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关于(F,ρ)—不变凸性函性多目标规划的充分性条件 总被引:1,自引:0,他引:1
本文给出了一类更一般的广义凸性函数的定义:(F,ρ)-不变凸性函数,并论证了其多目标规划关于有效解的充分性条件。本文的一些主要结论是对文献[2]-[5]中相应结论的改进和推广。 相似文献
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函数强伪凸性与映射强伪单调性 总被引:1,自引:0,他引:1
杨益民 《高等学校计算数学学报》2000,22(2):141-146
1 引 言Schaible在[1]中引入七类单调映射,并证明对其中六类,函数的某种广义凸性都和相应的梯度单调性等价,只有函数强伪凸和梯度强伪单调的等价性是否成立作为公开问题.其后,Schaible又在[2]中通过一个例子否定了两者的等价性,并引入了较弱的函数强伪凸和映射强伪单调的概念,在函数二次可微的条件下证明了函数强伪凸和梯度强伪单调等价.我们将引入强于[2]中概念的强伪凸和强伪单调性,对给出的定义,不附加条件便可保证函数强伪凸性和梯度强伪单调性等价.同时,对[2]中的一个错误予以指出,并给出正确的反例.还就[1]中问题给出远比[2]中简… 相似文献
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多目标变分问题的混合对偶性 总被引:2,自引:1,他引:1
本文给出了一类多目标变分问题的混合对偶 ,使得 Wolfe型对偶和 Mond-Weir型对偶是其特殊情况 ,并在函数 (F ,ρ) -凸性的条件下建立了多目标变分问题关于有效解的混合对偶理论 . 相似文献
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张连生 《高等学校计算数学学报》1983,(2)
[2]中给出了如下引理([2]中编号为9.2.7): 设S是E_n中非空紧集,f:S→E_i是下闭的,则f_c_0(x)=f″(x),x∈H(S). 但[2]中的证明是不正确的.因为在证明过程中实际上用到了f的凸性,而引理中的f无凸性假定.本文用其他方法证明这一结论,同时还得到了有关非凸函数共轭函数的其他性质. 为讨论方便起见,对某些记号和结论略作说明: 相似文献
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群体多目标决策联合有效解类的不变凸充分条件 总被引:2,自引:0,他引:2
对于群体多目标决策问题,文[1]引进它的联合有效解类的概念,并给出这类解的最优性必要条件,在对于问题的目标函数和约束函数附加凸性的条件下,文[2]又给出了联合有效解类的最优性充分条件,本文进一步在目标函数和约束函数具不变凸和不变广义 凸的情况下,分别给出了联合有效解类的若干最优性充分条件。 相似文献
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朱文兴 《应用数学与计算数学学报》1997,11(2):46-55
文[9,10]设计了直接求整数规划问题近似解的填充函数算法,但其所利用的文[2,3]的填充函数均带有参数,需要在算法过程中逐步调节。本文建立整数规划的广义填充函数的定义,说明了文[9,10]所利用的填充函数是整数规划问题的广义填充函数,并构造了一类不带参数的广义填充函数。进而本文设计了整数规划的一类不带参数的广义填充函数算法,数值试验表明算法是有效的。 相似文献
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Tianxiao HE 《数学研究及应用》2012,32(6):631-640
Here presented is a unified approach to generalized Stirling functions by using generalized factorial functions, k-Gamma functions, generalized divided difference, and the unified expression of Stirling numbers defined in [16]. Previous well-known Stirling functions introduced by Butzer and Hauss [4], Butzer, Kilbas, and Trujilloet [6] and others are included as particular cases of our generalization. Some basic properties related to our general pattern such as their recursive relations, generating functions, and asymptotic properties are discussed,which extend the corresponding results about the Stirling numbers shown in [21] to the defined Stirling functions. 相似文献
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The authors investigate the approximation of bounded functions with discontinuities of the first kind by generalized Shepard operators. Estimate for the rate of convergence at a continuity point is obtained, while at the points of discontinuity it is shown that the sequence of generalized Shepard operators is almost always divergent. It is also shown that the sequence of Cesàro means of generalized Shepard operators is convergent everywhere for bounded functions which have only discontinuities of the first kind in [0,1]. 相似文献
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本文在文献[2]的基础上引进广义数系统,定义了以广义数为基础的广义函数(本质不同于L.Schwartz的分布),研究了勒贝格积分的推广,将这理论应用于分布,便得到对σ函数等的自然理解,对广义数应用于量子场论中,也作了一些尝试性的工作。 相似文献
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This paper is a contionuation of [1] and is concerned with multiplication of weak functions. Here the weak functions are treated as generalized expansions in Hermite functions in [2]. 相似文献
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Jorge Aragona Antnio Ronaldo Gomes Garcia Stanley Orlando Juriaans 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(11):5187-5207
In [H. Brézis, A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pure Appl. (9) (1983) 73–97.] Brézis and Friedman prove that certain nonlinear parabolic equations, with the δ-measure as initial data, have no solution. However in [J.F. Colombeau, M. Langlais, Generalized solutions of nonlinear parabolic equations with distributions as initial conditions, J. Math. Anal. Appl (1990) 186–196.] Colombeau and Langlais prove that these equations have a unique solution even if the δ-measure is substituted by any Colombeau generalized function of compact support. Here we generalize Colombeau and Langlais’ result proving that we may take any generalized function as the initial data. Our approach relies on recent algebraic and topological developments of the theory of Colombeau generalized functions and results from [J. Aragona, Colombeau generalized functions on quasi-regular sets, Publ. Math. Debrecen (2006) 371–399.]. 相似文献
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《Mathematische Nachrichten》2018,291(10):1502-1513
We obtain sharp estimates for a generalized Zalcman coefficient functional with a complex parameter for the Hurwitz class and the Noshiro–Warschawski class of univalent functions as well as for the closed convex hulls of the convex and starlike functions by using an inequality from [6]. In particular, we generalize an inequality proved by Ma for starlike functions and answer a question from his paper [17]. Finally, we prove an asymptotic version of the generalized Zalcman conjecture for univalent functions and discuss various related or equivalent statements which may shed further light on the problem. 相似文献
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We continue the study of a Moutard-type transform for generalized analytic functions, which was initiated in [1]. In particular, we suggest an interpretation of generalized analytic functions as spinor fields and show that, in the framework of this approach, Moutard-type transforms for such functions commute with holomorphic changes of variables. 相似文献