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1.
利用中心投影的思想证明了一类n+1次平面拟齐次向量场的几何性质仅依赖于它的诱导向量场.并根据其诱导向量场的性质证明了该向量场有10种不同拓扑结构的扇形不变区域,进而讨论了其全局拓扑结构,得到了该向量场当n为偶数时有13种不同的全局拓扑等价类,当n为奇数时有12种不同的全局拓扑等价类. 相似文献
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本文讨论了n维欧氏空间Rn(n>2)上的多项式向量场集合的系数拓扑不变量,可分为具有不同全局拓扑性质的两类不交的子集合;证明了Rn上的多项式向量场可连续地延拓成n维射影空间RPn上的连续多项式向量场的充要条件,反应了其次数与系数相关的拓扑性质;还证明了平面上的多项式向量场的赤道是闭轨线和不变集的充要条件. 相似文献
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本文证明了赤道不是轨道弧的n次多项式向量场的Poincare紧化场之拓扑结构包含赤道是轨道弧的n-1次多项式向量场的Poincare紧化场之拓扑结构;当n=2时,这种包含关系是相等的,且其Poincare紧化场有五种不同的拓扑结构;当n=2k+1(k=1,2…)时,这种包含关系是真子集。 相似文献
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本文通过对R3中一类二次齐次向量场的全局分析,得到了正确分析R3中齐次向量场Q(x)(x∈R3)的切量场QT(u)(u∈S2)在球面S2上的拓扑分类的方法,指出了习惯上分析切向量场QT(u)的拓扑分类的一种错误。 相似文献
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构造了一类依赖于某一参数δ的多项式系统,位于此系统的向量场中的多个相邻的单重极限环可以随δ的单调变化而同时扩大(或缩小),不过这时极限环的扩大(或缩小)不一定是单调的.由于这种向量场类似于旋转向量,故称此系统的这些极限环关于δ形成“类旋转向量场”,它们可以作为研究重环和分界线环分支的一种有效工具. 相似文献
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复流形上全纯多向量场构成的线性空间有一个自然的Gerstenhaber代数结构.本文研究紧光滑环簇上全纯多向量场构成的Gerstenhaber代数上的BV算子,给出了该情形下BV算子存在的一个充要条件. 相似文献
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在拓扑向量空间内,研究了一类新的集值映射的广义向量均衡问题,利用KKM定理,证明了解的几个存在性定理,并讨论了解的性状.所得结果推广了近期一些作者的研究成果. 相似文献
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In this paper, the authors prove that the flows of homogeneous vector field $Q(x)$ at infinity are topologically equivalent to the flows of the tangent vector field $Q_T(u)$ $(u\in S^2)$
on the sphere $S^2$, and show the theorems for the global topological classification of $Q(x)$. They derive the necessary and sufficient conditions for the global asymptotic stability and the boundedness of vector field $Q(x),$ and obtain the
criterion for the global topological equivalence of two homogeneous vector fields. 相似文献
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J. X. Da Cruz Neto O. P. Ferreira L. R. Lucambio pérez 《Acta Mathematica Hungarica》2002,94(4):307-320
We introduce the concept of a strongly monotone vector field on a Riemannian manifold and give an example. We also demonstrate relationships between different kinds of monotonicity of vector fields and different kinds of definiteness of its differential operator. Some topological and metric consequences of the strict and strongly monotone vector fields" existence are shown. 相似文献
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A.P. Farajzadeh A. Amini-Harandi 《Journal of Mathematical Analysis and Applications》2008,344(2):999-1004
In this paper, generalized vector equilibrium problems are studied and some existence theorems of solutions for these problems in the setting of topological vector spaces are proved. Sufficient conditions for the set of solutions to be compact and convex are given. Our results improve some recent results in this field. 相似文献
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本文给出了模糊拓扑向量空间(X,W)到(Y,J)的函数族F上的模糊线性拓扑,证明了若值域空间(Y,J)是(Q)型的、局部凸的模糊拓扑向量空间,则(F,),也是型的、局部凸的模糊拓扑向量空间。 相似文献
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In this paper we investigate generalized bi-quasi-variational inequalities in locally convex topological vector spaces. Motivated and inspired by the recent research work in this field,we establish several existence theorems of solutions for generalized bi-quasi-variational inequalities,which are the extension and improvements of the earlier and recent results obtained previously by many authors including Sun and Ding [18],Chang and Zhang [23] and Zhang [24]. 相似文献
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《Optimization》2012,61(7):1053-1065
In this article, we consider the general forms of Stampacchia and Minty type vector variational inequalities for bifunctions and establish the existence of their solutions in the setting of topological vector spaces. We extend these vector variational inequalities for set-valued maps and prove the existence of their solutions in the setting of Banach spaces as well as topological vector spaces. We point out that our vector variational inequalities extend and generalize several vector variational inequalities that appeared in the literature. As applications, we establish some existence results for a solution of the vector optimization problem by using Stampacchia and Minty type vector variational inequalities. 相似文献
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§1. IntroductionThroughoutthispaper,Φdenoteseithertherealfieldorthecomplexfield.Foranonemp-tysetY,2YwillstandforthefamilyofallnonemptysubsetsofY.LetE,FbevectorspacesoverΦ,〈,〉:F×E→Φbeabilinearfunctional,andXbeanonemptysubsetofE.Givenamul-ti-valuedmapp… 相似文献
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Xianqiang Luo 《数学研究通讯:英文版》2011,27(3):268-278
In this paper, we establish a fixed point theorem for set-valued mapping
on a topological vector space without "local convexity". And we also establish some
generalized Ky Fan's minimax inequalities for set-value vector mappings, which are
the generalization of some previous results. 相似文献