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1.
Let G(V, E) be a unicyclic graph, Cm be a cycle of length m and Cm G, and ui ∈ V(Cm). The G - E(Cm) are m trees, denoted by Ti, i = 1, 2,..., m. For i = 1, 2,..., m, let eui be the excentricity of ui in Ti and ec = max{eui : i = 1, 2 , m}. Let κ = ec+1. Forj = 1,2,...,k- 1, let δij = max{dv : dist(v, ui) = j,v ∈ Ti}, δj = max{δij : i = 1, 2,..., m}, δ0 = max{dui : ui ∈ V(Cm)}. Then λ1(G)≤max{max 2≤j≤k-2 (√δj-1-1+√δj-1),2+√δ0-2,√δ0-2+√δ1-1}. If G ≌ Cn, then the equality holds, where λ1 (G) is the largest eigenvalue of the adjacency matrix of G.  相似文献   

2.
刘耕滔  谢子康 《大学数学》2021,37(4):121-125
为了探究乘方的指数与其幂的位数的关系,定义了几个有关的新概念,并且证明了两个关于乘方以及进制进位的定理,由此建立起关于乘方以及进制进位的理论体系,其中包括进位理论中判定乘方的指数与其幂的位数是否存在周期规律的判别法,以及进位规律的求解法和四条相关的性质.  相似文献   

3.
潘江敏  马丽  罗森月 《数学杂志》2008,28(2):137-140
本文研究了自由群的直积的检验元素,通过对直积的自同态的分解,得到了直积中的元素为检验元素的充分必要条件,改进了O'neill和Turner的结果.此外,构造了两类具体的检验元素.  相似文献   

4.
树的最大特征值的上界的一个注记   总被引:2,自引:2,他引:0  
扈生彪 《数学学报》2007,50(1):145-148
设T是一个树,V是T的顶点集.记dv是υ∈V的度,△是T的最大顶点度.设υ∈V且dw=1.记k=ew+1,这里ew是w的excentricity.设δj′= max{dυ:dist(υ,w)=j},j=1,2,…,k-2,我们证明和这里μ1(T)和λ1(T)分别是T的Laplacian矩阵和邻接矩阵的最大特征值.特别地,记δo′=2.  相似文献   

5.
利用上下解方法,研究如下一类具有转向点的三阶微分方程的边值问题{ε~2y″′=f(t,y,ε)y″ g(t,y,ε)y′ h(t,y,ε),a相似文献   

6.
在1968年墨西哥奥运会上,美国选手海因斯撞线后,转过身看着9.95秒的成绩牌,摊开双手自言自语地说了一句话.这一情景通过电视有好几亿人看到,可是由于当时他身边没有话筒,因此海因斯到底说了句什么话,谁都不知道.16年后,一位记者看墨西哥奥运会的资料片,当再次看到海因斯的镜头时,他想,这是人类历史上第一次有人在百米赛道上突破10秒大关,海因斯在看到记录的那一瞬间,一定说了一句不同凡响的话.这一新闻点,竟被那么多记者给漏掉了.于是他决定去采访海因斯,问海因斯当  相似文献   

7.
数与形是一个数学问题的两个层面,数能精细,形可直观,但同学们也须注意,如果你在解题时,出现了疏漏,数也可能出现貌似精细的蒙蔽,形也可以导致似乎明了的误导.本文通过两个典型例子,提醒同学们在学习  相似文献   

8.
有两个来自农村的人,准备外出打工.一个打算去上海,一个决定去北京.在候车厅等车的时候,他们俩又改变了主意,因为他们同时听到邻座的人议论说:上海人精明,外地人问路都收费.北京人质朴,见了吃不上饭的人,不仅给馒头,还送旧衣服.  相似文献   

9.
向平静的湖面投入一颗石子,形成水波纹,这水波纹构成以投入点为圆心的一族同心圆,给我们以点膨胀为圆的最好形象.反之如图1,⊙O的半径OA=r,让⊙O的半径逐渐缩小,形成一族同心圆,当⊙O的半径r趋近于零时,⊙O收缩为一点O,因此,把点看成半径长为零的圆.  相似文献   

10.
给出了随机变量 X1,X2 ,X3 ,X4 每三个相互独立 ,但 X1±X2 与 X3 ± X4 不相互独立的例子 ,以及 X1,X2 ,X3 每两个相互独立 ,但 X1± X2 与 X3 不相互独立的例子 .  相似文献   

11.
本文分析了15具白骨化尸体标本的股骨汞(Hg),铅(Pb),镉(Cd)元素含量数据,在三年的时间内采集了3次,一共收集到45个数据。首先将这组数据看着纵向数据,利用线性随机效应混合模型、Cox随机混合效应模型进行分析,结果显示,如果对每个白骨化尸体标本建立线性模型,可以精确预测出死亡时间,而且不需要采集铅元素含量数据。混合效应模型的预测效果也很好,最大误差不会超过1个月。其次我们对数据不作任何假设,利用机器学习中随机森林方法分析数据,并利用5折交叉验证方法来判断结果的可靠性,训练集和测试集的NMSE分别为0.1205944,0.5604286,因此可以用训练出的模型来预测死亡时间。  相似文献   

12.
The aim of this paper is to establish the uniform convergence of the densities of a sequence of random variables, which are functionals of an underlying Gaussian process, to a normal density. Precise estimates for the uniform distance are derived by using the techniques of Malliavin calculus, combined with Stein?s method for normal approximation. We need to assume some non-degeneracy conditions. First, the study is focused on random variables in a fixed Wiener chaos, and later, the results are extended to the uniform convergence of the derivatives of the densities and to the case of random vectors in some fixed chaos, which are uniformly non-degenerate in the sense of Malliavin calculus. Explicit upper bounds for the uniform norm are obtained for random variables in the second Wiener chaos, and an application to the convergence of densities of the least square estimator for the drift parameter in Ornstein–Uhlenbeck processes is discussed.  相似文献   

13.
有资格限制的指派问题的求解方法   总被引:3,自引:0,他引:3  
在实际的指派工作中,常会遇到某个人有没有资格去承担某项工作的问题,因此,本建立了有资格限制的指派问题的数学模型。在此数学模型中,将效益矩阵转化为判定矩阵,由此给出了判定此种指派问题是否有解的方法;在有解的情况下,进一步将效益矩阵转化为求解矩阵,从而将有资格限制的指派问题化为传统的指派问题来求解。最后给出了一个数值例子来说明这样的处理方法是有效的。  相似文献   

14.
We discuss how to obtain exact and approximate distributions for various statistical characteristics of the spectra of quantum graphs using previously found exact solutions of the spectral problem. We indicate the relation between the appearing spectral decompositions and the theory of weakly dependent random variables and indicate the relation between the known limit theorems for trigonometric sums and the universal statistical properties of the spectra of quantum chaotic systems. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 1, pp. 38–66, July, 2008.  相似文献   

15.
The problem of estimating the probability of unobserved outcomes or, as it is sometimes called, the conditional probability of a new species, is studied. Good's estimator, which is essentially the same as Robbins' estimator, namely the number of singleton species observed divided by the sample size, is studied from a decision theory point of view. The results obtained are as follows: (1) When the total number of different species is assumed bounded by some known number, Good's and Robbins' estimators are inadmissible for squared error loss. (2) If the number of different species can be infinite, Good's and Robbins' estimators are admissible for squared error loss. (3) Whereas Robbins' estimator is a UMVUE for theunconditional probability of a new species obtained in one extra sample point, Robbins' estimator is not a uniformly minimum mean squared error unbiased estimator of the conditional probability of a new species. This answers a question raised by Robbins. (4) It is shown that for Robbins' model and squared error loss, there are admissible Bayes estimators which do not depend only on a minimal sufficient statistic. A discussion of interpretations and significance of the results is offered. Research supported by NSF Grant DMS-88-22622.  相似文献   

16.
设G是一个具有二分类(X_1,X_2)的简单偶图,|X_1|=|X_2|=n,如果对于给定的c>0,|M(S)|≥(1+c)|S|对任意满足|S|≤n/2的S(?)X_i(i=1,2)都成立,其中N(S)是S的邻集,则称G是(n,c)-扩张图.给出了(n,c)-扩张图的k-匹配数与完美匹配数之比的顺从界.  相似文献   

17.
本文在LF拓扑空间中建立了L-fuzzy集网的弱收敛(R-收敛)概念,应用文[4]中的R-闭包,系统讨论了它们的性质,证明了等式RlimA_n=∧(∨A_m)_R和RlimA_n=A_n=∧(∨A_m)_R并且给出了L-fuzzy集网与其子网之间的关系。  相似文献   

18.
Interferons are active biomolecules, which help fight viral infections by spreading from infected to uninfected cells and activate effector molecules, which confer resistance from the virus on cells. We propose a new model of dynamics of viral infection, including endocytosis, cell death, production of interferon and development of resistance. The novel element is a specific biologically justified mechanism of interferon action, which results in dynamics different from other infection models. The model reflects conditions prevailing in liquid cultures (ideal mixing), and the absence of cells or virus influx from outside. The basic model is a nonlinear system of five ordinary differential equations. For this variant, it is possible to characterise global behaviour, using a conservation law. Analytic results are supplemented by computational studies. The second variant of the model includes age-of-infection structure of infected cells, which is described by a transport-type partial differential equation for infected cells. The conclusions are: (i) If virus mortality is included, the virus becomes eventually extinct and subpopulations of uninfected and resistant cells are established. (ii) If virus mortality is not included, the dynamics may lead to extinction of uninfected cells. (iii) Switching off the interferon defense results in a decrease of the sum total of uninfected and resistant cells. (iv) Infection-age structure of infected cells may result in stabilisation or destabilisation of the system, depending on detailed assumptions. Our work seems to constitute the first comprehensive mathematical analysis of the cell-virus-interferon system based on biologically plausible hypotheses.  相似文献   

19.
杨海宣 《数学学报》1998,41(4):727-730
本文研究了完全正则半群簇的子簇格[V+∩PV,V+∩PV]的某些格运算性质,我们证明了簇V+∩PV可分解为V与V+∩PV的并;对任意完全正则半群簇W,有W∩(V∨V+∩PV)=(W∩V)∨(W∩V+∩PV).特别地,我们得到了等式V+∩PV=V成立的若干条件.  相似文献   

20.
Tai Keun Kwak  Yang Lee 《代数通讯》2013,41(9):4033-4046
We study the nilpotency of the sums of all coefficients of some sorts of products of polynomials over reversible, IFP, and NI rings, and introduce an SCN ring as a generalization. We characterize SCN rings in relation with related ring properties, and also provide several useful properties and ring extensions of SCN rings.  相似文献   

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