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1.
陈刚  朱文辉 《大学数学》2011,27(5):89-93
对指数级数中前n次多项式的零点的性质进行分析,得到了零点数量及其变化趋势的一系列结果.利用Taylor公式给出了具有解析表达式的零点控制区间,进一步运用指数级数的余项分析和Stirling公式给出了精度更高的零点控制区间,同时得到了寻求零点的计算方法,这种算法的精度能够达到任意要求,对高次多项式零点的计算能大幅减少运算...  相似文献   

2.
<正>同学们知道,函数零点问题是高中数学中常见的问题.由于零点问题具有较强的综合交汇性,这给解决零点问题的思维路径也提供了较多的选择余地.基于此,本文拟对零点问题给出三点注释,以资同学们参考.1准确理解零点内涵对零点内涵的准确理解至少包含以下三个方面:其一、准确理解零点定义  相似文献   

3.
记Δ(λ)是一个具有以π为周期的势q(x)的Hill方程的判别式,Hochstadt在文献[1]中给出了2+4(λ)仅有二重零点的充要条件,在文献[2]中给出了2-Δ(λ)的零点除最小零点外都是二重零点的充要条件。Hochstadt和Goldberg在文献[3],[4]中给出了2+Δ(λ)的零点除二个单零点外都是二重零点的充要条件。对r(x)=q~H(x)的AKNS方程具有q(x+x)=q(x),记2a_R(ξ)为其判别式,Yan-Chow Ma和Ablowitz在文献[5]中给出了1-a_R~2(ξ)的零点一些性质。本文给出了1—a_R(ξ)(或1+a_R(ξ))的零点都是二重零点或除两个单零点外都是二重零点(等价于具有特殊形式带)的充要条件。  相似文献   

4.
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   

5.
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   

6.
魏利  刘元星 《数学杂志》2016,36(3):573-583
本文研究了m-d增生映射的零点以及有限个m-d增生映射公共零点的迭代设计问题.利用Lyapunov泛函与广义f投影映射等技巧,在Banach空间中,证明了迭代序列强收敛或弱收敛到m-d增生映射的零点或有限个m-d增生映射的公共零点.与以往的相关研究工作相比,迭代设计中考虑了误差项、迭代格式被简化、限定条件被削弱.  相似文献   

7.
王天泽 《数学学报》1999,42(4):723-740
本文给出了DirichletL函数零点实部的一些定量上界估计及其在直线σ=1附近零点密度的定量上界估计.  相似文献   

8.
<正>导数题是高考的压轴题之一,本质上是用求导的方法来确定原函数的单调区间,进而解决函数的各种问题.通常的步骤是求原函数f(x)的导函数f′(x),接着令f′(x)=0解出f′(x)的零点,得到零点,单调区间就迎刃而解了.不过,有些函数的导数我们可以通过零点存在定理证明它确实有零点,但因为所求方程并非初等方程,无法算出其零点,即便继续求二次导也无济于事.我们将这种导数确实有零点却不能求出具体值的问题称为导数的"隐零点"问题.下面通过几道真题来介绍一些解决"隐零点"问题的方法.  相似文献   

9.
<正>我们通常把导数零点不可求问题称之为隐零点问题.隐零点并不是零点不存在,而是存在但无法用具体的数值或显性代数式把它表示出来.由于隐零点问题涉及函数与导数的核心知识,因此深受高考试题及各地模拟试题的喜爱.如何处理隐零点问题呢?下面就以一道高考题和一道模拟试题为例来总结隐零点问题的解决策略.  相似文献   

10.
特征标表各列零点个数不超过2个的有限群   总被引:1,自引:0,他引:1  
继续考虑特征标的零点对有限群结构的影响, 并给出了特征标表中 每列至多有两个零点的有限群的分类,从而完成了特征标表中每列至多 $p$ ($p$是群的阶的最小素因子)个零点的有限群的完全分类.  相似文献   

11.
《数学季刊》2016,(1):51-59
In this paper, we show the asymptotic limit for the 3D Boussinesq system with zero viscosity limit or zero diffusivity limit. By the classical energy method, we prove that as viscosity(or diffusivity) coefficient goes to zero the solutions of the fully viscous equations converges to those of zero viscosity(or zero diffusivity) equations, which extend the previous results on the asymptotic limit under the conditions of the zero parameter(zero viscosity ν = 0 or zero diffusivity η = 0) in 2D case separately.  相似文献   

12.
Zero dispersion and viscosity limits of invariant manifolds for focusing nonlinear Schrödinger equations (NLS) are studied. We start with spatially uniform and temporally periodic solutions (the so-called Stokes waves). We find that the spectra of the linear NLS at the Stokes waves often have surprising limits as dispersion or viscosity tends to zero. When dispersion (or viscosity) is set to zero, the size of invariant manifolds and/or Fenichel fibers approaches zero as viscosity (or dispersion) tends to zero. When dispersion (or viscosity) is nonzero, the size of invariant manifolds and/or Fenichel fibers approaches a nonzero limit as viscosity (or dispersion) tends to zero. When dispersion is nonzero, the center-stable manifold, as a function of viscosity, is not smooth at zero viscosity. A subset of the center-stable manifold is smooth at zero viscosity. The unstable Fenichel fiber is smooth at zero viscosity. When viscosity is nonzero, the stable Fenichel fiber is smooth at zero dispersion.  相似文献   

13.
Bouchet's conjecture asserts that each signed graph which admits a nowhere‐zero flow has a nowhere‐zero 6‐flow. We verify this conjecture for two basic classes of signed graphs—signed complete and signed complete bipartite graphs by proving that each such flow‐admissible graph admits a nowhere‐zero 4‐flow and we characterise those which have a nowhere‐zero 2‐flow and a nowhere‐zero 3‐flow.  相似文献   

14.
We define new parameters, a zero interval and a dual zero interval, of subsets in P- or Q-polynomial association schemes. A zero interval of a subset in a P-polynomial association scheme is a successive interval index for which the inner distribution vanishes, and a dual zero interval of a subset in a Q-polynomial association scheme is a successive interval index for which the dual inner distribution vanishes. We derive bounds of the lengths of a zero interval and a dual zero interval using the degree and dual degree respectively, and show that a subset in a P-polynomial association scheme (resp. a Q-polynomial association scheme) having a large length of a zero interval (resp. a dual zero interval) induces a completely regular code (resp. a Q-polynomial association scheme). Moreover, we consider the spherical analogue of a dual zero interval.  相似文献   

15.
The zero forcing number of a graph is the minimum size of a zero forcing set. This parameter is useful in the minimum rank/maximum nullity problem, as it gives an upper bound to the maximum nullity. Results for determining graphs with extreme zero forcing numbers, for determining the zero forcing number of graphs with a cut-vertex, and for determining the zero forcing number of unicyclic graphs are presented.  相似文献   

16.
《Journal of Algebra》2005,283(1):190-198
The zero divisor graph of a commutative semigroup with zero is a graph whose vertices are the nonzero zero divisors of the semigroup, with two distinct vertices joined by an edge in case their product in the semigroup is zero. We continue the study of this construction and its extension to a simplicial complex.  相似文献   

17.
In this paper, we study minimal zero norm solutions of the linear complementarity problems, defined as the solutions with smallest cardinality. Minimal zero norm solutions are often desired in some real applications such as bimatrix game and portfolio selection. We first show the uniqueness of the minimal zero norm solution for Z-matrix linear complementarity problems. To find minimal zero norm solutions is equivalent to solve a difficult zero norm minimization problem with linear complementarity constraints. We then propose a p norm regularized minimization model with p in the open interval from zero to one, and show that it can approximate minimal zero norm solutions very well by sequentially decreasing the regularization parameter. We establish a threshold lower bound for any nonzero entry in its local minimizers, that can be used to identify zero entries precisely in computed solutions. We also consider the choice of regularization parameter to get desired sparsity. Based on the theoretical results, we design a sequential smoothing gradient method to solve the model. Numerical results demonstrate that the sequential smoothing gradient method can effectively solve the regularized model and get minimal zero norm solutions of linear complementarity problems.  相似文献   

18.
A zero set of a holomorphic vector field is totally degenerate, if the endomorphism of the conormal sheaf induced by the vector field is identically zero. By studying a class of foliations generalizing foliations of C*-actions, we show that if a projective manifold admits a holomorphic vector field with a smooth totally degenerate zero component,then the manifold is stably birational to that component of the zero set.When the vector field has an isolated totally degenerate zero, we prove that the manifold is rational. This is a special case of Carrell's conjecture.  相似文献   

19.
In this paper, we prove the global in time regularity for the 2D Boussinesq system with either the zero diffusivity or the zero viscosity. We also prove that as diffusivity (viscosity) tends to zero, the solutions of the fully viscous equations converge strongly to those of zero diffusion (viscosity) equations. Our result for the zero diffusion system, in particular, solves the Problem no. 3 posed by Moffatt in [R.L. Ricca, (Ed.), Kluwer Academic Publishers, Dordrecht, The Netherlands, 2001, pp. 3-10].  相似文献   

20.
This study investigates two sixth grade students’ dilemmas regarding the parity of zero. Both students originally claimed that zero was neither even nor odd. Interviews revealed a conflict between students’ formal definitions of even numbers and their concept images of even numbers, zero, and division. These images were supported by practically based explanations relying on everyday contexts. By using mathematically based explanations that rely solely on mathematical notions, students were able to correctly conclude that zero is an even number. Extending the natural number system in elementary school to include zero can be used as springboard to encourage the use of mathematically based explanations.  相似文献   

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