延迟微分方程隐式Euler方法的收敛性

本文讨论了用隐式Euler方法求解一类延迟量满足Lipschitz条件且Lipschitz常数小于1的非线性变延迟微分方程初值问题的收敛性.获得了带线性插值的隐式Euler方法的收敛性结果.     

Congruences on eventually regular semigroups

Let S be an eventually regular semigroup. The extensively P-partial congruence pairs and P-partial congruence pairs for S are defined. Furthermore, the relationships between the lattice of congruences on S, the lattice of P-partial kernel normal systems for S, the lattice of extensively P-partial kernel normal systems for S and the poset of P-partial congruence pairs for S are explored.     

具有与多项式复合齐次相容的项序

设K[x1,X2,…,xn]是域K上关于变量x1,x2,…,xn的多项式环,θ=(θ1,…,θn)是K[x1,x2,…,xn]的一组有序多项式.多项式复合θ是用θi代替xi的一种运算.我们说多项式复合θ与项序>齐次相容,是指对任意项P与q,p>q,deg p=deg q(→)polt(θ)>qolt(θ).怎样判断多项式复合与项序>是否齐次相容是困难的.将给出明确的判定方法.     

An optimization method for solving some differential algebraic equations

In this paper, the problem of differential algebraic equations has been solved via Chebyshev integral method combined with an optimization method. Two approaches are used based on the index of the problem: in the first, the proposed method is applied on the original problem and in the second, the index of the problem is decreased and the modified problem is solved. An optimization technique is proposed to solve the resulting algebraic equations. Numerical results are included to confirm the efficiency and accuracy of the method.     

Synthesis of 1-aryl-2-propanones

A new convenient synthesis of a series of 1-aryl-2-propanones using aromatic amines as precursors, via diazo-reaction and improved Meerwein arylation reaction under mild conditions, was achieved. In addition, 1-[3,5-bis(trifluoromethyl)phenyl]-2-propanone is a new compound among the synthesized compounds. This approach is an efficient synthetic method for the aryl-propanones with different substituting groups. __________ Translated from Chinese Journal of Organic Chemistry, 2007, 27(10): 1244–1249 [译自: 有机化学]     

Transmission through a perforated metal film by applying an external magnetic field

We theoretically and numerically studied the transmission of light through a subwavelength-perforated metal film in the presence of an external magnetic field. The perforated metal films are found to exhibit a magnetoinduced light transparency due to cyclotron resonance. The localized waveguide surface plasmon (SP) resonance mode and periodicity-structure-factor-induced SP resonance mode are discussed by application of a static magnetic field. The field distributions are localized separately on the left and right metal-air surfaces for structure-factor-induced resonance mode. And for localized cavities resonance mode, standing electromagnetic fields can also be entirely localized inside the nanohole region.     

催化光度法测定煤矸石中的微量镍

在 pH 6 3的KH2 PO4 Na2 B4O7缓冲体系中 ,利用痕量Ni(Ⅱ )催化H2 O2 氧化胭脂红的褪色反应 ,反应受温度、反应时间影响 ,冷却可终止反应。基于此 ,建立一种测定痕量Ni(Ⅱ )的光度法。结果表明方法的检出限为 2 5× 10 -11g·mL-1,催化程度与Ni(Ⅱ )量在 0 0～ 1 2 μg·5 0mL-1范围内符合比耳定律。本法结合萃取分离 ,满意地测定了煤矸石中的微量Ni。     

DESs: Green solvents for transition metal catalyzed organic reactions

In this review, the recent development about using DESs as green solvents in transition metal catalyzed organic reactions was highlighted. Firstly, the development of DESs was simply introduced. After presenting the advantages of DESs, transition metals catalyzed organic reactions using DESs as green solvents were classified and introduced in detail. Different transition metals such as Au, metal impregnated on magnetite, Pd and Ru catalyzed organic reactions proceeded smoothly in DESs and gave corresponding products in good yields. And in some cases, the catalytic systems could be recycled up to several times without any decrease in activity.