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设G是一个简单图,(?)e∈E(G),定义e=uv在G中的度d(e)=d(u)+d(v),其中d(u)和d(v)分别为u和v的度数。若连通图G的每个桥都有一个端点度数为1,则称G是几乎无桥的图。本文的主要结果是:设G是p≥2阶几乎无桥的简单连通图,且G≠K1,p-1若对任何无公共顶点的两边e0及e1,d(e0)+d(e1)≥p+4,则G有一个D-闭迹,从而G的线图L(G)是哈密顿的。 相似文献
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刘春峰 《纯粹数学与应用数学》1998,14(1):42-46
设G是一个简单图,L=u1u2…ut是G中的一个路,定义L的度d(L)=∑ti=1d(ui),其中d(ui)为ui在G中的度数.本文证明了:若G是n≥3阶几乎无桥的简单连通图,GK1,n-1,且对G中任何两个无公共点的二长路L1,L2,有d(L1)+d(L2)≥2n-1,则G有一个D-闭迹,从而G的线图L(G)是Hamilton图. 相似文献
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设G是无爪图.对x∈V(G),若G[N(x)]不连通,则存在yi∈V(G)-{x}(i-1,2),使|N(yi)∩Ki(x)|≥2,且|N(yi)∩N(Ki+1(x)){x}|≥2(i模2),那么称无爪图G是强2-阶邻域连通的,其中K1(x),K2(x)分别表示G[N(x)]的两个分支.本文证明了:连通且强2-阶邻域连通的无爪图是Hamilton图. 相似文献
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关于二部图K(m,n)-2的色唯一性 总被引:7,自引:0,他引:7
设K(m,n)-2表示从完全二部图K(m,n)中删去任意2条边所得之图.本文证明了:1.若n≥m≥3,且n+m>((n-m)2+8)1/2+1/2(n-m)2+4,则K(m,n)-2是色唯一图;2.当m≥3时,K(m,m)-2,K(m,m+1)-2和K(m,m+2)-2均是色唯一图. 相似文献
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本文讨论了积流形的P-形式上Laplace算子谱的唯一性问题,在紧Kachler流形乘积和紧Sasaki流形乘积的两类积流形中,CPn×CPn和S2n+1(1)×S2n+1(1)是P-形式上Laplacce算子谱特征。 相似文献
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本文给出了一个关于长圈和长路的新的充分条件.主要结果是:设在3-连通图G中,任一对距离为2的顶点u,v,都满足max{d(u),d(v)}≥m/2,那么d*(G)≥min{n-1,m-2}. 相似文献
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一个图G是泛圈的,如果它含有长为3,4,…,n(=|V(G)|)的圈.本文探讨了一类无爪Hamilton图的圈结构,主要结果为:设G=(V,E)是n阶无爪Hamilton图.如果G中有节点x使d(x)≧n/2且N(x)连通,则除少数几个例外,G是泛圈的. 相似文献
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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
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ZHENG ShiJun 《分析论及其应用》2004,20(3)
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
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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
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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
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Pankaj Mathur 《分析论及其应用》2006,22(2)
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
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《高校应用数学学报(英文版)》2014,29(4)
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
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《数学研究及应用》2014,(6)
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
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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