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NotesonSmoothMapGermsYuLi(余立);ZhangGuobin(张国滨)(ZhanjiangTeachersCollege,China)Abstract:Inthispaper,westudythedeterminacyofrea... 相似文献
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In the paper [1], the author told us that he provides new proofs for the three classical theorems on real singularity theory: Mather's two theorms, and the splitting lemma. And in the paper [2], the author used this method to catastrophe theory.The journal "Mathematical Reviews" ever commented the above papers successively in Vol.57, No.3 (1979) and Vol.58, No.3 (1979).This paper points out that the proofs about Mather′s theorems Ⅰand Ⅱ in [1] are wrong, and then presents an counter-example to show that the corollary and conjecture are false. 相似文献
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光滑映射芽的开折的分级稳定性 总被引:3,自引:0,他引:3
光滑映射芽各种稳定性的讨论,一直是奇点理论的一个重要部分. Thom R.[1]在创立突变论时,提出了映射芽的,r-开折的稳定性理论.Wassermann G.[2]将之发展为开折的(r,s)稳定理论.本文将他们的结论发展为(r1,r2,…,rd)稳定性,在任意的分级情况下,得到强稳定性、弱稳定性及无穷小稳定性的等价性,并得到了一些基本结果. 相似文献
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A.du Plessis[1]对实奇点理论中?决定的阶数作了很好的估计。T.Ga-ffney等[2]发展到I-?及M-?的情形。李养成[4]则将[1]向?_k作了推广。本文以[2]为特例,也推广了[4]的部分结果。作为推论,本文建立了∞-?_k的一个估计,当k=0是[7]的主要结果。§4例说明[1]的定理(2.8)不能推广到M情况。 相似文献
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带参数的函数芽的无限决定性 总被引:1,自引:1,他引:0
本文讨论奇点理论在分问题中的应用.用有限决定性的方法于光滑函数的奇点,得到如下结果:当m(n q)^∞包含m(n q)(δf/δx)时,带参数的函数芽f是无穷决定的.这一结果发展了Wilson定理([2]),可应用于分支问题. 相似文献
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本文的目的在于用微分拓扑的方法讨论从R^n到R^3的光滑映射的generic奇点的分类问题,我们证明这样的映射只有三类奇点:折点,尖点和燕尾点,并给出了它们的标准型。它推广了J.Martinet(1)的结果。 相似文献
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In1970sR.Thomestabllshedthefamousbasictheoremofcatastr0phetheoryinwhichThom'scelebratedlistofthesevenelementarycatastr0PhesisinfaCtaclassilicationofstableunfoldingsoflowunfoldingdimension.However,byG-Wassermann'soptal0nsl3,4],theequlvalencerelationonunfoldingsusedinThom'stheoryisfairlyc0arse-SoG.Wassermanndevel0pedastabilitytheoryforunfoldingsbased0nafinerequlVaencen0tion(i.e.(r,s)-equlvalence)thantheordinaryoneandcarriedouttheclassilicationsfor(3,1)-and(1,3)-stabilityTheretheparametersare… 相似文献
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In the paper [1], the author told us that he provides new proofs for the three classical theorems on real singularity theory: Mather′s two theorms, and the splitting lemma. And in the paper[2], the author used this method to catastrophe theory. The journal "Mathematical Reviews" ever commented the above papers successivelly in Vol.57, No.3 (1979) and Vol.58, No.3 (1979). This paper points out that the proofs about Mather's theorems I and Ⅱ in [1] are wrong, and then presents an counter-example to show that the corollary and conjecture are false. 相似文献