SPECTRAL SEQUENCES OF COHOMOLOGIES OF SINGULARITIES OF C∞ MAPPINGS

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Sufficient Optimality Condition for Vector Optimization Problems under D.C. Data

In this paper, we establish sufficient optimality conditions for D.C. vector optimization problems. We also give an application to vector fractional mathematical programming in a ordred separable Hilbert space.     

无限维Hillbert空间中单调变分不等式解的近似迭代算法

在无穷维Hillbert空间中研究了一类单调型变分不等式，把求单调型变分不等式解的问题转化为求强单调变分不等式的解，建立了一种新的迭代算法，并证明了由算法生成的迭代序列强收敛于单调变分不等式的解，从而推广了所列文献中的许多重要结果．     

相位测量轮廓术中三维坐标校准新方法

提出了一种新的用于相位测量轮廓术中的三维坐标校准方法。该方法用一个含有三个虚拟校准平面的标准块代替传统相位测量轮廓术校准方法中使用的标准平面，每个虚拟校准平面由多个高度相同但空间离散分布的子区域组成，相应的连续相位恢复是通过一个迭代过程实现的，同时各个子区域还被用于横向坐标的校准。由于各个虚拟校准平面间高度是垂直变化的，传统的相位展开不能得到正确的相对位置关系，基于等效波长概念，提出了一种准确的虚拟校准平面连续相位间相对位置恢复的办法。此校准方法的特点是：在校准过程中不需要标准平面的多次精确平移；仅需要一次测量就可以完成高度和横向坐标的同时校准。文中给出的实验结果说明了该校准方法的有效性和可行性。     

On Set-Valued Differentiation and Integration

Both the notion of differential of a set-valued mapping and the concept of a set-valued integral are introduced in such a way that, on the one hand, the class of differentiable mappings is rather extensive, while on the other hand, the concept of integral includes as special cases Dinghas' approach and Pontryagin's alternated integral. At the same time, the differential of an integral with respect to the upper limit of integration equals in some sense the integrant. Thus the differentiation of a set-valued mapping can be interpreted as an operation inverse to set-valued integration. Both the differential and the integral are defined via approximation by quasi-affine mappings introduced below. The class of quasi-affine mappings is compared with the classes of affine, semi-affine, eclipsing and multi-affine mappings.     

Estimation for the Dilatation of the Generalized Beurling-Ahlfors' Extension

51.IntroductionLethbeahomeomorphismontherealaxisR,andsatisfyh(lco)=loo.Wecallaquasisymmetricfunction.lfthereexistsa'constantMsuchthatM-1Sp(x,t)SM,x,teR,(l.2)then(1.2)iscalledtheM-condition-Byvirtueoftheclassicresultofpaper[lj,ifp(x,t)sat-isfiestheM-condition,thenthereexistsaK(M')-quasiconformaIextensiononthel1alfplaneH,whichisthewell-knownBeurling-Ahlfors'extension:ytz)=u(x,y) iv(x,y),whereAfterpaper[lj,manyworkshavebeendoneforestimatingK-Particularly,itshouldbere-markedheretl1atM.Leht…     

Sufficient global optimality conditions for weakly convex minimization problems

In this paper, we present sufficient global optimality conditions for weakly convex minimization problems using abstract convex analysis theory. By introducing (L,X)-subdifferentials of weakly convex functions using a class of quadratic functions, we first obtain some sufficient conditions for global optimization problems with weakly convex objective functions and weakly convex inequality and equality constraints. Some sufficient optimality conditions for problems with additional box constraints and bivalent constraints are then derived.      

PMUCR方法在高维非线性动力学系统中的应用

对现有的若干种胞映射方法应用于高维非线性动力学系统全局分析时存在的局限性进行了分析,在此基础上,提出了胞映射方法应用于高维系统时需遵循的几个原则:选择合适的分析平面;减少数据量;确定吸引子在相空间中的位置。根据这些原则,对胞参考点映射法(PMUCR)进行了改进,并对该改进方法应用于2维系统和4维系统时消耗的相对CPU时间进行了比较,结果表明,该改进方法能有效地应用于高维非线性动力学系统中。最后以船舶机械非线性隔振系统为例,分别分析了该改进方法在系统呈现周期运动和混沌运动时的应用。     

Non‐standard analysis in ACA0 and Riemann mapping theorem

This research is motivated by the program of reverse mathematics and non‐standard arguments in second‐order arithmetic. Within a weak subsystem of second‐order arithmetic ACA₀, we investigate some aspects of non‐standard analysis related to sequential compactness. Then, using arguments of non‐standard analysis, we show the equivalence of the Riemann mapping theorem and ACA₀ over WKL₀. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

广义Landau-Ginzburg-Higgs方程孤子解的扰动理论

利用扰动方法研究了一类广义Landau-Ginzburg-Higgs方程.引入一个同伦映射，将原方程的解表示为渐近展开式，然后用相应的线性方程的解来近似地表示.讨论了方程的解与得到的近似解的关系. 关键词： 孤子 扰动 同伦映射