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1.
分别讨论了以第二类Chebyshev多项式的零点、Jacobi多项式的零点、第一类Chebyshev多项式的零点为插值结点组的五类Kantorovich型插值算子在Orlicz空间内的逼近问题,得到了逼近阶的上界估计.  相似文献   

2.
邵仪  赵育林 《数学学报》2007,50(2):451-460
利用Abel积分与第一、第二型完全椭圆积分,本文研究一类具有两个中心奇点的平面二次系统在n次小扰动下的Abel积分零点个数上界问题,得到了较小的上界估计.  相似文献   

3.
本文讨论一平面Hamilton系统在一般n次多项式扰动下的系统的Abel积分的零点个数估计问题,得到的结论是:该系统的Abel积分的零点个数的上界为[(3n-1)/2]。  相似文献   

4.
研究一类五次扰动Hamiltonian系统的Abel积分零点个数上界.证明所研究的Abel积分的生成元构成精度为1的Chebeyshev系统,得到Abel积分零点个数上界是4(考虑零点重数).并指出前人文献中关于Abel积分零点个数上界的研究存在的错误,给出了最新结果.  相似文献   

5.
讨论了首次积分为H(x,y)=x~k(1/2y~2+Ax~2+Bx+C)的Abel积分的代数构造,并研究了k=2时具有一个中心的平面二次可积系统在n次扰动下的Abel积分零点个数上界问题,得到了较小的上界估计,  相似文献   

6.
本文通过L-函数的整体积分幂矩,来推导某些自守L-函数集合的整体零点密度的上界估计.具体而言,假设I是某些自守表示π构成的集合,对任意π有非负系数c(π)且级数∑π∈I c(π)收敛.假设■其中l≥1,0 <α≤1,θ≥α.则可以得到整体零点密度■的上界估计,这里Nπ(σ,T1,T2)表示满足σ<β<1及T1≤γ≤T2的L(s,π)的零点ρ=β+iγ的个数.  相似文献   

7.
利用Picard-Fuchs方程法及Riccati方程法,研究了一类二次可逆系统在任意n次多项式扰动下Abel积分的零点个数估计,得出当n≥5时,上界为10[(4n+1)/3]+4[(4n)/3]+[(4n-1)/3]+13.  相似文献   

8.
利用Picard-Fuchs方程法及Riccati方程法,研究了一类二次可逆系统在任意n次多项式扰动下Abel积分零点个数的线性估计,得到了当n≥3时,上界为4[2n/3]+2[2n+1/3]+[2n+2/3]+16.  相似文献   

9.
张广厚 《数学学报》1987,30(3):317-354
<正> A.Edrei和W.Fuchs曾经考虑零点和极点的分布受某种限制的亚纯函数类,并且获得此类函数的亏值个数的上界估计。在本文,我们先证明几个涉及亚纯函数的零点和极点分布的一般性定理,然后应用这些定理重新证明Edrei-Fuchs的结果及其改进,并由此导出杨乐-张广厚的结果.最后,我们应用这些一般性定理讨论亚纯函数的亏值个数  相似文献   

10.
邱凎悌 《数学研究》1996,29(4):82-86
本文主要得到亚纯函数及其导数的多项式的零点的定量估计,推广并改进了W.K.Hayman及敖海龙等人的有关结果.  相似文献   

11.
12.
给出了Fuzzy集合依零测度的包含,依零测度的相等。依零测度的并.交,补运算等。并补充地研究了这些基本运算,获得了若干好的性质。Fuzzy集依零测度的基本运算比标准fuzzy集合论的相应运算更有人情味,更为接近人的智能机理。有望在智能信息处理和软计算领域取得好的应用。  相似文献   

13.
Let a1, a2, ... be elements of an abelian group such that amhas order larger than mm. Then the multiset of the am's can be partitioned into two parts which are free of zero subsums. The result was motivated by a question of Pál Erds.  相似文献   

14.
Gentner and Rautenbach conjectured that the size of a minimum zero forcing set in a connected graph on n vertices with maximum degree 3 is at most 13n+2. We disprove this conjecture by constructing a collection of connected graphs {Gn} with maximum degree 3 of arbitrarily large order having zero forcing number at least 49|V(Gn)|.  相似文献   

15.
Recent years have seen active developments of various penalized regression methods, such as LASSO and elastic net, to analyze high-dimensional data. In these approaches, the direction and length of the regression coefficients are determined simultaneously. Due to the introduction of penalties, the length of the estimates can be far from being optimal for accurate predictions. We introduce a new framework, regression by projection, and its sparse version to analyze high-dimensional data. The unique nature of this framework is that the directions of the regression coefficients are inferred first, and the lengths and the tuning parameters are determined by a cross-validation procedure to achieve the largest prediction accuracy. We provide a theoretical result for simultaneous model selection consistency and parameter estimation consistency of our method in high dimension. This new framework is then generalized such that it can be applied to principal components analysis, partial least squares, and canonical correlation analysis. We also adapt this framework for discriminant analysis. Compared with the existing methods, where there is relatively little control of the dependency among the sparse components, our method can control the relationships among the components. We present efficient algorithms and related theory for solving the sparse regression by projection problem. Based on extensive simulations and real data analysis, we demonstrate that our method achieves good predictive performance and variable selection in the regression setting, and the ability to control relationships between the sparse components leads to more accurate classification. In supplementary materials available online, the details of the algorithms and theoretical proofs, and R codes for all simulation studies are provided.  相似文献   

16.
单级零点较少的亚纯函数的一个界囿不等式   总被引:1,自引:0,他引:1  
张庆德 《数学学报》2004,47(2):285-290
本文证明了:若.f(z)为复平面上的非线性亚纯函数,满足N1(r,1/f)=S(r,f),则对任何非零复数c,成立T(r,f)<11N(r,f)+11N(r,1/f'-c)+S(r,f).这里N1(r,1/f)表示f(z)的单级零点的计数函数.  相似文献   

17.
In this paper, we study a discrete search game on an array of N ordered cells, with two players having opposite goals: player I (searcher) and player II (hider). Player II has to hide q objects at consecutive cells and player I can search p consecutive cells. The payoff to player I is the number of objects found by him. In some situations, the players need to adopt sophisticated strategies if they are to act optimally.  相似文献   

18.
By means of variational method, we give some observations about the location of zeros of Neumann Sturm-Liouville eigenfunctions.  相似文献   

19.
设F是在区域D内的一族亚纯函数,其零点重级至少为k,k是一个正整数,a(z)(≠0)在区域D内全纯.若对于任意的f∈F,有(1)f(z)与a(z)没有公共的零点;(2)f(z)=0f(k)(z)=a(z)■0|f~((k+1))(z)-a'(x)||a(z)|,则F在D内正规.  相似文献   

20.
The convergence rate in the central limit theorem (CLT) is investigated in terms of a wide class of probability metrics. Namely, optimal estimates for the proximity between a probability distribution and its zero bias transformation are derived. These new inequalities allow one to establish optimal rates of convergence in the CLT for sums of independent random variables with finite moments of order s, s∈(2,3], in terms of ideal metrics introduced by V.M. Zolotarev.  相似文献   

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