共查询到20条相似文献,搜索用时 38 毫秒
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<正> 引言 关于复合形或更一般的空間在欧氏空間中的实現問題,Whitney和Thom分別有下面的結果: 定理.(Whitney)n維紧致微分流形M~n可微分实現于R~N中的必要条件为 W~k(M~n)=0,k≥N-n.(1) 定理.(Thom)一个有可数基而局部可縮的紧致Hausdorff空間X可以拓扑实現 相似文献
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V. I. Berdyshev 《Mathematical Notes》1974,16(3):888-893
The modulus of continuity of the operator of best approximation on a subspace tends towards zero uniformly on the class of all subspaces of an n-dimensional space only if the unit ball of the space contains no extremal subsets of dimensionality k (0 < k < n-1).Translated from Matematicheskie Zametki, Vol. 16, No. 3, pp. 501–511, September, 1974. 相似文献
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Michael Grüter 《manuscripta mathematica》1987,58(3):295-343
We consider the problem to minimize n-dimensional area among currents T whose boundary (or part of it) is supposed to lie in a given hypersurface S of n+1. We prove dim (sing T)n-7. Thus, optimal regularity is obtained as shown by an example. 相似文献
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Tim N.T. Goodman 《Constructive Approximation》2007,25(3):279-301
We construct local generators, comprising r functions, for refinable spaces of bivariate Cn-1 spline functions of degree n on meshes comprising all lines through points of the integer lattice in the directions of n
+ r + 1 pairwise linearly independent vectors with integer components. The generators are characterised by their Fourier transforms.
Their shifts are shown to form a Riesz basis if and only if at most r lines in the mesh intersect other than in the integer
lattice, which can occur for n ≤ 2r - 1. The symmetry of these generators is studied and examples are given. 相似文献
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Let (l) and n be positive integers such that l ≥ n,and let Gn,l be the Grassmannian which consists of the set of n-dimensional subspaces of Cl.There is a Z-graded algebra isomorphism between the cohomology H*(Gn,l,Z) of Gn,l and a nat-ural Z-form B of the Z-graded basic algebra of the type A cyclotomic nilHecke algebra(H)(0) =<ψ1,… ψn-1,y1,…,yn>.We show that the isomorphism can be chosen such that the image of each (geometrically defined) Schubert class (a1,...,an) coincides with the basis element bλ constructed by Hu and Liang by purely algebraic method,where 0 ≤ a1 ≤ a2 ≤ … ≤ an ≤ l-n with ai ∈ Z for each i,and λ is the l-multipartition of n associated to (l + 1-(an + n),l + 1-(an-1 + n-1),...,l + 1-(a1 + 1)).A similar correspondence between the Schubert class basis of the cohomology of the Grassmanni-an Gl-n,l and the bλ's basis (λ is an l-multipartition of n with each component being either (1) or empty) of the natural Z-form B of the Z-graded basic algebra of (H)(0)l,n is also obtained.As an application,we obtain a second version of the Giambelli formula for Schubert classes. 相似文献
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C. Thas 《Journal of Geometry》1980,14(2):143-150
In this paper we prove a theorem about the reduction of the codimension of n-dimensional submanifolds of a space form Rm(k), with an (n-1)-dimensional asymptotic distribution and with 1-asymptotic lines (i.e. asymptotic curves for which the (1+1)-dimensional osculating spaces are subspaces of the tangent spaces). We also give a result for (n–1)-asymptotic lines in connection with Enneper's formula. Finally we construct an example.Dedicated to Prof.dr.J.Bilo on his 65th birthday 相似文献
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在另一文中,我们讨论了由全体2维實向量所成的有序环,在该文最後並说當维数n>2时(n为有限)也可类似地作初步讨论.为了显示这种向量环的用途,我们考虑用向量环来表现一般有序环的问题.在本文中我们证明:任一“n级的”(见以下定义)有序环都能与一个由若干n维實向量所组成的有序环同构.(主要在於证出关於n级有序加羣的类似结果.)我们希望有较好的结果,即:任一n级有序环都能与由全体n维實向量所成的一个有序环的一个子环同构,但未能证明或否定. 相似文献
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设Fq(n)是Fq上的n维正交空间,设P是任一个给定的m维全奇异子空间.计算了F(qn)中满足dim(P∩Q)=i的r维全奇异子空间Q的个数,给出了用子空间构作认证码的例子. 相似文献
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设Fq2(n)是 Fq2上的 n 维行向量空间, Un( Fq2)是 Fq2上的 n 阶酉群. 设M(m, r; n)是Un(Fq2}作用下的一个子空间轨道, L(m, r; n)是 M (m, r; n)中子空间的和生成的集合.该文讨论了各个轨道生成的集合L(m, r; n)之间的包含关系, 给出了一个子空间是属于给定的由M(m, r; n)生成的集合L(m, r, n)中的一个元素的条件, 以及L}(m, r; n)做成几何格的条件. 相似文献
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Liang Zhao 《偏微分方程(英文版)》2012,25(1):90-102
We establish sufficient conditions under which the quasilinear equation $$-div(|∇u|^{n-2}∇u)+V(x)|u|^{n-2}u=\frac{f(x,u)}{|x|^β}+εh(x) in \mathbb{R}^n,$$ has at least two nontrivial weak solutions in $W^{1,n} (\mathbb{R}^n)$ when ε > 0 is small enough, 0≤β < n, V is a continuous potential, f(x,u) behaves like $exp{γ|u|^{n/(n-1)}}$ as $|u|→∞$ for some γ > 0 and h≢ 0 belongs to the dual space of $W^{1,n} (\mathbb{R}^n)$. 相似文献
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複合形在歐氏空間中的實現問题Ⅰ 总被引:2,自引:0,他引:2
<正> 在拓撲發展之初很早就知道一個抽象的n維單純複合形(有限或無限)必可在2n+1維歐氏空間及R~(2n+1)中得到實現,它的證明也很簡單(例如見[1]§2或[2]第Ⅲ章§2).從這一定理知道2n+1維的歐氏空間實際上已包括了所有想像得到的n維複合形,可是是否有不能在R~m中實現但能在R~(m+1)中實現的 相似文献
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DING QING 《数学年刊B辑(英文版)》1994,(1)
A NEW LAPLACIAN COMPRISON THEOREM AND THE ESTIMATE OF EIGENVALUES ¥DINGQINGAbstract:ThispaperestablishesanewLaplaciancomparis... 相似文献
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<正> 球上同倫羣的研究,是近代拓撲學中一種最重要的工作,三、四年來,這工作發展得尤其迅速,但是像同緯映像術E:π_q(S~n)→π_(q+1)(S~(n+1))這樣,雖然是很重要的一種工具,而E的像和E的核,除有限種情况外,長久沒有一種表示 相似文献
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P. V. Ceccherini 《Journal of Geometry》1984,22(1):57-74
Summary We give an arithmetical characterization of graphs which are realizable as graphs of the lattice of the subspaces of a graphic (or projective) space of finite dimension and of finite order q 1. In other words is any complemented modular lattice of finite rank and of finite order q. When q 2 and the rank is at least four, is the lattice of the subspaces of a finite dimensional vector space over the field GF(q). Two independent axioms are required involving the number of geodesies between any two vertices. This number must be a simple function of the distance.Our characterization may be consider as a q-analogous of the characterization of hypercubes, given by S.Foldes [6], obtained here for q=1 in a slightly different form.After the formulation of the two axioms (n.1) and some recalls on graphic spaces and on projective spaces (n.2), we study the graph of their subspaces establishing the necessity of the axioms (n.3). The sufficiency and the independence of the axioms are obtained in n.4.Dedicated to Professor Adriano Barlotti on the occasion of his 60-th birthday.Work partially supported by GNSAGA (Section 4) of the Italian CNR. Communicated at University of Bordeaux (June 1982) and at Oberwolfach (Gründlagen der Geometrie, October 1982). 相似文献
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分数次积分在局部Hardy空间上的有界性质 总被引:1,自引:1,他引:0
证明了当0<αn/(n-α)时,分数次积分Iα是局部Hardy空间hp(Rn)到空间hp(Rn)+Lq(Rn)的一个线性映射. 相似文献
19.
The present paper is a continuation of the authors' work [1]. As in [1], we consider a sample from a general collection with distribution density f(x– ) depending on the shift parameter . In contrast to [1] it is assumed that the function f(x) is unbounded in a neighborhood of points x1,h., xN where it can be represented in the form (1.1). The main results assert that for the Bayes estimates tn the normalized differences n1/(1+)(tn–) have a proper limit distribution.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 55, pp. 175–184, 1976. 相似文献
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