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1.
本文我们将介绍三种不同于文献[1]中的正则.分别记作[正则]1、[正则]2、[正则]3。并讨论它们之间以及与[1]中正则的关系,我们将证明[正则]2不仅拓宽了原正则[1]。而且还具有相应好的性质。同时还将证明[正则]3在可拓扑生成条件下与[1]中正则是等价的。  相似文献   

2.
有理样条不可约解的行列式表示   总被引:3,自引:0,他引:3  
1引言在文[1]中,对于剖分a=x0<x1<…<mn=b及给定的y0,y1,…, …,L+M-1,我们构造了有理样条S[L,M(x)Q[L,M]为次数不超过m的多项式全体.在[1]中,已经讨论了S[L,M](x)的存在性,并指出:若问题(1)(2)(3)可解,则解唯一这里总假设问题(1)(2)(3)可解.2有理样条解不可约的充要条件由S[L,M](x)的依区间递推算法(见[1]),我们只需讨论[x0,x1]上的情形.当[X0,x1]时,将S[L,M] (x),P[L,M] (x)和Q[L,M](…  相似文献   

3.
陈贻源[1]和张文修[2]分别引入了Fuzzy弱自反关系的定义和有关的证明。本文在[1]和[2]给出Fuzzy弱自反关系定义的基础上,对[1]和[2]的有关Fuzzy弱自反关系证明提出了异议,并给出了新的证明。  相似文献   

4.
数学问题解答1997年11月号问题解答(解答由问题提供人给出)1101设a,b,c,d,e是正整数,且a<b<c<d<e,[m,n]是m与n的最小公倍数.求:1[a,b]+1[b,c]+1[c,d]+1[d,e]的最大值.解设S=1[a,b]+1[b...  相似文献   

5.
也谈费马─斯坦勒尔问题刘凯年(重庆师范学院数学系630047)文献[1](见本刊1994年第3期)、[2]、[3]用不同方法解决了费马一斯坦勒尔问题.但[3]为实验解,未给出严格的数学证明,[1]、[2]的方法又比较繁难,且[1]的方法很难为中学生所...  相似文献   

6.
本文给出了应用矩阵方法求矩阵A的加权广义逆A^[1,2,W3],A^[1,2,w3]和A^[1,2][w,w]的充要条件。  相似文献   

7.
也谈对数大小的比较万兴灿(湖北省宜昌市第一中学443000)探究文[1]、[2]、[3]获益非浅,对比言之,文[3]方法从形式到实质仍是文[2]的方法.本文倾向文[1]处理方法,加以推广,则可较全面、简捷地解决对数大小的比较.定理1设1<a<b,m>...  相似文献   

8.
指出了[1]的定理2中的一个错误,推广了[1]中定理1给出的华罗庚-王中烈型不等式,避开控制不等式与动态规划模型等专门工具,改用较为初等的平均值不等式证明之,使改正后的[1]中的定理2成其推论  相似文献   

9.
§1. IntroductionIn1908,E.Landauintroducedthefollowingwellknownsequenceofoperators[1]Ln[f(t);x]=Kn∫1-1f(t)[1-(t-x)2]ndt,    (1.1)where     Kn=[∫1{-1(1-t2)ndt]-1~nπ  (n→∞).(1.1)wasusedintheproofoftheWeierstrassTheorem.Sincethen,theapproximationprop-ert…  相似文献   

10.
文[1] 利用文[3]的结果证明了一般有约束线性模型下参数的最优估计的方差协方差阵与有约束错误指定模型下最优估计的方差协方差阵间差是非负定的充分条件[2]也是必要的。更进一步,文[4]将[1]中的定理1推广到奇异线性模型上。该文的主要目的是证明了[2]的猜想在奇异线性模型中也是正确的,同时,推广了[1]中的定理2。  相似文献   

11.
12.
Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.  相似文献   

13.
张丽娜  吴建华 《数学进展》2008,37(1):115-117
One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the'living world. In his seminal paper "The Chemical Basis of Morphogenesis", Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates(1990) on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing's prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows  相似文献   

14.
We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.  相似文献   

15.
In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).  相似文献   

16.
It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.  相似文献   

17.
18.
正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with  相似文献   

19.
正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.  相似文献   

20.
A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].  相似文献   

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