The Degree Theory of a New Operator

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An Improved Solow—Swan Model

§1.　IntroductionThetheoryofeconomicgrowthisanimportanttopicinMacroeconomics.Afterador-mancynearlytwodecades,thestudyofeconomicgrowthbecamevigorousagaininthemid-1980s.TheSolow-Swanmodel[1]isoneofthemostusedinthisfield.Thismodelhasarousedmanyresearchersinterestintherecentyears.N.G.Manki,etal(1992)[2]appliedthismodeltoexaminewhetheritisconsistentwiththeinternationalvariationinthestandardofliving.W.Easterly(1993)[3]gavearevisedSolow-SwanmodelbyintroducingtheCESproductionfunction.Inthepaper…     

Geometry, Electronic Structure, and Related Properties of Dye Sensitizer:3,4-bis[1-(carboxymethyl)-3-indolyl]-1H-pyrrole-2,5-dione

运用密度泛函理论中的杂化泛函B3LYP研究了太阳能电池染料敏化剂3,4-二-[1-(羧甲基)-3-吲哚]-1H-吡咯-2,5-二酮(BIMCOOH)的几何结构、电子结构、极化率和超极化率,并用半经验量子化学方法ZINDO-l和含时密度泛函理论(TDDFT)研究了电子吸收谱．自然键轨道方法的研究结果表明,布居于二酮、吲哚和乙酸基团的自然电荷分别为-0.15e、-0.29e、0.44e．计算的各向同性极化率、极化率各向异性不变量和平均超极化率分别是305.4、188.3、1155.4 a.u.．基于TDDFT的计算结果和实验结果的定性符合指认了在可见和近紫外区的吸收属于∏→∏*跃迁,并且TDDFT的计算结果显示,第9～11个激发态的跃迁与光诱导分子内电荷转移过程有关．对电子结构和紫外-可见吸收谱的分析表明,吲哚基团对光电转换过程的敏化起主要作用,发生于染料敏化剂BIMCOOH和TiO2电极界面之间的电荷转移是由染料分子激发态向半导体导带的电子注入过程．     

Spatially Homogeneous Bianchi Type V Cosmological Model in the Scale-Covariant Theory of Gravitation

We discuss spatially homogeneous and anisotropic Bianchi type-V spacetime filled with a perfect fluid in the framework of the seale-covariant theory of gravitation proposed by Canuto et al. By applying the law of variation for Hubble＇s parameter, exact solutions of the field equations are obtained, which correspond to the model of the universe having a big-bang type singularity at the initial time t = 0. The cosmological model, evolving from the initial singularity, expands with power-law expansion and gives essentially an empty space for a large time. The physical and dynamical properties of the model are also discussed.     

考虑损伤效应的正交各向异性板的弹塑性后屈曲分析

基于弹塑性力学和损伤理论,建立了一个与应力球张量有关的正交各向异性材料的混合硬化屈服准则,该准则无量纲化后与各向同性材料的Mises准则同构,进而建立了混合硬化正交各向异性材料的增量型弹塑性损伤本构方程和损伤演化方程．基于经典非线性板理论,得到了考虑损伤效应的正交各向异性板的增量型非线性平衡方程,且采用有限差分法和迭代法进行求解．数值算例中,讨论了损伤演化、初始缺陷对正交各向异性板弹塑性后屈曲行为的影响．数值结果显示了弹塑性后屈曲与弹性后屈曲的不同,并且损伤和损伤演化对板的弹塑性后屈曲的影响不可忽略．     

一个Erdis问题在二次曲线下的推广

著名数学家Paul Erd■s曾提出过这样一个有趣的问题:"设U为平面上一些单位圆所成之集,如果平面上任一条直线总和U中至少一个圆相交或相切,那么是否可以肯定:对任给的自然数m,总能找到一条直线,它至少和U中的m个圆相交或相切?"张景中,杨路等人解决了这个问题.本文探讨了该问题在二次曲线下的推广,得到了和原Erd■s问题相似的结论.     

在Freud正交多项式零点处的Gr\"{u}nwald插值算子的收敛性

设$W_{\beta}(x)=\exp(-\frac{1}{2}|x|^{\beta})~(\beta > 7/6)$ 为Freud权, Freud正交多项式定义为满足下式$\int_{- \infty}^{\infty}p_{n}(x)p_{m}(x)W_{\beta}^{2}(x)\rd x=\left \{ \begin{array}{ll} 0 & \hspace{3mm} n \neq m , \\ 1 & \hspace{3mm}n = m \end{array} \right.$的     

THE RELATIONSHIP BETWEEN PROJECTIVE GEOMETRIC AND RATIONAL QUADRATIC B-SPLINE CURVES

For two rational quadratic B-spline curves with same control vertexes, the cross ratio of four eollinear points are represented; which are any one of the vertexes, and the two points that the ray initialing from the vertex intersects with the corresponding segments of the twocurves, and the point the ray intersecting with the connecting line between the two neighboring vertexes. Different from rational quadratic Beeier curves, the value is generally related with the loeation of the ray, and the necessary and sufficient condition o5 the ratio being independent of the ray‘s loeation is showed. Alsn another cross ratio o5 the following four collinear points are suggested, i.e. one vertex, the points that the ray from the initlal vertex intersects respectivdy with the curve segmentt the line connecting the segments end points, and the line connecting the two neighboring vertexes. This cross ratio is concerned only whh the ray‘s location, butnot with the weights of the curve. Furthermore, the cross ratio is projective invariant under the projective transformation between the two segments.     

半空间几何中含参数的抽象动力方程边值问题

本文在一般Banach空间中取值的向量值函数组成的Lebesgue空间中，用算子半群方法，研究了半空间几何中含参数的抽象动力方程边值问题的解．     

C_2H_x(x=4～6)在Ni(111)表面吸附的DFT研究

采用密度泛函理论与周期平板模型相结合的方法,对物种C_2H_x(x=4～6)在Ni(111)表面的top,fcc,hcp和bridge位的吸附模型进行了结构优化、能量计算,得到了各物种较有利的吸附位;并对最佳吸附位进行密立根电荷和总态密度分析.结果表明:C_2H_6和C_2H_4在Ni(111)表面的最稳定吸附位都是top位,吸附能分别是-36.41和-48.62 kJ·mol~(-1),物种与金属表面吸附较弱;而C_2H_5在Ni(111)表面的最稳定吸附位hcp的吸附能是-100.21 kJ·mol~(-1),物种与金属表面较强;三物种与金属表面之间都有电荷转移,属于化学吸附.