广义Bernoulli数和广义高阶Bernoulli数

定义了广义Bernoulli数和广义高阶Bernoulli数，建立了它们的递推公式和有关性质，从而推广了Bernoulli数和高阶Bernoulli数。     

丛上的相交数与Euler数

本文主要研究了带边流形上丛截面的相交数．应用作倍流形上的向量场的延拓，我们得到了带边流形上的Euler数用相交数的表示．     

Euler数，Bernoulli数及有序Bell数的渐近估计

利用特殊函数的发生函数为亚纯函数的特点,给出Euler数、Bernoulli数、有序Bell数等几个组合数的带有余项的渐进估计．     

涉及Euler数,Bernoulli数和推广的第一类Stirling数…

利用递推关系把文［１］、［２］中的有关结论推广到一般情形，建立起涉及Ｅｕｌｅｒ数、Ｂｅｒｎｏｕｌｌｉ数和推广的第一类Ｓｔｉｒｌｉｎｇ数的一些恒等式。     

Mersenne数$M_p$都是孤立数

设p是素数,M_P=2~P-1.本文证明了M_P都是孤立数.     

高阶Bernoulli数与Stirling数的几个恒等式

利用第一、二类高阶Bernoulli数和二类Stirling数S1(n,k),S2(n,k)的定义.研究了二类高阶Bernoulli数母函数的幂级数展开,揭示了二类高阶Bernoulli数之间以及与第一类Stirling数S1(n,k)、第二类Stirling数S2(n,k)之间的内在联系,得到了几个关于二类高阶Bernoulli数和第一类Stirling数S1(n,k)、第二类Stirling数S2(n,k)之间有趣的恒等式.     

Euler数与Bernoulli数的一些恒等式

本文的主要目的是利用初等方法给出Ｅｕｌｅｒ数与Ｂｅｒｎｏｕｌｌｉ数的一些有关恒等式。     

独立数的另一类关系

本文研究了图的独立数与边独立数、独立数与全独立数、边独立数与全独立数、图的独立数与其补图边独立数、图的独立数与其补图的全独立数、图的边独立数与其补图全独立数之间的关系,得到了不可改进的结果     

数一数水

正小矮人在数豆子。他边数边苦恼地说:"像这样数下去,一年也数不完啊!"多到像这堆豆子一样的东西,该怎么数清楚呢?盐和砂糖一看就知道很难数清楚。水的话,更是连抓都抓不起来。那么,盐和水就真的没有办法数了吗?像这样把盐或水放进容器里,就可以进行比较,从而知道哪个更多了。     

我国数感研究进展

本文整理了自2001年《全日制义务教育数学课程标准实验稿》颁布以来我国在数感方向的研究成果,包括数感的定义,学生关于数感的形成,我国学生对数感内涵掌控的情况,以及学生数感发展与问题解决、课堂教学实践的联系,介绍了数感跨文化研究和国际比较研究。     

The incompatibility of crossing number and bridge number for knot diagrams

We study methods for computing the bridge number of a knot from a knot diagram. We prove equivalence between a geometric and a combinatorial definition of the bridge number of a knot diagram. For each notion of diagrammatic bridge number considered, we find crossing number minimizing knot diagrams which fail to minimize bridge number. Furthermore, we construct a family of minimal crossing diagrams for which the difference between diagrammatic bridge number and the actual bridge number of the knot grows to infinity.     

Relation between the correspondence chromatic number and the Alon–Tarsi number

We study the relation between the correspondence chromatic number, also known as the DP-chromatic number, and the Alon–Tarsi number, both upper bounds on the list chromatic number of a graph. There are many graphs with Alon–Tarsi number greater than the correspondence chromatic number. We present here a family of graphs with arbitrary Alon–Tarsi number, with correspondence chromatic number one larger.     

The ratio of the irredundance number and the domination number for block-cactus graphs

Let γ(G) and ir(G) denote the domination number and the irredundance number of a graph G, respectively. Allan and Laskar [Proc. 9th Southeast Conf. on Combin., Graph Theory & Comp. (1978) 43–56] and Bollobás and Cockayne [J. Graph Theory (1979) 241–249] proved independently that γ(G) < 2ir(G) for any graph G. For a tree T, Damaschke [Discrete Math. (1991) 101–104] obtained the sharper estimation 2γ(T) < 3ir(T). Extending Damaschke's result, Volkmann [Discrete Math. (1998) 221–228] proved that 2γ(G) ≤ 3ir(G) for any block graph G and for any graph G with cyclomatic number μ(G) ≤ 2. Volkmann also conjectured that 5γ(G) < 8ir(G) for any cactus graph. In this article we show that if G is a block-cactus graph having π(G) induced cycles of length 2 (mod 4), then γ(G)(5π(G) + 4) ≤ ir(G)(8π(G) + 6). This result implies the inequality 5γ(G) < 8ir(G) for a block-cactus graph G, thus proving the above conjecture. © 1998 John Wiley & Sons, Inc. J. Graph Theory 29: 139–149, 1998     

On the edge-binding number of some plane graphs

1. IntroductionSince WOodall gave out the concept of biIldi11g Ilu1lJber in 1973[l] ! the bil1ding nunlber fOrsome specia1 classes have beeIl studied by Kane and WaIlg Jianfang[']. Mirolawa Skowronskahave studied the binding number of Halin-graph[']. ZI1ang Zhongfu, Liu Li1lzhong andZhang Jianxun have extended the bil1di11g nuInber to the edges and studied tlle edge-bindingnumber of path, cycle, coInplete grapl1. I1l this paper, we study the edge-binding number ofouter plane graph, Ha…     

A note on the disconnection number

We present a simple way to obtain all graphs with a given disconnection number if we know all the graphs with smaller disconnection number. Using this method we answer a question of Sam B. Nadler, i.e. we prove that there exist precisely 26 continua with disconnection number four. Some known results concerning disconnection number are also obtained as simple corollaries. Further we give some estimates on the number of distinct continua with a fixed disconnection number which concerns a problem of Sam B. Nadler.     

Some results on the achromatic number

Let G be a simple graph. The achromatic number ψ(G) is the largest number of colors possible in a proper vertex coloring of G in which each pair of colors is adjacent somewhere in G. For any positive integer m, let q(m) be the largest integer k such that ≤ m. We show that the problem of determining the achromatic number of a tree is NP-hard. We further prove that almost all trees T satisfy ψ (T) = q(m), where m is the number of edges in T. Lastly, for fixed d and ϵ > 0, we show that there is an integer N₀ = N₀(d, ϵ) such that if G is a graph with maximum degree at most d, and m ≥ N₀ edges, then (1 - ϵ)q(m) ≤ ψ (G) ≤ q(m). © 1997 John Wiley & Sons, Inc. J Graph Theory 26: 129–136, 1997     

Metric properties of the nearest extended parametric fuzzy number and applications

We propose the notion of extended parametric fuzzy number, which generalizes the extended trapezoidal fuzzy number and parametric fuzzy number, discussed in some recent papers. The metric properties of the nearest extended parametric fuzzy number of a fuzzy number, proved in the present article, help us to obtain the property of continuity for the parametric approximation operator and to simplify the solving of the problems of parametric approximations under conditions.     

树的3-彩虹控制数的上界

对树的3-彩虹控制数进行研究,首先用构造法找到直径较小的树的3-彩虹控制数的上界.再通过分类讨论思想和数学归纳法得到一般的阶n大于等于5的树的3-彩虹控制数的上界.     

On the b-chromatic number of Kneser graphs

In this note, we prove that for any integer n≥3 the b-chromatic number of the Kneser graph KG(m,n) is greater than or equal to . This gives an affirmative answer to a conjecture of [6].     

On the complexity of the circular chromatic number

Circular chromatic number, χ_c is a natural generalization of chromatic number. It is known that it is NP ‐hard to determine whether or not an arbitrary graph G satisfies χ(G)=χ_c(G). In this paper we prove that this problem is NP ‐hard even if the chromatic number of the graph is known. This answers a question of Xuding Zhu. Also we prove that for all positive integers k ≥ 2 and n ≥ 3, for a given graph G with χ(G) = n, it is NP ‐complete to verify if . © 2004 Wiley Periodicals, Inc. J Graph Theory 47: 226–230, 2004