环Z/pkZ上s次幂等矩阵及矩阵的加权广义逆

设R=Z/pkZ是模pk的有限局部环,其中p是素数,k>1,p≠2.本文确定了R上n阶s(s≥3)次幂等矩阵的伪标准形,得到了R上n阶矩阵A的加权{ , }-广义逆矩阵的计数定理.     

广义谱分解与亏损矩阵幂的算法

提出了亏损矩阵广义谱分解概念,所得广义特征矩阵具有类似若当链的性质AA(h)i=λiA(h)i+A(h+1)i.亏损矩阵可分解成A=∑si=1(λiA(0)i+A(1)i),由Am=∑si=1∑mh=0Chmλm-hiA(h)i可生成线性方程组,求出各A(h)i,进而计算A的较大次幂Am.介绍了广义谱分解在计算矩阵幂级数中的应用.     

物质抗磁性的经典统计解释

介绍一种解释物质抗磁性的经典统计方法.     

多曲面反射体的计算机辅助设计及优化

研究了自由曲面反射式照明系统的设计理论和方法.根据反射器的尺寸、位置以及配光要求按点光源设计得到曲面型值点初始坐标后,将双三次B样条曲面引入照明系统的设计,反算出控制顶点.给出了空间任意一条入射光线与反射器区块的交点及其曲面法线向量的求法,为了提高光路追迹的效率,针对多曲面反射体给出了一种快速判断相交区块的算法.探讨了用阻尼最小二乘法对B样条曲面反射器进行优化设计的方法,通过优化运算修正控制顶点Z轴坐标,使得曲面在使用扩展光源时光形分布尽可能满足设计要求.     

Ring-opened Crystal Structure and Photochromism of 2,2-Bis（4-tertiary butyl phenyl）-3H-naphtho[2,1-b]pyran

The title compound, 2,2-bis（4-tertial butyl phenyl） naphthopyran, has been prepared and characterized by means of IR, ^1H NMR and elemental analysis, and its crystal structure was determined with X-ray diffraction in the ring-opened form after hydrolyzation. It belongs to monoclinic, space group P21/c, with a = 14.358（3）, b = 7.6725（15）, c = 24.470（5） А, β= 97.147（4）°, C_33H_36O2, Mr=464.62, V= 2674.8（9）А^3, Z = 4, Dc = 1.154 g/cm^3,μ= 0.070 mm^-1, F（000） = 1000, the final R = 0.0514 and wR = 0.1272 for 5444 observed reflections （I 〉 2σ（I））. X-ray analysis revealed that the C（13）-O（1） bond of the title compound cracks after UV irradiation, the six-membered heterocycles are destroyed, and zwitterionic intermediates come into being. The molecular structure in the ring-opened form is obtained after hydrolyzation. It is infrequent that the single-crystal structure is determined in a ring-opened form. A two-dimensional framework is formed by O-H…O and CAr-H…O hydrogen bonds. The UV-vis spectra show that the title compound exhibits excellent photochromic properties in solutions and polymers.     

Catalytic Oxidation of Dopamine at a Nickel Hexacyanoferrate Surface Modified Graphite Wax Composite Electrode Coated with Nafion

A chemically modified electrode was successfully fabricated by means of depositing a thin layer of nickel hexacyanoferrate (NiHCF) on an amine adsorbed graphite paraffin wax composite electrode using a new approach. The electrode was further coated with Nafion. The electrochemical characteristics of the modified electrode were studied using cyclic voltammetry and electrochemical impedance spectroscopy (EIS). The modified electrode catalyzed dopamine (DA) oxidation in the concentration range of 1.5×10^?6 to 1.2×10^?3 M without the interference from ascorbic acid (AA). A detection limit of 4.9×10^?7 M was obtained for DA in the presence of AA with a correlation coefficient of 0.9972 based on S/N=3. Flow injection analysis was used for the determination of dopamine with excellent reproducible results. The analytical utility of the sensor was evaluated for detection of DA in urine.     

Comparison theorems for the third order trinomial differential equations with delay argument

In this paper we study asymptotic properties of the third order trinomial delay differential equation (*) y‴(t) − p(t)y′(t) + g(t)y(τ(t)) = 0 by transforming this equation to the binomial canonical equation. The results obtained essentially improve known results in the literature. On the other hand, the set of comparison principles obtained permits to extend immediately asymptotic criteria from ordinary to delay equations. Research was supported by S.G.A. No.1/003/09.     

Systems of linear differential equations symmetric with respect to transformations nonlinear in a function

We show that if a system of first order linear differential equations with constant coefficients admits an operator whose coordinates responsible for the transformation of independent variables depend on functions then it admits an operator whose coordinates responsible for the transformation of functions depend nonlinearly on functions.     

Homogeneous hypersurfaces in complex hyperbolic spaces

We study the geometry of homogeneous hypersurfaces and their focal sets in complex hyperbolic spaces. In particular, we provide a characterization of the focal set in terms of its second fundamental form and determine the principal curvatures of the homogeneous hypersurfaces together with their multiplicities.      

Extension of the Lasserre-Avrachenkov theorem on the integral of multilinear forms over simplices

The Lasserre-Avrachenkov theorem on integration of symmetric multilinear forms over simplices establishes a method (called LA) for integrating homogeneous polynomials over simplices. Although the computational complexity of LA is generally much higher than that of the other known methods (e.g. Grundmann-Moller formula), it is still useful in deriving closed-form expressions for the value of such integrals. However, LA cannot be directly applied for nonhomogeneous polynomials. It is shown in this paper that Lasserre-Avrachenkov theorem holds for a wider class of symmetric forms, to be called quasilinear forms. This extension can substantially facilitate derivation of a closed-form expression (not computation) for integral of some nonhomogeneous polynomials (such as ) over simplices.