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1.
Summary In the course of the numerical solution of Eigenvalue-problems connected with linear differential equations, the so-called encompassing theorems are of great importantce. We generalize in this paper the most important results of the theory, especially the encompassing-theorems, to the case of systems of differential equations. We expound further a method of perturbation which can be well applied also in the practice for the solution of Eigenvalue-problems connected with the systems. The problem acrose in connection with the fixation of the number of critical self-oscillation of turbine shovels.

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2.
借助于截尾技术和强逼近原理,本文研究了独立同分布(i.i.d.)序列最大部分和的精确渐近性,给出了更加一般的结果.  相似文献   

3.
一、一个共同存在的问题 1976年V.I.Arnold提出:向量场是由固定次数带有有理系数多项式来给定,是否能给出—个稳定性的判定准则? 王联、王慕秋在文[2]中解决了当n=2情况下的V.I.Arnold问题,杨世藩同志在文[3]中对n=3的情况进行了研究。并得到很好的结果,但在对于系统:  相似文献   

4.
I.i.d. random sequence is the simplest but very basic one in stochastic processes, and statistically self-similar set is the simplest but very basic one in random recursive sets in the theory of random fractal. Is there any relation between i.i.d. random sequence and statistically self-similar set? This paper gives a basic theorem which tells us that the random recursive set generated by a collection of i.i.d. statistical contraction operators is always a statistically self-similar set.  相似文献   

5.
I.I.D.随机变量序列矩完全收敛的精确渐近性   总被引:2,自引:0,他引:2  
{X,Xn;n≥1}为独立同分布的随机变量序列, EX=0,01 p/2满足E|X|r<∞,且E|X|3<∞,那么其中Z服从均值为0,方差为σ2的正态分布.  相似文献   

6.
设随机变量X1,X2,…iid;称Un=1≤i<j≤nXiXj,为两两乘积之和,本文意在给出 Un/n~2→0即文中(0.3)式成立的充分必要条件.我们在这部分工作中虽未能彻底解决这个问题,但却揭示出这类条件与Sn/n→0(Sn=ni=1Xi)之条件间的本质上的不同之处,就是说,这是一类不能完全用X1的矩来刻划的条件,它们要更为深层次地依赖于X1的尾分布性质.  相似文献   

7.
I.I.D.随机变量两两乘积之和的Hsu-Robbins型定理(Ⅰ)   总被引:3,自引:0,他引:3  
苏淳  梁汉营  王岳宝 《数学学报》2000,43(5):875-886
设随机变量X1,X2,…iid;称Un=1≤i<j≤nXiXj,为两两乘积之和,本文意在给出 Un/n~2→0即文中(0.3)式成立的充分必要条件.我们在这部分工作中虽未能彻底解决这个问题,但却揭示出这类条件与Sn/n→0(Sn=ni=1Xi)之条件间的本质上的不同之处,就是说,这是一类不能完全用X1的矩来刻划的条件,它们要更为深层次地依赖于X1的尾分布性质.  相似文献   

8.
苏淳  梁汉营  王岳宝 《数学学报》2000,43(6):1041-105
在本部分中,采用由 Levy函数(4.l)所确定的值bn取代(I)[1]中的1/n“位点”an,使得(I)中定理1中的附加条件(A)得以解除,从而获得了可以称之为Hsu-Robbins型的充分必要条件.作为推论,还给出了两个互为复制的iid随机变量三角阵对应行之和乘积的Kolmogorov强大数律.  相似文献   

9.
文献 [1]— [5 ]连续讨论了 I.J.Matrix定理的一些推广及应用 ,特别是文 [5 ]利用高阶微分的知识简明地给出了一个推广 ,本文给出其进一步的推广 .设 a0 ,a1 ,… ,an 是 n 1个互不相同且不为零的数 ,f ( x)是次数为 m的多项式 ,文 [5 ]讨论的是m相似文献   

10.
I.J.Matrix定理的更广泛推广   总被引:1,自引:1,他引:0  
I.J.Matrix定理的更广泛推广张之正(河南洛阳师专数学系471022)近年来,数学通报连续讨论了1.J.Matrix定理的一些推广及其应用(文[l],[2]用复交函数中的留数定理,文[3J用初等方法,文[4]用线性代数中的Vandermonde...  相似文献   

11.
LetB(p) andB(q) be Bernoulli shifts on {0, 1,...,d - 1}. Ifh(p)>h(q), it is a classical theorem of Sinai that there is a factor map takingB(p) toB(q). If, in addition,p stochastically dominatesq, we can ask whether there is such a factor map ϕ which is monotone: ϕ(x) i≤xi for each coordinatei of almost every pointx. Here we show that there is a monotone finitary code fromB(p) toB(q) in the case whereB(q) is a shift on two symbols.  相似文献   

12.
In this paper, we consider the preservation of stability by using the notion of twisted stability. As applications, (1) we show that moduli spaces of stable sheaves on K3 and abelian surfaces are irreducible and (2) we compute Hodge polynomials of some moduli spaces of stable sheaves on Enriques surfaces.  相似文献   

13.
The author has proposed a new approach to extrapolation of operators from the scale of Lebesgue spaces to the Orlicz spaces beyond this scale. In this article comprising two parts we develop some mathematical method that enables us to prove extrapolation theorems for arbitrary behavior of an operator in the Lebesgue scale (i.e., in the case when the norm of the operator is an arbitrary function of p) and also in the case when the basic scale is an interval of the Lebesgue scale with exponents separated from 1 or +∞. In this event, we face ill-posed problems of inversion of the classical Mellin and Laplace type integral transforms over nonanalytic functions in terms of their asymptotic behavior on the real axis and also the question about the properties of convolution type integral transforms on classes of N-functions. In the first part of the article we study integral representations for N-functions by expansions in power functions with a positive weight and the behavior of convolution type integral transforms on classes of N-functions.  相似文献   

14.
《代数通讯》2013,41(7):2711-2721
Abstract

In this note, we classify all the polarized Fano threefold (X, H) with Bs|H|¬ = ?. As corollaries we obtained that (1) the very ample part of the conjecture of Fujita holds for smooth Fano threefolds and (2) global Seshadri constants of ample divisors on Fano threefolds are bounded from below by 1 except three types of polarized Fano threefolds.  相似文献   

15.
Any real-valued nonlinear function in 0–1 variables can be rewritten as a multilinear function. We discuss classes of lower and upper bounding linear expressions for multilinear functions in 0–1 variables. For any multilinear inequality in 0–1 variables, we define an equivalent family of linear inequalities. This family contains the well-known system of generalized covering inequalities, as well as other linear equivalents of the multilinear inequality that are more compact, i.e., of smaller cardinality. In a companion paper [7]. we discuss dominance relations between various linear equivalents of a multilinear inequality, and describe a class of algorithms for multilinear 0–1 programming based on these results. Research supported by the National Science Foundation under grant ECS7902506 and by the Office of Naval Research under contract N00014-75-C-0621 NR 047-048.  相似文献   

16.
Given a prime idealP in a noetherian ringR we examine the following two properties: (1)P is Ore localizable. (2) The completion ofR atP is Noetherian. For rings satisfying the 2nd layer condition a strong connection is discovered between (1) and (2) and consequently questions by Goldie and McConnell are answered. As a corollary we also obtain a new characterization for non-maximal primitive idealP inR to satisfy (1), whereR is the enveloping algebra of complex solvable finite dimensional Lie algebra Dedicated to the memory of Shimshon Amitsur  相似文献   

17.
Let X 1,...,X n be a sequence of i.i.d. random variables taking values in an alphabet =1,...,q,q 2, with probabilities P(X a=i)=p i,a=1,...,n,i=1,...,q. We consider a fixed h-letter word W=w1...wh which is produced under the above scheme. We define by R(W) the number of appearances of W as Renewal (which is equal with the maximum number of non-overlapping appearances) and by N(W) the number of total appearances of W (overlapping ones) in the sequence X a 1 a1n under the i.i.d. hypothesis. We derive a bound on the total variation distance between the distribution (R(W)) of the r.v. R(W) and that of a Poisson with parameter E(R(W)). We use the Stein-Chen method and related results from Barbour et al. (1992), as well as, combinatorial results from Schbath (1995b) concerning the periodic structure of the word W. Analogous results are obtained for the total variation distance between the distribution of the r.v. N(W) and that of an appropriate Compound Poisson r.v. Related limit theorems are obtained and via numerical computations our bounds are presented in tables.  相似文献   

18.
19.
Summary A recursive way of constructing preconditioning matrices for the stiffness matrix in the discretization of selfadjoint second order elliptic boundary value problems is proposed. It is based on a sequence of nested finite element spaces with the usual nodal basis functions. Using a nodeordering corresponding to the nested meshes, the finite element stiffness matrix is recursively split up into two-level block structures and is factored approximately in such a way that any successive Schur complement is replaced (approximated) by a matrix defined recursively and thereform only implicitely given. To solve a system with this matrix we need to perform a fixed number (v) of iterations on the preceding level using as an iteration matrix the preconditioning matrix already defined on that level. It is shown that by a proper choice of iteration parameters it suffices to use \left( {1 - \gamma ^2 } \right)^{ - \tfrac{1}{2}} $$ " align="middle" border="0"> iterations for the so constructedv-foldV-cycle (wherev=2 corresponds to aW-cycle) preconditioning matrices to be spectrally equivalent to the stiffness matrix. The conditions involve only the constant in the strengthened C.-B.-S. inequality for the corresponding two-level hierarchical basis function spaces and are therefore independent of the regularity of the solution for instance. If we use successive uniform refinements of the meshes the method is of optimal order of computational complexity, if . Under reasonable assumptions of the finite element mesh, the condition numbers turn out to be so small that there are in practice few reasons to use an accelerated iterative method like the conjugate gradient method, for instance.Dedicated to the memory of Peter HenriciThe research of the second author reported here was supported in part by the Committee of Science, Bulgaria, under Grant No. 55/26.03.87  相似文献   

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