一类非交换群环的代数结构

通过利用半单环的结构定理、环的单位群的性质、环的阶及环的单位群的阶的关系等,确定了当n为素数,m=2~(t+1),t为正整数时,群环z_nD_m的代数结构和性质.     

A study of aromatic three membered rings

The resonance energies (REs) of neutral three membered ring analogs of the cyclopropenyl cation, computed using block localized wave function (BLW) methods, reveal considerable variations. The RE's of cyclopropenes substituted with exocyclic double bonded groups C?X, (X = O, NH, CH₂, S, PH, SiH₂) increase with the electronegativity of X in the same row (SiH₂ < PH < S and CH₂ < NH < O). The extra cyclic resonance energies (ECREs) (an energetic measure of aromaticity based on comparisons with the RE's of acyclic models) of these derivatives range from +10.5 kcal/mol for cyclopropenone (X = O) (somewhat aromatic; the benzene ECRE is 29.3 kcal/mol) to ?2.4 kcal/mol (slightly antiaromatic) for X = SiH₂. Additional disubstitution of the C?C double bond by X′ groups (X′ = CH₃, NH₂, OH, SiH₃, PH₂, SH) increases the REs considerably, but has only small effects on the ECREs. Even the ECRE of deltic acid (X = O, X′ = OH) is only increased to +13.3 kcal/mol. The conclusion based on ECRE's, that all 12 of the three membered rings are only marginally aromatic/antiaromatic, is supported by the satisfactorily plot (R² = 0.92) of ECRE against values of NICS(0)_πzz (a superior nucleus chemical independent shift magnetic index of aromaticity), which range only from ?6.1 ppm (diatropic) for deltic acid (cf., ?35.5 ppm for benzene and ?14.2 ppm for the parent cyclopropenium ion) to +8.9 ppm (paratropic) for the silicon derivative, X = SiH₂, X′ = SiH₃. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Catalytic Synthesis of 8-Membered Ring Compounds via Cobalt(III)-Carbene Radicals

The metalloradical activation of o-aryl aldehydes with tosylhydrazide and a cobalt(II) porphyrin catalyst produces cobalt(III)-carbene radical intermediates, providing a new and powerful strategy for the synthesis of medium-sized ring structures. Herein we make use of the intrinsic radical-type reactivity of cobalt(III)-carbene radical intermediates in the [Co^II(TPP)]-catalyzed (TPP=tetraphenylporphyrin) synthesis of two types of 8-membered ring compounds; novel dibenzocyclooctenes and unprecedented monobenzocyclooctadienes. The method was successfully applied to afford a variety of 8-membered ring compounds in good yields and with excellent substituent tolerance. Density functional theory (DFT) calculations and experimental results suggest that the reactions proceed via hydrogen atom transfer from the bis-allylic/benzallylic C−H bond to the carbene radical, followed by two divergent processes for ring-closure to the two different types of 8-membered ring products. While the dibenzocyclooctenes are most likely formed by dissociation of o-quinodimethanes (o-QDMs) which undergo a non-catalyzed 8π-cyclization, DFT calculations suggest that ring-closure to the monobenzocyclooctadienes involves a radical-rebound step in the coordination sphere of cobalt. The latter mechanism implies that unprecedented enantioselective ring-closure reactions to chiral monobenzocyclooctadienes should be possible, as was confirmed for reactions mediated by a chiral cobalt-porphyrin catalyst.     

Hot deformation in nanocrystalline Ndben Feben B backward extruded rings

Radially oriented Nd-Fe-B rings are prepared by backward extrusion of fine grained melt-spun powder. Melt-spun powder with the nominal composition of Nd_30.5Fe_bal.Co_6.0Ga_0.6Al_0.2B_0.9 (wt%) is used as starting material. The effects of process variables, such as deformation temperature (T_d), strain rate (ε) and height reduction (Δh%), on the magnetic properties of the rings are investigated. A scanning electron microscope (SEM) equipped with an energy spectrum device is used to study the metallograph and microfracture of the extruded rings. The B_r and (BH)_max reach the optimum values at T_d=800℃, ε =0.01 mm/s, and Δh% =70%. It is found by SEM observations that the particle boundaries, which seemingly correspond to the interfaces of the starting melt-spun powders, emerge after the corrosion of metallography specimens. This is helpful for studying the effects of powder-powder interface on the local deformation and deformation homogeneity in the rings. For different spatial positions of the extruded rings, there are characteristic metallographies and microfractures. The upper end of the rings has the least deformation and worst texture, and therefore the worst magnetic properties. The magnetic properties in the radial direction increase slightly along the axis from the bottom to the middle, then steeply decrease at the upper end of the ring. The deformation and the formation-of-texturing processes are discussed. The deformation and the texturing formation of melt-spun Nd-Fe-B alloys probably involve grain boundary sliding and grain rotation, the solution-precipitation process and preferential growth of Nd₂Fe₁₄B nanograins along the easy growth a-axis.     

关于内射模的P-平坦性

通过引用P-平坦模的定义,引入了右IPF环的概念,推广了右IF环的概念,这对研究IF环及QF环具有重要的作用,同时对右IPF环的性质作了一些刻画,得到了右IPF环的若干个等价命题;最后,用P-平坦模及右IPF环推出了正则环的一些等价条件．     

Adaptive panel representation for oblique collision of two vortex rings

In this article, we use a hierarchical panel method for representing vortex sheet surface motion in 3D flow to investigate the oblique collision of two vortex rings. The particles representing the sheet are advected by a regularized Biot-Savart integral with smoothed Rosenhead-Moore kernel. The particle velocities are evaluated by an adaptive treecode algorithm based on Taylor expansions in Cartesian coordinates. The method allowed us to consider late stages of a vortex rings collision, producing a funnel region. Vorticity iso-surfaces evolution is also investigated.     

Investigation of the optical limiting properties of acid blue29 in various solvents

The optical limiting properties of acid blue29 solutions in different solvents are investigated. Experiments are performed using a CW He-Ne Laser beam at 632.8 nm wavelength and 35 mW power. The strength of the optical limiting action is dramatically influenced by the solvent. Multiple diffraction rings were observed when the samples were exposed to laser radiation. The effect of concentration, solvent and laser intensity on the diffraction rings are studied experimentally. Our results show that the nonlinear refraction is the dominant mechanism to explain the optical limiting behavior in acid blue29.     

Efficient algorithms for wavelength assignment on trees of rings

A fundamental problem in communication networks is wavelength assignment (WA): given a set of routing paths on a network, assign a wavelength to each path such that the paths with the same wavelength are edge-disjoint, using the minimum number of wavelengths. The WA problem is NP-hard for a tree of rings network which is well used in practice. In this paper, we give an efficient algorithm which solves the WA problem on a tree of rings with an arbitrary (node) degree using at most 3L wavelengths and achieves an approximation ratio of 2.75 asymptotically, where L is the maximum number of paths on any link in the network. The 3L upper bound is tight since there are instances of the WA problem that require 3L wavelengths even on a tree of rings with degree four. We also give a 3L and 2-approximation (resp. 2.5-approximation) algorithm for the WA problem on a tree of rings with degree at most six (resp. eight). Previous results include: 4L (resp. 3L) wavelengths for trees of rings with arbitrary degrees (resp. degree at most eight), and 2-approximation (resp. 2.5-approximation) algorithm for trees of rings with degree four (resp. six).     

可换环上辛代数与一般线性李代数之间的中间李代数

本文研究了含幺可换环上一般线性李代数的子代数结构.通过构造特殊矩阵并利用这些矩阵进行计算, 得到了任意含幺可换环上辛代数与一般线性李代数之间的所有中间李代数的形式.并且有利于研究可换环上相应的典型群的子群结构.     

Independence of vectors in codes over rings

We study codes over Frobenius rings. We describe Frobenius rings via an isomorphism to the product of local Frobenius rings and use this decomposition to describe an analog of linear independence. Special attention is given to codes over principal ideal rings and a basis for codes over principal ideal rings is defined. We prove that a basis exists for any code over a principal ideal ring and that any two basis have the same number of vectors. Hongwei Liu is supported by the National Natural Science Foundation of China (10571067).