关理论和方法 ,系统地研究了赤泥的化学、矿物成分、不良工程特性及其形成变化机理 ,并在此基础上提出了赤泥的储存、加固 (处理 )和综合利用的原理和途径。     

线性互补问题的一类新的带参数价值函数的阻尼牛顿法

本文给出了线性互补问题LCP(q ,M)的一类新的带参数光滑价值函数 ,基此价值函数提出了一种阻尼牛顿类算法 ,并证明了当M为P 矩阵时 ,该算法全局收敛且有限步终止 .通过数值实验说明了该算法高效可靠 .与互补问题的磨光方程组中所采用的带参数价值函数不同 ,这里的参数最终并不趋向于零 ,而是趋向于被称作解的乘子向量 (与凸非线性极小极大问题的Lagrange乘子完全一致 ) ,这一思想是本文作者首次提出来的 ,同时本文中所采用的阻尼牛顿类方法也有其独到之处 ,在互补问题的研究中有进一步发展的潜力