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1.
Banach空间中Moore-Penrose广义逆与不适定边值问题   总被引:17,自引:3,他引:14  
设X,Y为Banach空间,D(A)X,A:D(A)→Y为具有闭值域的闭稠定线性算子.本文不假设A具有“定义域可分解”条件[18],引入A的Moore-Penrose广义逆A+.与M.Z.Nashed引入的不同,A+一般非线性.本文在空间X,Y的一定几何框架下,证得A+的存在唯一性、极小性、连续性,并给出了线性的充要条件,便于将A+应用于方程、优化、控制等问题.作为应用,本文第二部分利用Moore-Penrose广义逆讨论空间LP(Ω)(1<P)中一类不适定的边值问题.在另文,给出广义逆在控制论中的应用.  相似文献   

2.
解不适定算子方程的一个定常二步隐式迭代法   总被引:1,自引:0,他引:1  
唐建国  贺国强 《计算数学》2000,22(4):473-486
1.引言 设X,Y是两个Hilbert空间,A:X→Y是有界线性算子,考虑算子方程 Ax=y(1.1)如果A的值域R(A)在Y中非闭,则方程(1.1)是不适定的[1].许多应用科学中都归结出这一类方程,特别地,许多反问题是不适定的[2,3].本文考虑方程(1.1)的 Moore-Penrose广义解,这里A是算子A的Moore-Penrose广义逆[1].A+y存在当且仅当本文均作这一假设.在实际中,通常代替(1.1)的是扰动方程这里右端项,为一给定的误差水平,Q是Y到R(A)的正交投影算子.对扰…  相似文献   

3.
紧致齐性空间上的调和分析──H~p空间的对偶空间   总被引:1,自引:0,他引:1  
本文证明了紧致齐性空间M上的原子Hardy空间(M)的对偶空间即为Campanato空间.特别当p=1时,H1(M)的对偶空间即为有界平均振动函数的空间BMO(M).  相似文献   

4.
该文对 Banach空间 LP(Ω)中二阶椭圆方程非齐次不适定 Neumann 问题,引入伪变分解的概念,应用Banach空间几何及[3]中关于Banach空间中线性算子的Moore-Penrose广义逆.证明了上述伪变分解为最小范数极值解,从而为适定的.  相似文献   

5.
Moore-Penrose Inverses and Group Inverses of Block k-Circulant MatricesMoore-PenroseInversesandGroupInversesofBlockk-Circulan...  相似文献   

6.
该文对Banach空间犔犘(Ω)中二阶椭圆方程非齐次不适定Neumann问题,引入伪变分解的概念,应用Banach空间几何及[3]中关于Banach空间中线性算子的Moore Penrose广义逆,证明了上述伪变分解为最小范数极值解,从而为适定的.  相似文献   

7.
复射影空间中复子流形的一点注记曹锡芳(杨州师范学院数学系,225002)关键词复射影空间,截面曲率.分类号AMs(1991)53C55,53C42/CCLO186.16设CP ̄(n+p)是具有Fubini-study度量的复n+p维射影空间,它的常数...  相似文献   

8.
关于具有泛分解的态射的广义逆   总被引:12,自引:1,他引:11  
曹永知  朱萍 《数学学报》2001,44(3):559-566
本文给出了预加范畴中具有泛分解的态射的(1,…,i)-逆存在的条件及其表达式.特别地,得到了这类态射的Moore-Penrose边和群逆存在的一些新的充要条件和新的表达式.  相似文献   

9.
关于度量投影的连续性   总被引:10,自引:1,他引:9  
王建华 《应用数学》1995,8(1):80-84
本文引入的Banach空间的(C-I)、(C-Ⅱ),(C-Ⅲ)等几何性质,证明了如下结果。设M是Banach空间的逼近凸子集,如果Banach空间有性质(C-I),(C-Ⅱ)(C-Ⅲ),则度量投影PM连续(范数-范数上半连续,范数-弱上半连续)。这些结果推广了文(4,7,8)相应的定理。最近,D.Kutzarova,Bor-Luh Lin等引入了一些新的凸性空间,本文还研究了这些凸性空间中度量投影  相似文献   

10.
1999年全国初中数学联合竞赛第一试第2道题是:△ABC的周长是24,M是AB的中点,且MC=MA=5,则△ABC的面积是().(A)12(B)16(C)24(D)30解∵MA=MB=MC=5,∴∠ACB=90°.已知周长是24,则AC+BC=14,...  相似文献   

11.
We show that, under some additional set-theoretical assumptions which are equiconsistent with the existence of a measurable cardinal, there is a weak Asplund space whose dual, equipped with the weak* topology, is not in Stegall's class. This completes a result by Kenderov, Moors and Sciffer.

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12.
In this paper, we use the game characterization of Kenderov and Moors [11] to construct an example of a non-fragmentable Banach space. More precisely, we will show that ifX is the tree-complete Banach algebra of Haydon and Zizler [3], (X/c 0, weak) is not fragmentable by any metric. In particular, this shows thatX/c 0 cannot be equivalently renormed to be rotund.  相似文献   

13.
Banach空间中线性算子的Tseng度量广义逆   总被引:11,自引:2,他引:9  
在 Banach空间中,利用 Banach几何方法及度量投影算子,将 E.H.Moors的学生,曾远荣(Y.Y. Tseng)在 Hilbert空间中为线性算子引入的 Tseng广义道,推广到 Banach空间,引入 Tseng度量广义逆(此时的 Tseng度量广义逆一般为齐性算子,而非线性算子),利用 Banach空间对偶映射与广义正交分解定理给出 Tseng度量广义道存在的充分必要条件.讨论了最大Tseng度量广义逆在最优化,控制论及微分方程不适定问题有着直接应用的一些基础性质.  相似文献   

14.
《Optimization》2012,61(1):11-29
Recently, Borwein and Moors introduced a new class of real-valued locally Lipschitz functions, that are similar in nature and definition to Valadier's saine functions, which they called arc-wise essentially smooth. They showed that if g n M is an arc-wise essentially smooth real-valued function and f m M n is strictly differentiable almost everywhere, then g f m M is also strictly differentiable almost everywhere. They also showed that this class possesses strong closure properties. In this paper, we give an appropriate extension of this class to locally Lipschitz mappings defined between Banach spaces. We show that the results established by Borwein and Moors in the finite dimensional setting also hold for arc-wise essentially smooth mappings defined between Banach spaces.  相似文献   

15.
Let f:X×KR be a separately continuous function and C a countable collection of subsets of K. Following a result of Calbrix and Troallic, there is a residual set of points xX such that f is jointly continuous at each point of {xQ, where Q is the set of yK for which the collection C includes a basis of neighborhoods in K. The particular case when the factor K is second countable was recently extended by Moors and Kenderov to any ?ech-complete Lindelöf space K and Lindelöf α-favorable X, improving a generalization of Namioka's theorem obtained by Talagrand. Moors proved the same result when K is a Lindelöf p-space and X is conditionally σ-α-favorable space. Here we add new results of this sort when the factor X is σC(X)-β-defavorable and when the assumption “base of neighborhoods” in Calbrix-Troallic's result is replaced by a type of countable completeness. The paper also provides further information about the class of Namioka spaces.  相似文献   

16.
In this paper we propose several goodness-of-fit tests based on robust measures of skewness and tail weight. They can be seen as generalisations of the Jarque–Bera test (Bera and Jarque in Econ Lett 7:313–318, 1981) based on the classical skewness and kurtosis, and as an alternative to the approach of Moors et al. (Stat Neerl 50:417–430, 1996) using quantiles. The power values and the robustness properties of the different tests are investigated by means of simulations and applications on real data. We conclude that MC-LR, one of our proposed tests, shows the best overall power and that it is moderately influenced by outlying values.  相似文献   

17.
In various countries, including the Netherlands and Austria, legislation is such that the question whether a specific game should be considered as a game of chance or as a game of skill is predominant in the exploitation decision of private casinos. This paper aims for an objective and operational criterium to quantify the relative level of skill with respect to chance of games in order to provide a juridical tool for classification. The various concepts are illustrated by means of variations of Poker. This research is sponsored by Novomatic Holland BV, Nieuwegein. We acknowledge comments and advise from Marcel Dreef, Stef Tijs and Hans Moors of Tilburg University, of Wilfried Grossmann of the University of Vienna and of Peter Zanoni of the Concord Card Casino in Vienna.  相似文献   

18.
Bertin and Theodorescu (1984,Statist. Probab. Lett.,2, 23–30) developed a characterization of discrete unimodality based on convexity properties of a discretization of distribution functions. We offer a new characterization of discrete unimodality based on convexity properties of a piecewise linear extension of distribution functions. This reliance on functional convexity, as in Khintchine's classic definition, leads to variance dilations and upper bounds on variance for a large class of discrete unimodal distributions. These bounds are compared to existing inequalities due to Muilwijk (1966,Sankhy, Ser. B,28, p. 183), Moors and Muilwijk (1971,Sankhy, Ser. B,33, 385–388), and Rayner (1975,Sankhy, Ser. B,37, 135–138), and are found to be generally tighter, thus illustrating the power of unimodality assumptions.  相似文献   

19.
仿照距离空间,2-距离空间中的一些概念,引入了p-距离空间及p-距离空间中的一些基本概念.根据研究2-距离空间中不动点理论的思想和方法,利用泛函分析的理论,对p-距离空间中的不动点问题进行了研究.把2.距离空间中压缩型映像的不动点理论移植到了p-距离空间中,形成了p-距离空间中压缩型映像的一些基本不动点理论.其距.离空...  相似文献   

20.
Two geometries can be considered in the structure of linear complements: an affine spine space and an affine space. An affine spine space arises from a space of pencils. In terms of this geometry an affine partial line space may be defined. It is extensible to the affine space. Automorphisms of the affine spine space are automorphisms of appropriate affine space.  相似文献   

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