Finitely Σ-CS Property of Excellent Extensions of Rings

For a right excellent extension S of a ring R, it is proved that R is right, finitely -CS if and only if S is the same. As an application of this result, a number of examples of group rings which are finitely -CS are presented. This generalizes a result of Jain, et al. [5], where it was shown that F[D] is CS when F is a field of characteristic 2. It is also proved that if R is a commutative domain with 2^–1 R and C₂ is the cyclic group of order 2, then R[C₂] is a CS-ring.2000 Mathematics Subject Classification: 16S20, 16D50The research was supported by the NSERC of Canada, grants A8775 and OGP0194196.     

Some families of strongly clean rings

A ring R with identity is called strongly clean if every element of R is the sum of an idempotent and a unit that commute with each other. For a commutative local ring R and for an arbitrary integer n?2, the paper deals with the question whether the strongly clean property of M_n(R[[x]]), , and M_n(RC₂) follows from the strongly clean property of M_n(R). This is ‘Yes’ if n=2 by a known result.     

Morphic rings and unit regular rings

A ring R is called left morphic if for every a∈R. A left and right morphic ring is called a morphic ring. If M_n(R) is morphic for all n≥1 then R is called a strongly morphic ring. A well-known result of Erlich says that a ring R is unit regular iff it is both (von Neumann) regular and left morphic. A new connection between morphic rings and unit regular rings is proved here: a ring R is unit regular iff R[x]/(xⁿ) is strongly morphic for all n≥1 iff R[x]/(x²) is morphic. Various new families of left morphic or strongly morphic rings are constructed as extensions of unit regular rings and of principal ideal domains. This places some known examples in a broader context and answers some existing questions.     

分光光度测定铬的灵敏的新方法——铬(Ⅵ)-二溴苯基萤光酮-CPB显色体系的研究

详细研究了Cr(Ⅵ)-二溴苯基萤光酮-CPB的显色反应,发现Cr(Ⅵ)与二溴苯基萤光酮在CPB存在下,pH3.5-5.0时经50℃水浴加热10分钟能生成紫红色组成为1:3的络合物,其最大吸收波长位于586nm处,摩尔吸光系数为1.44×10⁵.Cr(Ⅵ)在0-2.5μg/10ml范围内遵循比尔定律.CyDTA的存在可以消除大量常见离子的干扰.拟定了钢样及水中络的测定方法,并经实际样品的测定,取得较为满意的结果.     

三种六氯铈(Ⅳ)酸有机盐的研究

合成了2,6-二甲基-γ-吡喃酮、咪唑和吡啶铈(Ⅳ)的氯化物,化学式为(C₇H₈O₂H)₂CeCl₆、(C₃H₄N₂H)₂CeCl₆和(C₄H₉NH)₄CeCl₈.采用差热、热重分析法比较了上述三种化合物的热稳定性,并配合以电导、红外、紫外光谱等手段进行了结构分析.     

Ergodicity of the BMAP/PH/s/s+K retrial queue with PH-retrial times

Define the traffic intensity as the ratio of the arrival rate to the service rate. This paper shows that the BMAP/PH/s/s+K retrial queue with PH-retrial times is ergodic if and only if its traffic intensity is less than one. The result implies that the BMAP/PH/s/s+K retrial queue with PH-retrial times and the corresponding BMAP/PH/s queue have the same condition for ergodicity, a fact which has been believed for a long time without rigorous proof. This paper also shows that the same condition is necessary and sufficient for two modified retrial queueing systems to be ergodic. In addition, conditions for ergodicity of two BMAP/PH/s/s+K retrial queues with PH-retrial times and impatient customers are obtained. This revised version was published online in June 2006 with corrections to the Cover Date.     

Tubular bimetal oxysulfide CuMgOS catalyst for rapid reduction of heavy metals and organic dyes

Tubular bimetal oxysulfide CuMgOS catalyst was prepared using a feasible method at a low process temperature of 95°C. X‐ray diffractometry, X‐ray photoelectron spectrometry, field emission‐scanning electron microscopy, transmission electron microscopy, UV–Vis diffuse reflectance spectroscopy, photoluminescence emission spectrum, and nitrogen adsorption–desorption isotherms were used for CuMgOS characterizations. The CuMgOS reduction activities were investigated through the reduction of heavy metals of Cr (VI), Pb (II) and Hg (II) solutions, and the organic dyes of rhodamine‐B (RhB), methyl orange (MO) and methylene blue (MB) solutions under dark. The results showed that the CuMgOS prepared with an appropriate N₂H₄ amount for a suitable Cu (I)/Cu (II) ratio exhibited fast reduction activity without adding any reagents, with which the 100 mL Cr (VI), Pb (II) and Hg (II) solutions of 50 ppm were 100% reduced by 20 mg CuMgOS within 4 min, 6 min and 4 min, respectively. The 100 mL RhB, MO and MB solutions of 50 ppm were 100% reduced by 10 mg CuMgOS within 4 min, 5 min and 1 min, respectively, under the existence of NaBH₄. CuMgOS displayed excellent chemical stability for the re‐use tests on heavy metal ions and organic dyes. The excellent performance is attributed to CuMgOS bimetal oxysulfide catalyst with active surface reaction centers to interact with reactants, and the carrier hopping between Cu (I) and Cu (II).     

Characterizations of QF Rings

A ring R is called “left GP-injective” if for any 0 ≠ a ∈ R, there exists n > 0 such that a ⁿ  ≠ 0 and a ⁿ R = r(l(a ⁿ )). It is proved that (1) every right Noetherian left GP-injective ring such that every complement left ideal is a left annihilator is a QF ring, (2) every left GP-injective ring with ACC on left annihilators such that every complement left ideal is a left annihilator is a QF ring, and (3) every left P-injective left CS ring satisfying ACC on essential right ideals is a QF ring. Several well-known results on QF rings are obtained as corollaries.     

像散法离焦检测中的像散透镜参数设计

推导出了离焦量与聚焦误差信号功率的关系式。利用MATLAB软件仿真,详细分析了像散透镜系统各个参数对离焦量、灵敏度、光斑大小等的影响,得到了像散圆透镜与像散柱透镜焦距之间的距离关系。结果发现聚焦物镜和探测器参数对最小离焦量、灵敏度、精度有决定性的影响。提出了像散透镜系统各光学参数选择的原则和方法,并以德国Silicon Sensor公司的QP50-6型四象限探测器为例,详细分析了离焦量与聚焦误差信号功率的线性关系。这些工作对建立满足应用对象要求的像散法离焦检测系统具有重要的指导意义。     

Analysis of exact tail asymptotics for singular random walks in the quarter plane

In this paper, we consider all singular cases of random walks in the quarter plane. Specifically, exact light tail asymptotics for stationary probabilities are obtained for all singular random walks.