上海世博会的经济综合影响力指数模型

分析上海世博会在世博筹备建设和举办时期对上海市经济方面影响.筛选了世博会影响经济的四个方面(国民经济,财政收支,固定资产投资和对外经济贸易与旅游)的10个主要指标,构建了世博会影响经济的评价指标体系,针对每一项指标,利用1995年到2002的实际数据用指数回归拟合模型测算出2003-2010年在未筹办世博会情况下各项经济指标的估计(拟合)数据,并建立单指标的影响力指数模型,在分析2003年后的实际数据与拟合数据差异基础上,获得了上海世博会在每个指标方面对上海的影响力指数;建立了多指标综合影响力指数模型,得出总的经济影响力的指数为0.2403.考虑到2008年底金融危机势必会削弱世博会对经济的影响,通过参照另外两个同为中国直辖市的重庆和天津相同指标的变化,运用单独建立的模型,剔除金融危机对经济的影响,从而获得更客观地揭示世博对上海地区经济的真实影响程度.并就两个典型的指标给出了具体的演算过程,最后得到了消除了金融危机后的所有指标的影响力指数值,最终获得总的经济影响力的指数为0.2531,即世博会对上海市经济的实际贡献率为25.31%.     

Periodical interfacial cracks in anisotropic elastoplastic media

By using Fourier transformation the boundary problem of periodical interfacial cracks in anisotropic elastoplastic bimaterial was transformed into a set of dual integral equations and then it was further reduced by means of definite integral transformation into a group of singular equations. Closed form of its solution was obtained and three corresponding problems of isotropic bimaterial, of a single anisotropic material and of a bimaterial of isotropy- anisotropy were treated as the specific cases. The plastic zone length of the crack tip and crack openning displacement ( COD) decline as the smaller yield limit of the two bonded materials rises, and they were also determined by crack length and the space between two neighboring cracks . In addition , COD also relates it with moduli of the materials .     

二面角弯曲异构体：M2Pt20/-团簇的理论研究

本文采用密度泛函理论和波函数理论研究了M₂Pt₂^0/-团簇(M表示碱土金属元素)在气相中的几何结构和电子性质. 研究表明，拥有平面结构的D_2h异构体比拥有较小二面角及较短Pt-Pt键长的C_2v异构体更稳定. M(s,p)与Pt(5d)的相互作用和Pt-Pt共价键之间的相互竞争导致了这两种异构体在稳定性方面有所不同. M(s,p)与Pt(5d)的相互作用支持D_2h异构体的平面结构；Pt-Pt共价键作用导致了C_2v异构体的弯曲结构. Be₂Pt₂的单重态和三重态的势能曲线有两个不同的交点，但是Ra₂Pt₂和Ca₂Pt₂^-的不同多重度的势能曲线间只有一个交点，这可能是由于三重态Ra₂Pt₂和四重态Ca₂Pt₂^-较平坦的势能曲线造成的. 上述结果揭示了一个拥有最小原子数的二面角弯曲异构现象，并且为解释其他潜在的角度弯曲异构体提供了理论帮助.     

屈服后表面裂纹与穿透裂纹的等效裂纹长度换算

在较小范围屈服条件下，将D-M模型和弹塑性线弹簧模型相结合，建立了屈服后一般扁壳表面裂纹的计算模型，导出了其控制方程和相应的COD计算公式。在此基础上，提出了屈服后一般扁壳表面裂纹与平板穿透裂纹的等COD换算方法。通过各种影响因素的分析并去除次要因素，最终给出了该等效换算关系的简单拟合公式。计算结果表明，该分析方法简便且有足够的工程精度，适应于在役压力容器等结构的现场快速断裂评定。     

Judging or setting weight steady-state of rational Bezier curves and surfaces

Many works have investigated the problem of reparameterizing rational B~zier curves or surfaces via MSbius transformation to adjust their parametric distribution as well as weights, such that the maximal ratio of weights becomes smallerthat some algebraic and computational properties of the curves or surfaces can be improved in a way. However, it is an indication of veracity and optimization of the reparameterization to do prior to judge whether the maximal ratio of weights reaches minimum, and verify the new weights after MSbius transfor- mation. What＇s more the users of computer aided design softwares may require some guidelines for designing rational B6zier curves or surfaces with the smallest ratio of weights. In this paper we present the necessary and sufficient conditions that the maximal ratio of weights of the curves or surfaces reaches minimum and also describe it by using weights succinctly and straightway. The weights being satisfied these conditions are called being in the stable state. Applying such conditions, any giving rational B6zier curve or surface can automatically be adjusted to come into the stable state by CAD system, that is, the curve or surface possesses its optimal para- metric distribution. Finally, we give some numerical examples for demonstrating our results in important applications of judging the stable state of weights of the curves or surfaces and designing rational B6zier surfaces with compact derivative bounds.     

一种改进的遥感影像地形校正物理模型

遥感影像地形校正是提高光谱反射率反演精度的一个重要的预处理步骤。目前已经出现了多种遥感影像地形校正模型,这些模型各有优缺点。针对现有地形校正模型存在的问题和不足,在Shepherd地形校正模型的基础上,利用更高精度的天空散射辐射计算方法对其加以改进。将改进的地形校正模型和6S大气辐射传输模型相结合以2006年7月12日北京北部山区的Landsat 5 TM影像为数据源进行了地表光谱反射率反演试验。从三个方面对遥感影像地形校正效果进行了检验,结果表明该改进模型能够取得较好的地形校正效果,校正效果优于Shepherd和C校正模型。该改进模型是一种物理模型,可以应用于各种光学遥感影像。     

求解非线性方程组的混合遗传算法

非线性方程组的求解是数值计算领域中最困难的问题。大多数的数值求解算法例如牛顿法的收敛性和性能特征在很大程度上依赖于初始点。但是对于很多非线性方程组,选择好的初始点是一件非常困难的事情。本文结合遗传算法和经典算法的优点,提出了一种用于求解非线性方程组的混合遗传算法。该混合算法充分发挥了遗传算法的群体搜索和全局收敛性,有效地克服了经典算法的初始点敏感问题;同时在遗传算法中引入经典算法(Powell法、拟牛顿迭代法)作局部搜索,克服了遗传算法收敛速度慢和精度差的缺点。选择了几个典型非线性方程组,从收敛可靠性、计算成本和适用性等指标分析对比了不同算法。计算结果表明所设计的混合遗传算法有着可靠的收敛性和较高的收敛速度和精度,是求解非线性方程组的一种成功算法。     

Judging or setting weight steady-state of rational Bézier curves and surfaces

Many works have investigated the problem of reparameterizing rational Bézier curves or surfaces via Mbius transformation to adjust their parametric distribution as well as weights, such that the maximal ratio of weights becomes smallerthat some algebraic and computational properties of the curves or surfaces can be improved in a way. However, it is an indication of veracity and optimization of the reparameterization to do prior to judge whether the maximal ratio of weights reaches minimum, and verify the new weights after Mbius transformation. What's more the users of computer aided design softwares may require some guidelines for designing rational Bézier curves or surfaces with the smallest ratio of weights. In this paper we present the necessary and sufficient conditions that the maximal ratio of weights of the curves or surfaces reaches minimum and also describe it by using weights succinctly and straightway.The weights being satisfied these conditions are called being in the stable state. Applying such conditions, any giving rational Bézier curve or surface can automatically be adjusted to come into the stable state by CAD system, that is, the curve or surface possesses its optimal parametric distribution. Finally, we give some numerical examples for demonstrating our results in important applications of judging the stable state of weights of the curves or surfaces and designing rational Bézier surfaces with compact derivative bounds.     

VERIFYING THE IMPLICITIZATION FOR MULAE FORDEGREE n RATIONAL BEZIER CURVES

1.IntroductionInordertoinvestigateimplicitrepresentationsofparametriccurvesandsurfaces,thetraditionalalgebraicgeometrytheoryisalwaysused.Recentlysomeresearchreports,e.g.[1],showthattherisingBlossomingprinciple[213]ismoreintuitiveandefficientthanthemethodofalgebraicgeometryfortheimplicitization.Thispaperisacotinuationof[1].GivenadegreenplanerationalBenercurvewherePi~(wixi,fiji,fi)arethehomogeneousB6ziercontrolpoints.DenotebywhereP~(x,y,w)isthehomogeneouspoint.LetUsingpolynomialresultants,th…     

Rational cubic/quartic Said-Ball conics

In CAGD, the Said-Ball representation for a polynomial curve has two advantages over the Bézier representation, since the degrees of Said-Ball basis are distributed in a step type. One advantage is that the recursive algorithm of Said-Ball curve for evaluating a polynomial curve runs twice as fast as the de Casteljau algorithm of Bézier curve. Another is that the operations of degree elevation and reduction for a polynomial curve in Said-Ball form are simpler and faster than in Bézier form. However, Said-Ball curve can not exactly represent conics which are usually used in aircraft and machine element design. To further extend the utilization of Said-Ball curve, this paper deduces the representation theory of rational cubic and quartic Said-Ball conics, according to the necessary and sufficient conditions for conic representation in rational low degree Bézier form and the transformation formula from Bernstein basis to Said-Ball basis. The results include the judging method for whether a rational quartic Said-Ball curve is a conic section and design method for presenting a given conic section in rational quartic Said-Ball form. Many experimental curves are given for confirming that our approaches are correct and effective.