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设m是正整数,f(X,Y)=a0Xn+a1X(n-1)Y+...+anYn∈Z[X,Y]是Q上不可约化的叫n(n≥3)次齐次多项式。本文证明了:当gcd(m,a0)=1,n≥400且m≥10(35)时,方程|f(x,y)|=m,x,y∈z,gcd(x,y)=1,至多有6nv(m)组解(x,y),其中v(m)是同余式F(z)=f(z,1)≡0(modm)的解数。特别是当gcd(m,DF)=1时,该方程至多有6n(ω(m)+1)组解(x,y),其中DF是多项式F的判别式,ω(m)是m的不同素因数的个数. 相似文献
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设m,n∈N;m≥2,n≥2,mn≥6,f(x)=xm+a1xm-1+…+am∈Z[x],H=max(|a1|,…,|am|).本文运用组合分析方法证明了:当m≡0(modn),a1,…,am不全为零,而且其中第一个非零系数as与n互素时,方程f(x)=yn,x,y∈Z,仅有有限多组解(x,y),而且这些解都满足|x|<(4mH)2m/n+1以及|y|<(4mH)4m2/n2+m/n+1 相似文献
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本文研究变系数线性差分方程组x(n+1)=ax(n)+br-n(n),y(n+1)=crnx(n)+dy(n)的稳定性,利用参数a,b,c,d和r,给出了这一系统稳定性的完整分类.这一分类结果给我们提供了一种简单的方法构造违背常系数线性差分方程对应结果的各种反例. 相似文献
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费尔马最后定理的证明 总被引:2,自引:0,他引:2
(i)我们用(x-b)n+xn=(x+a)来代替xn+yn=zn作为费尔马最后定理(FLT)的普遍方程式.其中a及b是两个任意自然数.应用二项展开式,(0.1)可以写成因为ar-(-b)r始终包含a+b作为它的因数,(0.2)可写成其中фr=[ar-(-b)r]/(a+b)对于r=1,2,…,n.都是个整数.(ii)令s是a+b的一个因数,并令a+b=sc.我们可用x=sy来变换(0.3)成为下列(0.4)(iii)将(0.4)除以S2,我们得(0.5)式的左边,是的整系数多项式,而右边cф/s是个常数Cф/s.若Cф/s不是个整数,那末我们不能求得能适合(0.5)的整数y,这样FLT对这场合是对问.若Cфn/s是个整数,我们可以改变s和c,使cф/s≠整数。 相似文献
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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
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In this paper we determine the minimum and maximum values of the sum of squares of degrees of bipartite graphs with a given number of vertices and edges. 相似文献
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碾压混凝土坝施工层面变形分析模型 总被引:1,自引:0,他引:1
针对碾压混凝土坝施工层面对大坝变形产生显著影响的问题,深入研究了施工层面的变化性质及规律,提出了层面不同阶段变形的模拟方法,建立了施工层面有厚度和无厚度分析模型,提出的模型能反映层面的弹性变形、衰减蠕变、不可逆变形以及加速蠕变等变形状态.实例分析表明:所提出的碾压混凝土坝施工层面有厚度和无厚度分析模型能较客观地模拟大坝的结构变化形态,尤其是施工层面有厚度分析模型较完整地模拟了层面的渐变规律,其计算结果与原位监测成果吻合较好.同时,提出的方法和建立的分析模型可推广应用于常规混凝土坝,特别是坝基内断层和夹层等变形规律的分析. 相似文献
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Jogi Henna 《Annals of the Institute of Statistical Mathematics》2005,57(4):655-664
An estimator of the number of components of a finite mixture ofk-dimensional distributions is given on the basis of a one-dimensional independent random sample obtained by a transformation
of ak-dimensional independent random sample. A consistency of the estimator is shown. Some simulation results are given in a case
of finite mixtures of two-dimensional normal distributions. 相似文献
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N/Kbe a Galois extension of number fields with finite Galois group G.We describe a new approach for constructing invariants of the G-module structure of the K groups of the ring of integers of N in the Grothendieck group of finitely generated projective Z[G]modules. In various cases we can relate these classes, and their function field counterparts, to the root number class of Fröhlich and Cassou-Noguès. 相似文献
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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
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Nguyêñ Quoôć Thǎ;ńg 《代数通讯》2013,41(3):1097-1110
We present a unified approach to compute the number of connected components in the group of real points of adjoint almost simple real algebraic groups. 相似文献
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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
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The Gauss-Lucas Theorem on the roots of polynomials nicely simplifies the computation of the subderivative and regular subdifferential
of the abscissa mapping on polynomials (the maximum of the real parts of the roots). This paper extends this approach to more
general functions of the roots. By combining the Gauss-Lucas methodology with an analysis of the splitting behavior of the
roots, we obtain characterizations of the subderivative and regular subdifferential for these functions as well. In particular,
we completely characterize the subderivative and regular subdifferential of the radius mapping (the maximum of the moduli
of the roots). The abscissa and radius mappings are important for the study of continuous and discrete time linear dynamical
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Dedicated to R. Tyrrell Rockafellar on the occasion of his 70th birthday. Terry is one of those rare individuals who combine
a broad vision, deep insight, and the outstanding writing and lecturing skills crucial for engaging others in his subject.
With these qualities he has won universal respect as a founding father of our discipline. We, and the broader mathematical
community, owe Terry a great deal. But most of all we are personally thankful to Terry for his friendship and guidance.
Research supported in part by the National Science Foundation Grant DMS-0203175.
Research supported in part by the Natural Sciences and Engineering Research Council of Canada.
Research supported in part by the National Science Foundation Grant DMS-0412049. 相似文献