A cycle C of a graph G is a m-distance-dominating cycle if for all vertices of . Defining denotes the minimum value of the degree sum of any k independent vertices of G. In this paper, we prove that if G is a 3-connec...A cycle C of a graph G is a m-distance-dominating cycle if for all vertices of . Defining denotes the minimum value of the degree sum of any k independent vertices of G. In this paper, we prove that if G is a 3-connected graph on n vertices, and if , then every longest cycle is m-distance-dominating cycles.展开更多
不动点理论在研究方程解的存在性、唯一性及具体计算都有重要的理论与实用价值。本文基于巴拿赫度量空间中压缩映射原理通过两点之间距离的改变,借助于单调函数自映射原理在已有的结论基础上推广了度量空间上自映射的Pathak、Rekha Sha...不动点理论在研究方程解的存在性、唯一性及具体计算都有重要的理论与实用价值。本文基于巴拿赫度量空间中压缩映射原理通过两点之间距离的改变,借助于单调函数自映射原理在已有的结论基础上推广了度量空间上自映射的Pathak、Rekha Sharam、Khan、和Sastry and Babu函数和的一些不动点定理,并得出函数和唯一不动点定理。展开更多
Let Sigma (infinity)(n=1) X-n be a series of independent random variables with at least one non-degenerate X-n, and let F-n be the distribution function of its partial sums S-n = Sigma (n)(k=1) X-k. Motivated by Hilde...Let Sigma (infinity)(n=1) X-n be a series of independent random variables with at least one non-degenerate X-n, and let F-n be the distribution function of its partial sums S-n = Sigma (n)(k=1) X-k. Motivated by Hildebrand's work in [1], the authors investigate the a.s. convergence of Sigma (infinity)(n=1) X-n under a hypothesis that Sigma (infinity)(n=1) rho (X-n, c(n)) = infinity whener Sigma (infinity)(n=1) c(n) diverges, where the notation rho (X,c) denotes the Levy distance between the random variable X and the constant c. The principal result of this paper shows that the hypothesis is the condition under which the convergence of F-n(x(0)) with the limit value 0 < L-0 < 1, together with the essential convergence of Sigma (infinity)(n=1) X-n, is both sufficient and necessary in order for the series Sigma (infinity)(n=1) X-n to a.s. coverage. Moreover, if the essential convergence of Sigma (infinity)(n=1) X-n is strengthened to limsup(n=infinity) P(\S-n\ < K) = 1 for some K > 0, the hypothesis is already equivalent to the a.s. convergence of Sigma (infinity)(n=1) X-n. Here they have not only founded a very general limit theorem, but improved the related result in Hildebrand([1]) as well.展开更多
Let Mi be a compact orientable 3-manifold, and Ai a non-separating incompressible annulus on a component of δMi, say Fi, i = 1, 2. Let h ： A1 → A2 be a homeomorphism, and M→M1 ∪h M2, the annulus sum of Mi and M2 ...Let Mi be a compact orientable 3-manifold, and Ai a non-separating incompressible annulus on a component of δMi, say Fi, i = 1, 2. Let h ： A1 → A2 be a homeomorphism, and M→M1 ∪h M2, the annulus sum of Mi and M2 along A1 and A2. Suppose that Mi has a Heegaard splitting Vi ∪Si Wi with distance d（Si） ≥ 2g（Mi） ＋ 2g（F3-i） ＋ 1, i = 1, 2. Then g（M） = g（M1） ＋ g（M2）, and the minimal Heegaard splitting of M is unique, which is the natural Heegaard splitting of M induced from Vi∪S1 Wi and V2 ∪S2 W2.展开更多
文摘A cycle C of a graph G is a m-distance-dominating cycle if for all vertices of . Defining denotes the minimum value of the degree sum of any k independent vertices of G. In this paper, we prove that if G is a 3-connected graph on n vertices, and if , then every longest cycle is m-distance-dominating cycles.
文摘不动点理论在研究方程解的存在性、唯一性及具体计算都有重要的理论与实用价值。本文基于巴拿赫度量空间中压缩映射原理通过两点之间距离的改变,借助于单调函数自映射原理在已有的结论基础上推广了度量空间上自映射的Pathak、Rekha Sharam、Khan、和Sastry and Babu函数和的一些不动点定理,并得出函数和唯一不动点定理。
文摘Let Sigma (infinity)(n=1) X-n be a series of independent random variables with at least one non-degenerate X-n, and let F-n be the distribution function of its partial sums S-n = Sigma (n)(k=1) X-k. Motivated by Hildebrand's work in [1], the authors investigate the a.s. convergence of Sigma (infinity)(n=1) X-n under a hypothesis that Sigma (infinity)(n=1) rho (X-n, c(n)) = infinity whener Sigma (infinity)(n=1) c(n) diverges, where the notation rho (X,c) denotes the Levy distance between the random variable X and the constant c. The principal result of this paper shows that the hypothesis is the condition under which the convergence of F-n(x(0)) with the limit value 0 < L-0 < 1, together with the essential convergence of Sigma (infinity)(n=1) X-n, is both sufficient and necessary in order for the series Sigma (infinity)(n=1) X-n to a.s. coverage. Moreover, if the essential convergence of Sigma (infinity)(n=1) X-n is strengthened to limsup(n=infinity) P(\S-n\ < K) = 1 for some K > 0, the hypothesis is already equivalent to the a.s. convergence of Sigma (infinity)(n=1) X-n. Here they have not only founded a very general limit theorem, but improved the related result in Hildebrand([1]) as well.
文摘Let Mi be a compact orientable 3-manifold, and Ai a non-separating incompressible annulus on a component of δMi, say Fi, i = 1, 2. Let h ： A1 → A2 be a homeomorphism, and M→M1 ∪h M2, the annulus sum of Mi and M2 along A1 and A2. Suppose that Mi has a Heegaard splitting Vi ∪Si Wi with distance d（Si） ≥ 2g（Mi） ＋ 2g（F3-i） ＋ 1, i = 1, 2. Then g（M） = g（M1） ＋ g（M2）, and the minimal Heegaard splitting of M is unique, which is the natural Heegaard splitting of M induced from Vi∪S1 Wi and V2 ∪S2 W2.
