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ON k-DIAMETER OF k-CONNECTED GRAPHS

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Applied math.matics(A Journal of Chinese univ.rsities) 2001年第3期16卷 231-236页

作者： xu Junming xu Keli of math., univ. of Science and technology of China, Hefei 230026. Dept. of math. Univ. of Science and Technology of China Hefei

Let G be a k-connected simple graph with order n. The k-diameter, combining connectivity with diameter, of G is the minimum integer d k(G) for which between any two vertices in G there are at least k internally vertex-disjoint paths of length at most d k(G). For a fixed positive integer d, some conditions to insure d k(G)≤d are given in this paper. In particular, if d≥3 and the sum of degrees of any s (s =2 or 3) nonadjacent vertices is at least n+(s-1)k+1-d, then d k(G)≤d. Furthermore, these conditions are sharp and the upper bound d of k-diameter is best possible.

关键词： Diameter k-diameter connectivity independence number fault-tolerant networks.

A PARABOLIC EQUATION WITH HYSTERESIS

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Annals of Differential Equations 2004年第2期20卷 173-179页

作者：徐龙封 School of math.and phys.anhui univ.rsity of technology maanshan 243002

A parabolic equations with hysteresis is discussed. The existence of smoothstrong solution of one-dimension initial boundary problem of the equation isgiven.

关键词： parabolic equation hysteresis operator coercive strictly monotone

DIFFERENTIABILITY OF A CLASS OF HYSTERESIS FUNCTIONAL

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Annals of Differential Equations 2002年第1期18卷 72-80页

作者：徐龙封

In this paper, the differentiability of a class of hysteresis functional is discussed, and its expression formulas are given.

关键词： hysteresis functional g-path regular standing point weak convergence

SOME RESULTSON R_2-EDGE-CONNECTIVITY OF EVEN REGULAR GRAPHS

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Applied math.matics(A Journal of Chinese univ.rsities) 1999年第3期14卷 366-370页

作者： xu Junming Dept. of math., univ. ofScience and technology ofChina, Hefei230026.Em ail:xuJM@ *** Dept. of math. Univ. of Science and Technology of China Hefei

Let Gbe a connected k(≥3)-regulargraph w ith girth g. A setSofthe edgesin G is called an R2-edge-cutifG- Sis disconnected and contains neither an isolated vertex nor a one- degree vertex. The R2-edge-connectivity of G, denoted by λ″(G), is the m inim um cardinality over allR2-edge-cuts, w hich is an im portantm easure for fault-tolerance of com puter intercon- nection netw orks. In this paper, λ″(G)= g(2k- 2) for any 2k-regular connected graph G(≠ K5) that is either edge-transitive or vertex-transitive and g≥5 is given.

关键词： Connectivity conditionalconnectivity transitive graphs.

一种基于F-矩阵的最大频繁项目集快速挖掘算法

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计算机工程与应用 2003年第34期39卷 197-200页

作者：杨萍安徽工程科技学院数理系芜湖241000

最大频繁项目集挖掘是多种数据挖掘应用研究的一个重要方面,最大频繁项目集的快速挖掘算法研究是当前研究的热点。传统的最大频繁项目集挖掘算法要多遍扫描数据库并产生大量的候选项目集。为此,该文提出了基于F-矩阵的最大频繁项目集快... 详细信息

最大频繁项目集挖掘是多种数据挖掘应用研究的一个重要方面,最大频繁项目集的快速挖掘算法研究是当前研究的热点。传统的最大频繁项目集挖掘算法要多遍扫描数据库并产生大量的候选项目集。为此,该文提出了基于F-矩阵的最大频繁项目集快速挖掘算法FMMFIBFM,FMMFIBFM采用FP-tree的存储结构,仅须扫描数据库两遍且不产生候选频繁项目集,有效地提高了频繁项目集的挖掘效率。实验结果表明,FMMFIBFM算法是有效可行的。

关键词：数据挖掘频繁模式树频繁项目集关联规则最大频繁项目集

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Schrodinger算子的特征值之差

山东工业大学学报 1996年第4期26卷 418-424页

作者：程旭山东工业大学数理系

给出了紧Ｒｉｅｍａｎｎ流形上的Ｓｃｈｒｄｉｎｇｅｒ算子的第二、第一特征值之差的一个下界，这个下界仅依赖于流形的曲率、直径及势函数且易于验证．

关键词：微分算子特征值薛定谔算子黎曼流形

RIEMANN-HILBERT PROBLEMS OF DEGENERATE HYPERBOLIC SYSTEM

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Annals of Differential Equations 2010年第2期26卷 200-205页

作者： Zhongtai Ma, Guangshan xu (School of math., Shandong Institute of Business & technology, Yantai 264005, Shandong)

This paper is concerned with the Riemann-Hilbert problems of degenerate hyperbolic system in two general domains, where the boundary curves are given by the parameter equations of the arc length s. We prove the existence and uniqueness of solutions to the Riemann-Hilbert problems by conformal deformations. The corre-sponding representations of solutions to the problems are also presented.

关键词： Riemann-Hilbert problem degenerate hyperbolic system deforma-tion of hyperbolic domain uniqueness and existence

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独立数、连通度及r－消去图

山东工业大学学报 1995年第2期25卷 176-181页

作者：吴强山东工业大学数理系

改进了关于ｒ－因子的结果，给出了一个图是ｒ－消去图的充分条件．并且用例子说明此结果是最好的可能．结果如下：定理Ⅰ设ｒ≥１是奇数，Ｇ是一简单图，且Ｖ（Ｇ）为偶数，如果ｋ（Ｇ）＞（ｒ＋１）２／２，且（ｒ＋１）２α（Ｇ）＜... 详细信息

改进了关于ｒ－因子的结果，给出了一个图是ｒ－消去图的充分条件．并且用例子说明此结果是最好的可能．结果如下：定理Ⅰ设ｒ≥１是奇数，Ｇ是一简单图，且Ｖ（Ｇ）为偶数，如果ｋ（Ｇ）＞（ｒ＋１）２／２，且（ｒ＋１）２α（Ｇ）＜４ｒｘ（Ｇ），那么Ｇ为ｒ－消去图．定理Ⅱ设ｒ≥２为偶数，Ｇ是一简单图，如果ｋ（Ｇ）＞ｒ（＋２）／２，且（ｒ＋２）ａ（Ｇ）＜４ｋ（Ｇ），则Ｇ为ｒ－消去图．

关键词： r消去图图论独立数连通度

A new family of windows——convolution windows and their applications

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Science China(Technological Sciences) 2005年第4期48卷 468-480页

作者： ZHANG Jieqiu1,2, LIANG Changhong1 & CHEN Yanpu3 1. Department of Applied math. & phys., College of Science, Airforce Engineering univ.rsity, Xi’an 710051, China 2. National Key Laboratory of Antennas and Microwave technology, Xidian univ.rsity, Xi’an 710071, China 3. Computer Center, Xi’an Communication College, Xi’an 710106, China 1. Department of Applied math. & phys. College of Science Airforce Engineering University 710051 Xi’an China 2. National Key Laboratory of Antennas and Microwave technology Xidian University 710071 Xi’an China 3. Computer Center Xi’an Communication College 710106 Xi’an China

A new family of windows is constructed by convolutions via a few rectangular windows with same time width and is thus referred to as convolution windows. The expressions of the second-order up to the eighth-order convolution windows in both the time and frequency domains are derived. Their applications in high accuracy harmonic analysis of periodic signals are investigated. Comparisons between the proposed windows and some known windows with the same width shows that, when the synchronous deviation of data sampling is slight, the proposed ones have the least effect of spectral leakage. Therefore, the new windows are well suited for high accuracy harmonic analysis and parameter estimation for periodic signals. The error analysis and computer simulations show that the estimation errors, corresponding to frequency, amplitude and phase of every harmonic component of a signal, are proportional to the pth power of the relative frequency deviation in case of the pth-order convolution window is applied to windowing signal of approximately p cycles. By introducing real time adjustment in sampling interval, the proposed algorithm can adaptively trace signal frequency and lead to less sampling synchronous deviation. The proposed approach has the advantages of easy implementation and high measure precision and can be used in harmonic analysis of quasi-periodic signals whose fundamental frequency drifts slowly with time.

关键词： signal processing harmonic analysis window function convolution window synchronous error spoctral leakage