共查询到20条相似文献,搜索用时 420 毫秒
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本文主要讨论单个函数平移和伸缩的线性组合对Lp(Rn)中任一紧集内函数的逼近.给出一个很强的逼近结果.这在神经网络应用研究中具有重要意义. 相似文献
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文[1]证明了定义在有界闭集上的函数K<1集压缩映象是紧压缩映象,本文主要对定义在有界开集的闭包上的函数K<1集压缩映象场的拓扑度数的性质进行讨论. 相似文献
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Let X be a C~(1+) vector field on a compact Riemannian manifold M with dimension d ≥ 3.Let Λ be a transitive singular hypebolic set with positive volume. We show that Λ = M and Λ is a uniformly hyperbolic set without singularities. 相似文献
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不动点集为RP(2)∪L~1(p)的对合 总被引:2,自引:2,他引:0
(M3+ k,T)是在光滑闭流形上的一个非平凡光滑对合 ,它的不动点集为 RP(2 )∪ L 1 (p ) .本文给出了带对合的流形 (M3+ k,T)的协边类 相似文献
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SUBMANIFOLDS OF A HIGHER DIMENSIONAL SPHERE 总被引:1,自引:1,他引:0
Huang Xuanguo 《数学年刊B辑(英文版)》1983,4(1):33-40
Let M be an m-dimensional manifold immersed in S~(m+k)(r).Then △X=μH-(m/r~2)X,where X is the position vector of M and H is a unit normal vector field which is orthogonalto X everywhere.If M is a compact connected manifold with parallel mean curvature vector field ξimmersed inS~(m+k)(r),and the sectional curvature of M is not less than (1/2)((1/r~2)+|ξ|~2),thenM is a small sphere.For a compact connected hypersurface M in S~(m+1)(r),if the sectional curvature is non-nesative and the scalar curvature is proportional to the mean curvature everywhere,then M isa totally umbilical hypersurface or the multiplication of two totally umbilical submanifolds. 相似文献
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In this article, we prove the following results: (1) A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; (2) A Banach space X is midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively compact k-Chebyshev set. 相似文献
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本文研究了Kolmogorov-Tamarkin的紧性问题.利用鞅收敛定理,获得了任意测度空间上的Lp空间中紧集的判别准则,推广了Lp(Rd,dx)集合为紧集的Kolmogorv-Tamarkin准则. 相似文献
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E. V. Oshman 《Mathematical Notes》1976,19(4):324-328
The closed subspaces of finite codimension of the space C(X) of all continuous real-valued functions on a compact Hausdorff space X, for which the set of elements of best approximations of every function f C(X) is nonempty and compact, are characterized. It is shown that if the compact Hausdorff space X is infinite, then C(X) has no subspace of a finite Codimension n > 1 which has a nonempty set of elements of the best approximation for an arbitrary function f 6 (X) and which has an upper-semicontinuous metric projection.Translated from Matematicheskie Zametki, Vol. 19, No. 4, pp. 531–539, April, 1976. 相似文献
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设M是二维紧致、曲率K(M)≤0的Riemann流形.对任一x M,在M上类数≥3的点集非空且只有有限个点{α1,α2,…;αd}.用Kj表示αj的类数,即αj到x的最短测地线的条数.那么,M的Euler数X(M)可以表示为:X(M)=(d+1)=Kj.如果M上类数23的点只有一个,那么这个点是M上距离x最远的点. 相似文献
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F. Tardella 《Journal of Optimization Theory and Applications》1989,60(1):105-116
We study some topological properties of the vector sum of two sets, and we introduce the concept of strong cone compactness, a slightly strengthened version of the notion of cone compactness, which is used frequently in vector optimization. Furthermore, we establish a generalization of the well-known fact that the continuous image of a compact set is compact. 相似文献
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On Initial-boundary-value Problems for a Class of Systems of Quasi-linear Evolution Equations 下载免费PDF全文
Cheng Yan 《偏微分方程(英文版)》1994,7(4)
In this paper the initial-boundary-value problems for pseudo-hyperbolic system of quasi-linear equations: {(-1)^Mu_{tt} + A(x, t, U, V)u_x^{2M}_{tt} = B(x, t, U, V)u_x^{2M}_{t} + C(x, t, U, V)u_x^{2M} + f(x, t, U, V) u_x^k(0,t) = ψ_{0k}(t), \quad u_x^k(l,t) = ψ_{lk}(t), \quad k = 0,1,…,M - 1 -u(x,0) = φ_0(x), \quad u_t(x,0) = φ_1(x) is studied, where U = (u_1, u_x,…,u_x^{2M - 1}) V = (u_t, u_{xt},…,u_x^{2M - 1_t}), A, B, C are m × m matrices, u, f, ψ_{0k}, ψ_{1k}, ψ_0, ψ_1 are m-dimensional vector functions. The existence and uniqueness of the generalized solution (in H² (0, T; H^{2M} (0, 1))) of the problems are proved. 相似文献
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Marilyn Breen 《Journal of Geometry》1986,27(2):175-179
We will establish the following improved Krasnosel'skii theorems for the dimension of the kernel of a starshaped set: For each k and d, 0 k d, define f(d,k) = d+1 if k = 0 and f(d,k) = max{d+1,2d–2k+2} if 1 k d.Theorem 1. Let S be a compact, connected, locally starshaped set in Rd, S not convex. Then for a k with 0 k d, dim ker S k if and only if every f(d, k) lnc points of S are clearly visible from a common k-dimensional subset of S.Theorem 2. Let S be a nonempty compact set in Rd. Then for a k with 0 k d, dim ker S k if and only if every f (d, k) boundary points of S are clearly visible from a common k-dimensional subset of S. In each case, the number f(d, k) is best possible for every d and k. 相似文献