共查询到20条相似文献,搜索用时 93 毫秒
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本文构造了一个 n元实函数 f ( x1,… ,xn) ,这个函数定义在整个 n维空间 Rn。除了在任意指定的 m个点 P1,P2 ,… ,Pm 处连续且可微外 ,在其它点上皆不可微、皆不连续。不妨设 Pi 点的坐标为 ( ai1,… ,ain) ( i=1 ,… ,m)。定义 Rn上的实函数f ( x1,… ,xn) =D( x1,… ,xn) mi=1[ nj=1( xj-aij) 2 ]其中 D ( x1,… ,xn) =1 当 x1,… ,xn 全为有理数0 其它 ,则有如下命题命题 1 :f ( x1,… ,xn)仅在 P1,P2 ,… ,Pm 点连续。证明 :先证明 f ( x1,… ,xn)在 Pi 点连续。显然 f ( Pi) =0 ( i=1 ,… ,m)。当 P( x1,… ,xn)→ Pi 有 li… 相似文献
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马立志 《纯粹数学与应用数学》1990,6(1):4-10
1.引言设f(z)为一超越整函数,考虑由这个函数经过逐次迭代所得到的函数:这个函数序列构成一个函数族。我们记J(f)为这个函数族的非正规点集。这个点集与f的各阶不动点有密切关系,因而引起了关于这个点集的一些研究工作。在这方面, 相似文献
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本文首先对紧致的度量拓扑空间证明了有限点集的费马点是存在的,其次,运用度量几何的经典方法考察了度量空间(包括双曲空间和Banach空间)中有限点集的费马点的唯一性,此外,还对n维欧氏空间E^n中有限点集的费马作了进一步研究。 相似文献
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本文研究了具有公共实零点与实1点的整函数的唯一性问题。例子证实了Gzubiak和Gundersen1981年的一个结果是不正确的。本文纠正了Czubiak和Gundersen的这个结果。 相似文献
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Schumaker,L.L.在其名著《Spline Function;Basic Theory》中第九章给出了Tchebysheff样条函数空间的局部支集基定理,可惜其证明却是错的,本文给出了上述定理的正确证明。 相似文献
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连续树映射非游荡集的拓扑结构 总被引:10,自引:0,他引:10
顾荣宝 《数学年刊A辑(中文版)》1998,(5)
本文研究树(即不含有圈的一维紧致连通的分支流形)上连续自映射的非游荡集的拓扑结构.证明了孤立的周期点都是孤立的非游荡点;具有无限轨道的非游荡点集的聚点都是周期点集的二阶聚点,以及ω-极限集的导集等于周期点集的导集和非游荡集的二阶导集等于周期点集的二阶导集. 相似文献
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In this paper,we concerned with the problem of the unicity of meromorphic functions and its derivatives covering certain finite sets at the same points and obtain some results that are extensions of that of K.Tohge and Yi Hongxun etc., 相似文献
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本文讨论了实Banach*代数的Jordan结构.主要结果:第一部分指出映射到 *-半单实Banach*代数上的Jordan*同态是连续的,且其核空间是闭*理想;由映射到交换实Banach*代数上的Jordan*同态诱导的因子代数也是交换的.第二部分介绍了两个不同的锥,并讨论了他们间的关系.另外,我们得到了关于实Banach*代数*- 根基的一个新的刻画.本文是Satish Shirali的工作的实化. 相似文献
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A. I. Shtern 《Functional Analysis and Its Applications》2001,35(4):294-304
With the help of some structure results for locally compact groups, the second real continuous bounded cohomology group of a connected locally compact group is described and it is proved that the corresponding group is finite-dimensional for any almost connected locally compact group. 相似文献
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Paolo Albano 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(2):273-281
In an open bounded set Ω, we consider the distance function from ∂Ω associated to a Riemannian metric with C
1,1 coefficients. Assuming that Ω is convex near a boundary point x
0, we show that the distance function is differentiable at x
0 if and only if there exists the tangent space to ∂Ω at x
0. Furthermore, if the distance function is not differentiable at x
0 then there exists a Lipschitz continuous curve, with initial point at x
0, such that the distance function is not differentiable along such a curve.
相似文献
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Laurentiu Paunescu 《Mathematische Nachrichten》1995,174(1):265-272
We describe the connection between the Milnor fibre of a holomorphic function and the Milnor fibre of its real part and we derive some simple equations for manifolds appearing as real links of real parts of holomorphic functions. 相似文献
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The paper is devoted to a special class of real polynomials, so-called T-polynomials, which arise in the combinatorial version of the Viro theorem. We study the relation between the numbers of real critical points of a given index of a T-polynomial and the combinatorics of lattice triangulations of Newton polytopes. We obtain upper bounds for the numbers of extrema and saddles of generic T-polynomials of a given degree in three variables, and derive from them upper bounds for Betti numbers of real algebraic surfaces in
defined by T-polynomials. The latter upper bounds are stronger than the known upper bounds for arbitrary real algebraic surfaces in
. Another result is the existence of an asymptotically maximal family of real polynomials of degree min three variables with 31m
3/36 + O(m
2) saddle points. 相似文献
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Journal of Fourier Analysis and Applications - Suppose $$\Omega , A \subseteq \mathbb {R}\backslash {\left\{ {0}\right\} }$$ are two sets, both of mixed sign, that $$\Omega $$ is Lebesgue... 相似文献
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基于一维随机变量,通过阐释概率分布实函数实现的内在本质,给出了概率分布实函数实现的一个充分必要条件,得到分布函数族及其连续性特征,揭示出概率论中分布函数定义所蕴含的合理性和深刻性. 相似文献
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Mathematical Notes - 相似文献
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《代数通讯》2013,41(9):4255-4266
Abstract Given a real analytic function f(x, y) with one critical point P 0, we study deformations f t of fsuch that, for any t ≠ 0, the analytic function f t has no critical points in a neighborhood of P 0. We give explicitly a deformation without real critical points for any function which has only one real branch with characteristic exponents (4, 2q, r). 相似文献