共查询到20条相似文献,搜索用时 421 毫秒
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正项级数敛散性比值判别法的一种改进 总被引:1,自引:0,他引:1
正项级数的敛散性的判定是一个占老的课题,前人已给出了大量的判别方法。达郎贝尔(J.D.Alembert)给出了如下判别法: 相似文献
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讨论Fourier级数收敛性判定定理的Dini判别法和Jordan判别法,并通过列举实例说明这两种方法是相互不包含的. 相似文献
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可读证明是不等式机器证明领域中的热点问题.针对具有对称零点的实轮换对称型,文章提出了其线性空间的一组基以及分拆算法和两种分拆形式用于对不等式进行可读证明研究.讨论了该线性空间的维数,以及轮换对称型半正定性的判别方法.给出了一类具有对称零点的轮换对称型的半正定性判定条件.大量实例表明此分拆方式在轮换对称型半正定性的判定及可读证明上具有很好的实用性. 相似文献
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文献[1]给出了判定阶数不大于5的对称矩阵偕正性的充分必要条件.本文在此基础上,进一步给出了它们严格偕正的条件,并提出了三个算法,它们能够用来有效地判定3,4,5阶对称矩阵严格偕正、偕正或非偕正. 相似文献
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We demonstrate that quotients of septic theta functions appearing in Ramanujan’s Notebooks and in Klein’s work satisfy a new coupled system of nonlinear differential equations with symmetric form. This differential system bears a close resemblance to an analogous system for quintic theta functions. The proof extends an elementary technique used by Ramanujan to prove the classical differential system for normalized Eisenstein series on the full modular group. In the course of our work, we show that Klein’s quartic relation induces symmetric representations for low-weight Eisenstein series in terms of weight one modular forms of level seven. 相似文献
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Christian Batut. 《Mathematics of Computation》2001,70(233):395-417
From the classical Voronoi algorithm, we derive an algorithm to classify quadratic positive definite forms by their minimal vectors; we define some new invariants for a class, for which several conjectures are proposed. Applying the algorithm to dimension 5 we obtain the table of the 136 classes in this dimension, we enumerate the 118 eutactic quintic forms, and we verify the Ash formula.
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S.M. Rump 《BIT Numerical Mathematics》2006,46(2):433-452
We present a computational, simple and fast sufficient criterion to verify positive definiteness of a symmetric or Hermitian
matrix. The criterion uses only standard floating-point operations in rounding to nearest, it is rigorous, it takes into account
all possible computational and rounding errors, and is also valid in the presence of underflow. It is based on a floating-point
Cholesky decomposition and improves a known result. Using the criterion an efficient algorithm to compute rigorous error bounds
for the solution of linear systems with symmetric positive definite matrix follows. A computational criterion to verify that
a given symmetric or Hermitian matrix is not positive definite is given as well. Computational examples demonstrate the effectiveness of our criteria.
AMS subject classification (2000) 65G20, 15A18 相似文献
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《Journal of Pure and Applied Algebra》1994,96(3):279-297
We give a criterion for determining the existence of nonzero symmetric invariant bilinear forms on vertex operator algebras and we establish an analogue of the Cartan criterion for semi-simplicity. 相似文献
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Lu YANG~ 《中国科学A辑(英文版)》2007,50(11):1611-1620
By means of dimension-decreasing method and cell-decomposition,a practical algorithm is proposed to decide the positivity of a certain class of symmetric polynomials,the numbers of whose elements are variable.This is a class of mechanically decidable problems beyond Tarski model.To im- plement the algorithm,a program nprove written in maple is developed which can decide the positivity of these polynomials rapidly. 相似文献
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对一类对称五次近Hamilton系统在五次对称摄动下产生的极限环数目进行了研究.通过多参数摄动理论和定性分析,得到这类对称摄动下的五次系统至少可以存在28个极限环. 相似文献
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Dai Hua 《高等学校计算数学学报(英文版)》2000,9(1):91-110
1 IntroductionInmanyapplicationsweneedtosolvemultiplesystemsoflinearequationsAx(i) =b(i) ,i=1,… ,s (1)withthesamen×nrealsymmetriccoefficientmatrixA ,butsdifferentright handsidesb(i) (i=1,… ,s) .Ifalloftheright handsidesareavailablesimultaneously ,thentheseslinearsyste… 相似文献
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Invariant symmetric bilinear forms for reflection groups 总被引:1,自引:0,他引:1
In this paper we describe a connection between Vinberg's criterion for the existence of an invariant symmetric bilinear form
for a geometric representation of a Coxeter groups and other criteria which are formulated in terms of conjugation invariant
sets of reflections generating a given group. Similar methods lead to the result that every non-symmetrizable Kac--Moody Lie
algebra contains a non-symmetrizable subalgebra of rank 3. Finally we explain how the results for symmetric bilinear forms
can also be obtained for skew-symmetric forms.
Received 3 March 2000. 相似文献
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We give a sufficient condition for a class of jump-type symmetric Dirichlet forms on ? d to be conservative in terms of the jump kernel and the associated measure. Our condition allows the coefficients dominating big jumps to be unbounded. We derive the conservativeness for Dirichlet forms related to symmetric stable processes. We also show that our criterion is sharp by using time changed Dirichlet forms. We finally remark that our approach is applicable to jump-diffusion type symmetric Dirichlet forms on ? d . 相似文献
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We propose an algorithm that transforms a real symplectic matrix with a stable structure to a block diagonal form composed of three main blocks. The two extreme blocks of the same size are associated respectively with the eigenvalues outside and inside the unit circle. Moreover, these eigenvalues are symmetric with respect to the unit circle. The central block is in turn composed of several diagonal blocks whose eigenvalues are on the unit circle and satisfy a modification of the Krein-Gelfand-Lidskii criterion. The proposed algorithm also gives a qualitative criterion for structural stability. 相似文献