Geometry of 2 × 2 hermitian matrices

LetD be a division ring which possesses an involution a → α . Assume that is a proper subfield ofD and is contained in the center ofD. It is pointed out that ifD is of characteristic not two, D is either a separable quadratic extension of F or a division ring of generalized quaternions over F and that if D is of characteristic two,D is a separable quadratic extension ofF. Thus the trace map Tr:D → F, a → a + a is always surjective, which is formerly posed as an assumption in the fundamental theorem of n×n hermitian matrices overD when n ≥ 3 and now can be deleted. WhenD is a field, the fundamental theorem of 2 × 2 hermitian matrices overD has already been proved. This paper proves the fundamental theorem of 2×2 hermitian matrices over any division ring of generalized quaternions of characteristic not two This research was completed during a visit to the Academy of Mathematics and System Sciences, Chinese Academy of Sciences.     

X光二极管实验平台初步设计

采用Marx发生器结合水介质同轴线设计了高压脉冲功率源,在X射线二极管负载上可产生数 MV高压输出。通过电压波过程分析,给出了在负载上获得最大电压输出条件下的形成线、传输线的阻抗设计原则。通过集中参数电路模型分析,给出了一定预脉冲幅值下形成线、传输线电长度及中储设计原则。结合水介质正极性耐压Martin经验公式进行绝缘设计,二极管采用径向均压绝缘堆结构,给出了整个装置初步方案设计。基于Pspice的全系统电路模拟表明：当中储运行电压为2.6 MV时,对3 形成线充电电压为3.3 MV,并最终在40 负载上获得4 MV电压输出,且充电过程中负载脉冲幅值约为形成线充电电压的1.2%,在现有条件下,该平台设计指标能够满足实验预期。     

Metric generalized inverse for linear manifolds and extremal solutions of linear inclusion in Banach spaces

Let X,Y be Banach spaces and M a linear manifold in X×Y={{x,y}∣x∈X,y∈Y}. The central problem which motivates many of the concepts and results of this paper is the problem of characterization and construction of all extremal solutions of a linear inclusion y∈M(x). First of all, concept of metric operator parts and metric generalized inverses for linear manifolds are introduced and investigated, and then, characterizations of the set of all extremal or least extremal solutions in terms of metric operator parts and metric generalized inverses of linear manifolds are given by the methods of geometry of Banach spaces. The principal tool in this paper is the generalized orthogonal decomposition theorem in Banach spaces.     

Prox-regular functions in Hilbert spaces

This paper studies the prox-regularity concept for functions in the general context of Hilbert space. In particular, a subdifferential characterization is established as well as several other properties. It is also shown that the Moreau envelopes of such functions are continuously differentiable.     

非自治时滞微分方程的正周期解

By utilizing a fixed point theorem on cone,some new results on the existence of positive periodic solutions for nonautonomous differential equations with delay are derived.     

每个忙期中第一个顾客被拒绝服务的M／M/1排队模型的其他特征值

研究每个忙期中第一个顾客被拒绝服务的M／M／1排队模型的主算子在左半复平面中的特征值,证明对一切θ∈（0,1）,（2√λμ-λ—μ）θ是该主算子的几何重数为1的特征值．     

线性流形上矩阵方程BTXB=F的双对称最小二乘解

1引言令R~(n×m)、OR~(n×n)、SR~(n×n)(SR_0~(n×n))分别表示所有n×m阶实矩阵、n阶实正交阵、n阶实对称矩阵(实对称半正定阵)的全体,A~ 表示A的Moore-Penrose广义逆,I_k表示k阶单位矩阵,S_k表示k阶反序单位矩阵。R(A)表示A的列空间,N(A)表示A的零空间,rank(A)表示矩阵A的秩。对A=(a_(ij)),B=(b_(ij))∈R~(n×m),A*B表示A与     

A New Proof of Calabi-Yau＇s Theorem

We give a new proof of Calabi-Yau＇s theorem on the volume growth of Riemannian manifolds with non-negative Ricci curvature.     

带特殊重试时间的M／M／1重试排队模型的另一个特征值

研究对应于带特殊重试时间的M／M／1重试排队模型主算子在左半复平面的谱,证明-（2λ＋α＋β＋√（α＋β）^2＋4λβ/4是该主算子的几何重数为1的特征值．     

杂多化合物的酸催化特性及其在有机合成反应中的应用

杂多化合物在各个研究领域中的实际应用日趋广泛。特别是在催化领域内，对杂多化合物催化性能和研究越来越引起人们的关注。本文对在均相和非均相体系中杂多化合物的酸催化的最新研究成果和应用进行了综述，对杂多化合物的酸行为进行了简要的概括，并介绍了作者在这方面的工作。