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1.
实Grassmann流形上的道路空间   总被引:1,自引:0,他引:1  
贺龙光  邱超捷 《数学学报》1995,38(1):127-133
G(n,m)表示R ̄n+m中全体n维子空间所构成的实Grassmann流形。本文首先找到p,q∈G(n,m)沿任何测地线均不共轭的充要条件,因此连接这样两点的测地线有可数条。通过计算得到编号为(k_1,k_2,…,k_n)的测地线指标λ(k_1,k_2…,k_n).最后根据Morse基本定理得到:设p,q是G(n,m),上沿任何测地线均不共轭的两点,则连接p,q的分段光滑道路空间同伦于一可数CW-复形,该复形中的胞腔可编号为(k_1,k_2,…,k_n),k_i为整数,且编号为(k_1,k_2,…,k_n的胞腔的维数为λ(k_1,k_2…,k_n)。  相似文献   

2.
不等式(2十a_1)·(2十a_2)…(2十a_n)≥3 ̄n的推广063602河北乐亭县新寨中学于永平有这样一道数学竞赛题:已知。1,。2,”””,。。是n个正数,满足。1。2…q=1,求证(2十证明(当且仅当al—aZ=…一a。=l时“一”号成立)...  相似文献   

3.
用P_n表示有n个顶点的路。本文证明了,如果q>5是素数,则P_(q-1)的补图是色唯一的。  相似文献   

4.
龙顺潮  王键 《数学杂志》1998,18(3):349-354
本文证明了具有某种尺寸条件的L^q1到L^q2有界的分数次次线性算子是Kq1^a,p(ω1,ω2^q1)(或Kq1^q,p)(ω1,ω2^q1)到Kq2^a,p(ω1,ω2^q2)(或Kq2^a,p(ω1,ω2^q2)有界的以及HKq1^ap(ω1,ω2^q1)(或HKq1^ap(ω1,ω2^q1)到Kq2^ap(ω1,ω2^q2)(或Kq2^ap(ω1,ω2^q2)有界的。  相似文献   

5.
本文将Besov空间B_P~S,q推广为精细Besov空间RB_P~a,q,其中s∈R,而a∈R~(k+1),k为非负整数.给出了精细Besov空间的等价拟范数和嵌入定理.同时证明了在B_P~S,q和 UB_p~t,q之间还存在无穷多个精细Besov空间作为真子空间.  相似文献   

6.
关于三角形区域的Heilbronn数   总被引:5,自引:0,他引:5  
杨路  张景中  曾振柄 《数学学报》1994,37(5):678-689
设K是一个具有面积|K|的平面凸体。用(r_1r_2r_3)表示三角形r_1r_2r_3的面积,并令然后将K中n个点的Heilbronn数定义为对于三角形区域Δ,我们证明了  相似文献   

7.
考虑具有n个变时滞的泛函微分方程其中q_i(t),T_i(t)∈C([0,+∞),R ̄+),i=1,2,…,n。本文证明了Hunt-Yorke猜想;同时还得到了在Kwong-Patula意义下泛函微分方程强振动的充分条件。  相似文献   

8.
CH~2中的曲面 M称为(局部)齐性的,如果对任何一对点 p,q,存在变换。 σ U(1,2)把含p的一个邻域变为含q的邻域,且把q变为q.本文给出CH2中齐性曲面的完全分类.  相似文献   

9.
数列(p_1/(n+p_2))~(q_1n+q_2)单调性梁长林(华东地质学院)我们可以求出,极限,其中p1,p2,q1,q2为常数,下面讨论xn的单调性,因为xn与Inxn有相同的单调性,所以考虑函数单调性设x充分大,当P1〔2q2—2p2q1—P1q?..  相似文献   

10.
杨群峰  邓明华 《数学进展》1995,24(6):532-539
利用量子对称群的概念,我们给出U_q(sl_n)-多项式、U_q(sl_n)-外积的定义,说明U_q(sl_n)的q-振子、q-旋量表示不过是U_q(sl_n)标准表示的量子对称、量子反称张量积,这和经典情形是一致的。  相似文献   

11.
12.
Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.  相似文献   

13.
We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.  相似文献   

14.
张丽娜  吴建华 《数学进展》2008,37(1):115-117
One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the'living world. In his seminal paper "The Chemical Basis of Morphogenesis", Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates(1990) on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing's prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows  相似文献   

15.
In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).  相似文献   

16.
It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.  相似文献   

17.
18.
正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with  相似文献   

19.
正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.  相似文献   

20.
A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].  相似文献   

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