共查询到20条相似文献,搜索用时 62 毫秒
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本文将一些常见图形中的面积关系进行归纳,将其用来解有关的数学竞赛题.先介绍有关的基本定理:1.三角形的三条中线将该三角形分成面积相等的六个三角形,其中三条中线的交点是该三角形的重心(如图1).2.平行四边形两条对角线将该平行四边形分成面积相等的四个三角形(如图2).3.平行四边形的边上任一点和对边两端点的连线将该平行四边形分成面积相等的两部分.Rll图3中的S。一sl+sZ一会见。·I。·4.平行四边形内任一点与四个顶点的连线将其分成四个三角形,则对顶的两三角形面积之和相等.即图4中SI+SZ-S3+S4.5.任意四… 相似文献
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胡舒合 《数理统计与应用概率》1994,9(1):76-83
设(dni,i=1,...n),(Xni,i=1,...,n)分别为双下标常数列和随机变量列,众所周知,有关n∑i=1dniXni的收敛性问题,在统计推断中有着广泛的应用,例如在异方差的回归分析中的重要应用(3),当(Xni,Fni,-∞<i<∞)为鞅差序列时,文献(4)研究了∑iXni的渐进正态性,本文获得n∑i=1dniXni的P阶均方收敛及强收敛于零的充分条件,其(Xni,i=1,...,n 相似文献
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调和级数∑n=1^∞1/n是发散的,而极限lim n→∞(∑k=1^∞1/k-lnn)却是收敛的,其极限值称为欧拉常数γ,本文给出了欧拉常数γ的几个有趣的级数表示和积分表示. 相似文献
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范洪福 《应用泛函分析学报》2006,8(4):304-307
讨论向量值函数的Banach代数L∞(T;X)的极大理想空间的拓扑性质和代数性质,得到了若干结果;给出了Banach空间H∞(D;X)中闭单位球的端点的一条性质. 相似文献
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设{Y,Yi,-∞<i<∞}为一负相伴同分布随机变量序列,{ai,-∞<i<∞}绝对可和的实数序列,本文在适当的条件下,证明了平滑移动过程{∑k=1^n∑i=-∞^∞ai k Yi/n^1/t,n≥1}的完全收敛性.所得的结果改进了[1]中的定理1. 相似文献
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负相依样本平滑移动过程的完全收敛性 总被引:2,自引:0,他引:2
设{Yi;-∞<i<∞}为一负相伴的同分布随机变量序列,{ai;-∞<i<∞}为绝对可和的实数序列。本文在适当的条件下。证明了平滑移动过程{∑k=1^n∑i=-∞^∞ai kYi/n^1/t;n≥1}的完全收敛性。 相似文献
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1.定理及推论
定理 如图1,在△PAB中,M是边AB上任意一点,Q是PM上的任意一点,过点Q任作一条直线交边PA,PB于A′,B′,若PA=xPA,PB=yPB, 相似文献
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设P(z)是d(≥2)次多项式,J是P(z)的Julia集,σ:∑n→∑n是n个符号的单边符号空间∑n上的转移自映射.本文证明了当p(z)的某m(1≤m≤d-1)个有穷临界点的轨道收敛于∞时,p|J拓扑半共轭于σ:∑(m+1)→∑(m+1),而当m=d-1时,p|J拓扑共轭于σ:∑d→∑d。 相似文献
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We obtain new gauge-invariant forms of two-dimensional integrable systems of nonlinear equations: the Sawada-Kotera and Kaup-Kuperschmidt
system, the generalized system of dispersive long waves, and the Nizhnik-Veselov-Novikov system. We show how these forms imply
both new and well-known twodimensional integrable nonlinear equations: the Sawada-Kotera equation, Kaup-Kuperschmidt equation,
dispersive long-wave system, Nizhnik-Veselov-Novikov equation, and modified Nizhnik-Veselov-Novikov equation. We consider
Miura-type transformations between nonlinear equations in different gauges.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 160, No. 1, pp. 35–48, July, 2009. 相似文献
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Abstract In [1], Ding et al. studied the nonhomogeneous Burgers equation ut uux = μuxx 4x.(1.1) This paper will prove that when μ → 0 the solution of (1.1) will approach the generalized solution of ut uux = 4x.(1.2) The authors notice that the equation (1.2) is beyond the scope of investigations by Oleinik O. in [2]. The solutions here are unbounded in general. The paper also studies the δ-wave phenomenon when (1.2) is jointed with some other equation. 相似文献
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Wojciech Jab?oński 《Journal of Mathematical Analysis and Applications》2007,325(1):675-684
In the paper we examine Pexiderized ?-homogeneity equation almost everywhere. Assume that G and H are groups with zero, (X,G) and (Y,H) are a G- and an H-space, respectively. We prove, under some assumption on (Y,H), that if functions and satisfy Pexiderized ?-homogeneity equation
F1(αx)=?(α)F2(x) 相似文献
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1IntroductionUnique continuation of solutions to the linear partial di?erential equations with analyticcoe?cients is well known.There are more general results in elliptic,parabolic and hyperbolicequations(cf.[8-10,12-13]and references therein).The continu… 相似文献
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Martina Chirilus-Bruckner Wolf-Patrick Düll Guido Schneider 《Journal of Mathematical Analysis and Applications》2014
Bethuel et al. and and Chiron and Rousset [3] gave very nice proofs of the fact that slow modulations in time and space of periodic wave trains of the NLS equation can approximately be described via solutions of the KdV equation associated with the wave train. Here we give a much shorter proof of a slightly weaker result avoiding the very detailed and fine analysis of , and . Our error estimates are based on a suitable choice of polar coordinates, a Cauchy–Kowalevskaya-like method, and energy estimates. 相似文献
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New oscillation and nonoscillation criteria are established for the equation
,where p :]1,+[ R is the locally integrable function. These criteria generalize and complement the well known criteria of E. Hille, Z. Nehari, A. Wintner, and P. Hartman. 相似文献