Binding Number and Fractional k-Factors of Graphs

In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It is proved that a graph G has a fractional 1-factor if bind(G)≥1and has a fractional k-factor if bind(G)≥k−1k. Furthermore, it is showed that both results are best possible in some sense.

MIMUMUM DEGREE AND BINDING NUMBER FOR k-FACTORS WITH PRESCRIBED PROPERTIES

Let integer k≥1, G be a graph of order n,n≥max {4k - 6, 4} and kn=0 (mod 2). Assume that the binding number of G is more than 2-2/n or the minimum degree of G is more than n/2. We prove that (i) G hasa k-fartor that contains a given edge; (ii) G has a k-factor that does not contain a given edge.

数据中心变压器K-factor工程计算方法简析

由K-factor的定义推导其计算公式,并介绍K-factor工程计算方法——采用分类叠加方法对谐波进行简化计算。结合数据中心工程实例给出计算结果并对其进行分析,提出相关注意点,并在此基础之上提出降低数据中心谐波对变压器影响的措施和建议。

Non-perturbative QCD Effect on K-Factor of Drell-Yan Process

By using a non-perturbative quark propagator with the lowest-dimensional condensate contributions from the QCD vacuum, the non-perturbative egect to K-factor of the Drell-Yan process is numerically investigated for 6^12C- 6^12C collision at the center-of-mass energy √s- 200 GeV, 630 GeV respectively. Calculated results show that the non-perturbative QCD effect has just a weak influence on K-factor in the two cases.

PROPERTIES OF FRACTIONAL k-FACTORS OF GRAPHS

In this paper the properties of some maximum fractional [0, k]-factors of graphs are presented. And consequently some results on fractional matchings and fractional 1-factors are generalized and a characterization of fractional k-factors is obtained.

k-Factors and Spanning Subgraph in Graphs

In this paper, we discussed k-factors and spanning subgraph, and propose a conjecture which will lead to a series of important conclusion.

有关K-factor变压器的浅析和探讨

在过去几十年中,随着我国电力电子技术的迅速发展,大量可控硅的整流设备,制钢用电弧炉,电网用变压器群,饱和电抗器,敏感电子器件,UPS系统等具有非线性阻抗特性的电气设备投入到基础工业部门。这些设备在电力系统中产生大量的谐波,导致系统波形畸变严重,对输配电网络,通信线路,电气设备等造成巨大影响,尤其对配电变压器损害更大。K-factor变压器就是可应用于这些非线性负载(non-liner loads)条件下的变压器。

The Refractive Effect of k-Factor on Radio Propagation over Lokoja, Nigeria

The effective earth radius factor(k-factor)has a refractive propagation effect on transmitted radio signals thus making its study necessary for the proper planning of terrestrial radio links and power budget.This study was carried out over the city of Lokoja,Nigeria,using ten years(2011 to 2020)atmospheric data of temperature,pressure and humidity both at the surface(12 m)and at 100 m AGL.The data were retrieved from European Centre for Medium-Range Weather Forecasts(ECMWF)ERA5.The k-factor yearly variation follows the same trend with minimum and maximum values obtained during dry and wet season months respectively.In addition,the highest mean value of 1.00042 was recorded in the month of August while the lowest value of 1.00040 was recorded in the month of January with an overall mean value of 1.0003.This value is less than the recommended standard of 1.33 by ITU-R.The propagation effect corresponding to k<1.33 is sub-refractive.The implication of this on radio wave propagation,especially terrestrial communications is that transmitted wireless signal is prone to losses.This can be mitigated through an effective power budget:Choice of transmitting antenna’s height and gain,so as to improve the Quality of Service over the study area.

Remarks on Fractional ID-k-factor-critical Graphs

Let G be a graph, and k a positive integer. A graph G is fractional independent-set-deletable k-factor-critical(in short, fractional ID-k-factor-critical) if G-I has a fractional k-factor for every independent set I of G. In this paper, we present a sufficient condition for a graph to be fractional ID-k-factor-critical,depending on the minimum degree and the neighborhoods of independent sets. Furthermore, it is shown that this result in this paper is best possible in some sense.

Neighborhood Conditions for Fractional ID-k-factor-critical Graphs

Let G be a graph and k≥2 a positive integer. Let h ： E（G）→[0, 1] be a function. If e∑eЭxh（e） = k holds for each x∈V（G）, then we call G[Fh ] a fractional k-factor of G with indicator function h where Fh ={e∈E（G） ： h（e） 〉 0}. A graph G is fractional independent-set-deletable k-factor-critical（in short, fractional ID-k-factor-critical）, if G-I has a fractional k-factor for every independent set I of G. In this paper, we prove that if n≥9 k-14 and for any subset X？V（G） we have NG（X） = V（G） if ｜X｜ ≥ kn/（3k-1）; or ｜NG（X）3 k-1/k｜ ≥｜X｜if｜X｜〈 kn/（3k-1）,then G is fractional ID-k-factor-critical.

EXISTENCE OF HAMILTONIAN k-FACTOR

A Hamiltonian k-factor is a k-factor containing aHamiltonian cycle.An n/2-critical graph G is a simple graph of order n which satisfies δ(G)≥n/2 and δ(G-e)<n/2 for any edge e∈E(G).Let k≥2 be an integer and G be an n/2-critical graph of even order n≥8k-14.It is shown in this paper that for any given Hamiltonian cycle C except that G-C consists of two components of odd orders when k is odd,G has a k-factor containing C.

K-Factors and Hamilton Cycles in Graphs

We discuss k-factors and Hamiltonian Graphs in graph theory. We prove a general version of the conjecture by R. Haggkvist; as a result, we prove two extended versions of two well-known theorems due to O. Ore and B. Jachson, respectively.

k-Factors in Regular Graphs

Plesnik in 1972 proved that an （m - 1）-edge connected m-regular graph of even order has a 1-factor containing any given edge and has another 1-factor excluding any given m - 1 edges. Alder et al. in 1999 showed that if G is a regular （2n ＋ 1）-edge-connected bipartite graph, then G has a 1-factor containing any given edge and excluding any given matching of size n. In this paper we obtain some sufficient conditions related to the edge-connectivity for an n-regular graph to have a k-factor containing a set of edges and （or） excluding a set of edges, where 1 ≤ k ≤n/2. In particular, we generalize Plesnik＇s result and the results obtained by Liu et al. in 1998, and improve Katerinis＇ result obtained 1993. Furthermore, we show that the results in this paper are the best possible.

Binding Numbers for Fractional ID-k-factor-critical Graphs

LetG be a graph,and k≥2 be a positive integer.A graph G is fractional independentset-deletable k-factor-critical（in short,fractional ID-k-factor-critical）,if G I has a fractional k-factor for every independent set I of G.The binding number bind（G）of a graph G is defined as bind（G）=min｜NG（X）｜｜X｜：=X V（G）,NG（X）=V（G）.In this paper,it is proved that a graph G is fractional ID-k-factor-critical if n≥6k 9 and bind（G）〉（3k 1）（n 1）kn 2k＋2.

基于2次全国制图的土壤可蚀性因子变化趋势

2011年第1次全国水利普查水土保持专项普查基于全国各省(区、市)土壤类型图和土种志剖面数据,制作首张全国土壤可蚀性因子分布图(简称2011版K值)。为了提高土壤侵蚀评价的准确性和可信度,2022年利用全国土系调查数据和随机森林制图方法对中国土壤可蚀性因子分布图进行更新(简称2022版K值)。以全国水蚀区2011版和2022版的土壤可蚀性因子(简称K值)为研究对象,分别在流域尺度和不同土壤类型下对K值大小及空间分布进行研究。结果表明:2022版全国平均K值(0.0298 t·hm^(2)·h/(MJ·mm·hm^(2)))略低于2011版K值(0.0323 t·hm^(2)·h/(MJ·mm·hm^(2))),说明全国水土流失治理发展状况有向好的趋势。其中栗钙土、暗棕壤、盐碱土等土壤类型K值的降低幅度最大,潮土、褐土、黄壤等土壤类型的K值则有所升高。K值降低主要与退耕还林、土壤改良等政策措施的出台和布设有关,升高则与集约化耕作及坡地侵蚀有关。该结果可为水土流失动态监测及治理成效评价提供科学依据。

一种融合节点变化信息的动态社区发现方法

动态社区发现旨在检测动态复杂网络中蕴含的社区结构,对于揭示网络的功能及演化模式具有重要研究价值.由于相邻时刻网络的社区结构具有平滑性,前一时刻网络的社区划分信息可以用于监督当前时刻网络的社区划分过程,但已有方法均难以有效提取这些信息来提高动态社区发现性能.针对该问题,提出一种融合节点变化信息的动态社区发现方法(Semi-supervised Nonnegative Matrix Factorization combining Node Change Information,NCI-SeNMF).NCI-SeNMF首先采用k-core分析方法提取前一时刻社区网络的degeneracy-core,并选取degeneracy-core中的节点构造社区隶属先验信息,然后对相邻时刻网络的节点局部拓扑结构变化程度进行量化,并将其用于进一步修正社区隶属先验信息,最后通过半监督非负矩阵分解模型集成社区隶属先验信息进行动态社区发现.在多个人工合成动态网络和真实世界动态网络上进行大量对比实验,结果表明,NCI-SeNMF比现有动态社区发现方法在主要评价指标上至少提升了4.8%.

结合精英初始化和K近邻的蛇优化算法

蛇优化算法(SO)是一种受自然界中蛇生存行为启发产生的元启发式优化算法。原始蛇优化算法存在收敛速度慢、易陷入局部最优的问题,因此提出了一种结合精英初始化和K近邻的改进蛇优化算法(elite initia-lization and K-nearest neighbors improved snake optimizer,EKISO)。首先,为了提高初始种群质量,在种群初始化阶段提出精英初始化的方法,根据种群精英个体产生优质初始种群个体;其次,通过振荡因子优化螺旋觅食策略扩大全局勘探阶段的搜索范围、提高算法的局部逃逸能力;最后,在局部开发阶段提出K近邻思想的位置更新方法,增强种群个体之间的信息交互能力,从而加快收敛速度、提高收敛精度。利用14个经典测试函数和4个CEC2017测试函数将该方法与其他7种优化算法进行对比,证明EKISO收敛速度更快、精度更高且不易陷入局部最优。为了进一步验证EKISO的实用性与可行性,将EKISO应用于压力容器设计问题中,通过实验对比分析可知,EKISO在处理实际优化问题上具有一定的优越性。

基于N-K模型的石化储罐事故风险耦合度分析

为预防石化储罐事故,通过收集212份石化储罐事故报告,将事故风险因素归纳为人为、设备、环境、管理4个类别,利用N-K模型分析事故风险因素之间的耦合作用,并运用N-K模型计算各种耦合模式下的风险耦合度,得出了石化储罐事故风险因素的耦合关系及耦合作用规律。结果表明,随着参与耦合的因素增多,风险耦合值总体呈现上升趋势;人为因素与其它因素耦合更容易导致事故;石化储罐区事故各风险因素之间的耦合作用程度相比其它行业更高。研究结果可为石化企业储罐事故管控提供依据和参考。

基于改进N-K模型的地铁盾构掘进安全风险耦合研究

为预防和控制地铁盾构掘进施工过程中的关键安全风险,并精准判断哪些风险耦合情境是导致事故发生的显著情境,提出改进N-K模型研究地铁盾构掘进安全风险耦合;综合运用文献研究、事故案例、专家访谈等方法,辨识地铁盾构掘进的关键安全风险因素;基于N-K模型提出新的地铁盾构掘进安全风险耦合评估模型,并选用安全事故案例验证该模型的适用性。结果表明:辨识得到地铁盾构掘进关键安全风险因素清单,包括4类一级风险因素,21个二级风险因素;地铁盾构掘进施工安全风险随着耦合因素种类的增加而变大,4因素风险耦合值最高,3因素风险耦合值次之,双因素风险耦合值最低,作业人员安全意识薄弱和机械故障参与作用的耦合情境更容易发生安全事故。

基于气候资源禀赋的TMY权重因子调整方法研究

提出一种基于气候资源禀赋的典型气象年(TMY)权重因子调整方法。在参数间相关分析的基础上,遴选干球温度、相对湿度、日照时数与气温日较差作为分区指标,采用K-均值聚类算法对中国地域气候进行分区,依据台站所处地域的太阳能、风能等资源动态调整TMY权重因子。结果显示,调整后的权重因子构建的TMY更加精准,更能体现地域的气候特征。