与Smarandache函数有关的两个方程

对于任意自然数n,Smarandache函数S(n)指最小的正整数m,能够满足n│m!。对于任意给定的正整数n,著名的伪Smarandache函数Z(n)定义为最小的正整数m,使得n│1+2+…m=m(m+1)2。文章用初等方法研究了方程S(n)+Z(n)=n和S(n)=P(n),并给出了它们的全部解。     

关于含四个未知函数的费马型丢番图函数方程的非平凡解的研究

本文利用亚纯函数值分布论的思想方法,对费马型丢番图函数方程fn1(z)+fn2(z)+fn3(z)+fn4(z)=1的非平凡解的状况进行研究,得到如下结果:假设函数方程fn1(z)+fn2(z)+fn3(z)+fn4(z)=1存在非常数的亚纯函数解f1,f2,f3,f4令τn:=|f31 f32 f33 f34 f21f′1 f22f′3 f23f′3 f24f′4L1(f1)L1(f2)L1(f3)L1(f4)L2(f1)L2(f2)L2(f3)L2(f4)|及T*(r)=T(r,f1)+T(r,f2)+T(r,f3)+T(r,f4),这里L(1fm)=(n-1)fmf′m2+f m2f″m,L(2fm)=(n-1)(n-2)f′m3+3(n-1)fmf′mf″m+f m2+fm''(m=1,2,3,4)。那么,(1)当n≥17时,τ(nz)是整函数;(2)当n≥13时,m(r,τn)=S*(r);这里S*(r)=O{T*(r)(}r→∞,rE),E是R+的线性测度有限的某子集。     

s=4的完全多部图K_(a_1n_1,a_2n_2,…,a_sn_s)的无符号Laplace特征多项式

文中计算得到了完全多部图K(n1,n2,…,n)t=Ka1n1,a2n2,…,asns当s=4时的无符号Laplace特征多项式。     

两个关于Smarandache函数的方程

对任意正整数n,著名的Smarandache函数S（n）定义为最小的正整数m,使得n｜m!对于任意给定的正整数n,著名的伪Smarandache函数Z（n）定义为最小的正整数m,使得n｜1＋2＋…m=m（m＋1）/2。文章用初等方法研究了方程S（n）=Z（n）和S（n）＋Z（n）=n,并给出了它们的全部解.     

社会外延扩大再生产的优化数量关系

一、引言马克思在《资本论》中提出两大物质生产部类的理论,即生产资料生产,称之为Ⅰ部类生产,和消费资料生产,称之为Ⅱ部类生产.设以c,v,m,p分别表示不变资本、可变资本、剩余价值和产品价值,右脚标1和2分别代表Ⅰ和Ⅱ部类的生产,则有 p_1=c_1+v_1+m_1 (1) p_2=c_2+v_2+m_2 (2)并把剩余价值m分为消费和积累两部分,用下标c和a来分别表示,即 m_1=m_(1c)+m_(1a) (3) m_2=m_(2c)+m_(2a) (4)     

产业结构的地区差异及其衡量

产业结构的地区差异反映着生产的地区分工情况。产业结构的地区差异越大,表明生产的地区分工程度越高。本文将提出衡量产业结构地区差异程度的综合指标,并将其应用于我国实际情况的研究之中。一、衡量产业结构的地区差异程度的综合指标我们令m为地区数,n为产业部门数,W_(ij)为第i地区第j产业产出占该地区产出     

基于GIS的榆林市降水对土壤影响的调查

根据榆林市以及周边地区19个站点10年间的降雨资料,用相关的计算方法和地理信息软件对榆林市全部区域降雨侵蚀力(R值)进行差异分析,并重点分析榆林市内3个站点的数据空间特征和时间特征.结果表明:榆林市降雨侵蚀力由西北向东南方向延伸变化,与降雨量的变化基本保持一致.研究区的降雨侵蚀力范围介于82 J·cm/(m2·h2·a2)~105 J·cm/(m2·h2·a2)之间,且降雨侵蚀力有继续增高的趋势.研究结果为榆林市的水土流失防治工作提供了参考依据.     

国家限制生产低档陶瓷

据悉 ,国家建材局计划在 1999～ 2 0 0 0年间把采用低水平技术的 1.5亿 m2瓷砖生产线淘汰掉 ,使高级瓷砖在总量中所占比例达 30 %。这种意图也准备在卫生陶瓷业实施。在淘汰以低档技术所生产的 30 0万件 / a情况下 ,2 0 0 0年该行业的总产量将限制在 550 0万件 / a的水平上 ,同时 ,高级产品将在卫生陶瓷总产量中达到 2 0 %左右的比例。在一部分产能被淘汰之时 ,将实施严格的行业规定 ,包括 :(1)关闭采用圆形、多孔及煤烧隧道窑生产线 ;(2 )关闭年产能力不足 70万 m2的中低档瓷砖生产线 ,但作为第 3次烧结用的生产线例外 ;(3)关闭年生产能力…     

图像恢复的处理与算法分析

<正>在图像生成的过程中,由于成像系统各种因素的影响和监视图像往往受到各种因素的影响。目前已经提出了许多有效的图像恢复方法,这些经典方法大致可以分为确定性的分析计算方法和统计得方法两类。图像的退化模型可以用下式表示:g(ij)=s[∫∫(a,b)∈σf(a,b)h(a,bi,j)dadb]+n(i,j),此为式(1),式中g     

混凝土温度特性参数的试验及其反演分析

根据试验得到混凝土实测点的实测温度值,通过反演分析得到混凝土温度特性参数。混凝土温度特性参数主要有导热系数λ、导温系数a,混凝土绝热温升参数θo、n(绝热温升模型为θ=θoτ/n+τ)和混凝土表面散热系数β(有模板)。其中主要反演绝热温升参数θo,n和有模板的混凝土表面散热系数β。     

关于正整数的四次方部分数列

设n是正整数,u(n)表示不超过n的最大四次方部分,v(n)表示不小于n的最小四次方部分。本文的主要目的是研究数列u(n)和v(n)的均值性质,并对罗马尼亚数论专家F.Smarandach教授在文献[1]中提出的第41个问题做出实质性进展,利用解析分析方法给出了包含这两个数列及除数函数的几个有趣的渐近公式。     

关于数论函数方程φ(φ(n))=S(n)

对于任意正整数n,设φ(n)和S(n)分别是关于n的Euler函数和Smarandache函数。本文利用初等及分类讨论的方法,研究并得到了方程φ(φ(n))=S(n)的所有正整数解。     

Calculating Cumulants of a Taylor Expansion of a Multivariate Function

A method, which we believe is simpler and more transparent than the one due to McCullagh (1984) , is described for obtaining the cumulants of a scalar multivariate stochastic Taylor expansion. Its generalisation is also suggested. An important feature, previously not reported, is that the expansion of every cumulant of order ≥ 2 is made up of separate subseries.
In order to handle certain frequently occurring sums over permutations of members of compound index sets, we introduce a new notation  [ m ]_*,  where   m   is a positive integer.     

一个新数论函数及其均值

对任意正整数n,设h(kn)表示不大于n的最大k次幂,以及h(kn)=n-IK(kn),利用初等方法和解析方法,研究了新定义的数论函数h(kn)的均值性质;并给出了一个较强的均值渐近公式。     

Scheduling identical jobs on uniform parallel machines

We address the problem of scheduling n identical jobs on m uniform parallel machines to optimize scheduling criteria that are nondecreasing in the job completion times. It is well known that this can be formulated as a linear assignment problem, and subsequently solved in O ( n ³) time. We give a more concise formulation for minsum criteria, and show that general minmax criteria can be minimized in O ( n ²) time. We present faster algorithms, requiring only O ( n + m log m ) time for minimizing makespan and total completion time, O ( n log n ) time for minimizing total weighted completion time, maximum lateness, total tardiness and the weighted number of tardy jobs, and O ( n log² n ) time for maximum weighted tardiness. In the case of release dates, we propose an O ( n log n ) algorithm for minimizing makespan, and an O ( mn ^2m+1) time dynamic programming algorithm for minimizing total completion time.     

On Hypothesis about the Second Eigenvalue of the Leontief Matrix

If an arbitrarily positive eigenvector is repeatedly premultiplied by a positive matrix, then the result tends towards a unique, positive (Frobenius) eigenvector. Brady has demonstrated that the expected absolute magnitude of the estimate of the second largest eigenvalue of a positive random matrix (with identically and independently distributed entries) declines monotonically with the increasing size of the matrix. Hence, the larger the system is, the faster is the convergence. Molnár and Simonovits examined Brady's conjecture in the case where entries of a stochastic matrix are close to 1/n. We prove this hypothesis for any stochastic and positive matrix.     

On the exponential law

A characterization of the exponential law is given using its property thatE[(X–a)^r|X>a] is constant for alla0,r being a positive integer. Then this result is applied to the order statistics and some further characterizations are found.     

一类有理型时滞差分方程的稳定性研究

在这篇文章中,我们研究如下形式的有理型时滞方程xn+1=(β4xn-4/A+B4xn-4)+Cxn-k-4,n=0,1,2,…的稳定性,得到了上述方程零解渐近稳定的充分条件,其中A,C,β4,B4是实常数,且A≠0,C≠0,k>1正整数。     

A core equivalence theorem with an arbitrary communication structure

We formalize the concept of a communication structure by identifying it with a partition of the set of agents. Thus, a coalition can form if and only if it belongs to the given partition. Within this framework we are able to show that for every integer J≧2, if we put the uniform distribution on the space of partitions that contain exactly (or, no more than) J coalitions, the probability that such a partition will contain a blocking coalition for any Pareto optimal allocation which is bounded away from being competitive, is arbitrarily close to 1, as the number of individuals increases.     

A LIMIT THEOREM FOR BERNOULLI RV'S AND FELLER'S SHOE PROBLEM

Consider n sets of objects, each set consisting of m distinct types (for instance n place settings each made up of m distinct dishes and silverware pieces.) s items are drawn at random from the mn items. The distribution of the number of complete sets (each consisting of all m items) in the sample of s is asymptotically Poisson distributed with parameter (a /m )^m if s = an ^1–1 and n →∞. This fact can be interpreted in terms of a certain limit theorem for a sequence of i.i.d Bernoulli rv's.