共查询到20条相似文献,搜索用时 171 毫秒
1.
本文针对F-空间中闭算子方程的一般逼近格式,研究其相容性、收敛性和稳定性之间的关系.所得的主要结果是:这种一般逼近格式在相容性条件下,其收敛性与稳定性是等价的.此定理可以看作是对Lax等价原理的推广,是求解第一类闭算子方程的一般逼近格式的基本定理.为得到这一主要结果,本文还给出了F-空间中的一条基本定理,众所周知的一致有界原理,闭图像定理和开映像定理是其简单推论. 相似文献
2.
本文研究了在险值和 Lp-空间上的连续一致风险度量之间的关系.利用凸集分离定理和截尾逼近方法,获得了在险值可以用 Lp-空间上的连续一致风险度量表示的结果,并且得到了 Lp-空间上的表示定理的一种新的证明方法.它们分别是文献[2]的相关结论从 L∞-空间到 Lp-空间上的推广和对Inoue [4]做的一些补充证明. 相似文献
3.
本文研究了 Fp空间上的复合算子的几个问题.应用泛函分析的方法研究了 Fp(相应地, Fp,0)空间到Bloch空间的复合算子的有界性和紧性的若干充分和必要条件.此外,也刻画了当1 ≤ p < ∞时从Bloch空间到 Fp空间的等距复合算子并且证明了当0 < p < ∞时 Fp,0上的复合算子不具有Fredholm性. 相似文献
4.
本文研究了一类重要的形如 F= α + εβ + β arctan( β/ α) ( ε为常数)的弱Berwald ( α, β)-度量.利用 S-曲率公式,获得了这类度量为弱Berwald度量的充要条件.并且还证明了 F为具有标量旗曲率的弱Berwald度量当且仅当它们为Berwald度量且旗曲率消失. 相似文献
5.
本文研究了在局部凸Hausdorff拓扑向量空间中的集值映射 ε-严有效次梯度和 ε-严有效次微分的问题.利用凸集分离定理的方法,获得了该次微分(次梯度)的存在性及它的一些性质,推广了一类参数扰动集值优化问题在 ε-严有效意义下的稳定性的结果. 相似文献
6.
本文研究了环 Fp+ vFp上互补对偶(1-2 v)-常循环码.利用环 Fp+ vFp上(1-2 v)-常循环码的分解式 C= vC1-v ⊕(1- v) Cv,得到了环 Fp+ vFp上互补对偶(1-2 v)-常循环码的生成多项式.然后借助从 Fp+ vFp到 Fp2的Gray映射,证明了环 Fp+ vFp上互补对偶(1-2 v)-常循环码的Gray像是 Fp的互补对偶循环码. 相似文献
7.
本文研究了行 m-NSD随机变量阵列的完全收敛性问题.主要利用 m-NSD随机变量的Kolmogorov型指数不等式,获得了行 m-NSD随机变量阵列的完全收敛性定理,将Hu等(1998)andSung等(2005)的结果从独立情形推广到了 m-NSD随机变量阵列.本文的结论同样推广了Chen等(2008),Hu等(2009),Qiu等(2011)和Wang等(2014)的结果. 相似文献
8.
本文研究了矩阵方程 AX = B 的Hermitian R-对称最大秩和最小秩解问题. 利用矩阵秩的方法, 获得了矩阵方程 AX = B有最大秩和最小秩解的充分必要条件以及解的表达式, 同时对于最小秩解的解集合, 得到了最佳逼近解. 相似文献
9.
本文研究了推广的Roper-Sufiridge算子保持一些双全纯映照子族的性质.利用一些双全纯映照子族的定义,得到了推广后的Roper-Sufiridge算子在复Banach空间单位球上保持 ρ次抛物形 β型螺形映照及强 α次殆星形映照的性质,由此得到复Hilbert空间上推广的Roper-Sufiridge算子的相应性质,推广了已有的结论. 相似文献
10.
本文研究了 p-可除 kG-模,这是一类由群阶的素数因子来控制的模类.利用Heller算子,证明了 n次Heller算子置换非投射不可分解 p-可除 kG-模的同类;利用模的诱导和限制方法,证明了若 H是 G的强 p-嵌入子群,则Green对应建立了不可分解 p-可除 kG-模的同构类与不可分解 p-可除kH-模的同构类之间的一一对应.推广了不可分解相对投射 kG-模上的Green对应. 相似文献
11.
Let E, F be two Banach lattices with E order continuous. If F can be mapped positively onto E then the dual F* contains a weak * -null sequence of positive and norm-one elements (Theorem 1). This is a Banach-lattice version of the classical Josefson-Nissenzweig theorem. It is an immediate consequence of the dual characterization of order continuity: E is order continuous iff E is Dedekind complete and every norm-one and pairwise disjoint sequence in E* is weak *-null (Theorem 2). 相似文献
12.
The purpose of this paper is to state and prove a theorem (the CMS Theorem) which generalizes the familiar Ceva's Theorem and Menelaus' Theorem of elementary Euclidean geometry. The theorem concerns n -acrons (generalizations of n-gons) in affine space of any number of dimensions and makes assertions about circular products of ratios of lengths, areas, volumes, etc. In particular it contains, as special cases, many results in this area proved by earlier authors. 相似文献
13.
Four ways of proving Menger's Theorem by induction are described. Two of them involve showing that the theorem holds for a finite undirected graph G if it holds for the graphs obtained from G by deleting and contracting the same edge. The other two prove the directed version of Menger's Theorem to be true for a finite digraph D if it is true for a digraph obtained by deleting an edge from D. 相似文献
14.
In this paper we are dealing with positive linear functionals on W-algebras. We introduce the notion of a positive linear functional with ∑-property (see Definition 1.1). It is shown that each positive linear functional on a W-algebra possesses the ∑-property. This fact allows to give a short proof of UHLMANN's conjecture on unitary mixing in the state space of a W-algebra. In proving our main theorem (see Theorem 1.2.) we obtain some results on positive linear functionals and orthoprojections which are useful in other context, too. 相似文献
15.
Abstract The classical theorem of Dunford and Pettis identifies the bounded, uniformly integrable subsets of L 1(μ) with the relatively weakly compact sets. Another characterization of uniform integrability is given in a theorem of De La Vallée Poussin which states that a subset K of L1 (μ) is bounded and uniformly integrable if and only if there is an N-function F so that sup{f F(f)dμ: f ε K} < ∞. De La Vallée Poussin's theorem is the focal point of the fmt part of this paper as well as the driving force for the results in the second part. We refine and improve this theorem in several directions. The theorem of De La Vallée Poussin does not, for instance, specify just how well the function F can be chosen. It gives little additional information in case the set in question is relatively norm compact in L1 (μ). Finally it gives no information on the structure of the set in the corresponding Band space of F-integrable functions. More specifically we establish the fact that a subset K of L1 is relatively compact if and only if there is an N-function F ε δ' so that K is relatively compact in L*F. Furthermore we prove that a subset K of L1 is relatively weakly compact if and only if there is an N-function F ε δ' so that K is relatively weakly compact in L*F. We then go on to show that a large class of non-reflexive Orlicz spaces has the weak Band-Saks property, by establishing a result for these spaces, very similar to the Dunford-Pettis theorem for L1. 相似文献
16.
By means of the general form of Stokes' theorem on manifolds a divergence theorem is derived for hypersurfaces which bound a compact region of ann-dimensional Finsler spaceF
n
. In general the integrand of then-fold volume integral will depend on the covariant derivatives of an arbitrary vector field which defines the element of support; certain conditions under which this dependence may be circumvented are discussed. The scalar curvature ofF
n
is expressed in terms of the divergence of a certain vector field: forn=2 this formula reduces to a particularly simple form, and its substitution into the aforementioned divergence theorem gives rise to a formula which represents a generalization of the classical Gauss-Bonnet Theorem. 相似文献
17.
Let ( M, F) be a closed C
∞ Finsler manifold. The lift of the Finsler metric F to the universal covering space defines an asymmetric distance [( d)\tilde]{\widetilde d} on [( M)\tilde]{\widetilde M}. It is well-known that the classical comparison theorem of Aleksandrov does not exist in the Finsler setting. Therefore,
it is necessary to introduce new Finsler tools for the study of the asymmetric metric space ([( M)\tilde], [( d)\tilde]){(\widetilde M, \widetilde d)}. In this paper, by using the geometric flip map and the unstable-stable angle introduced in [ 2], we prove that if ( M, F) is a closed Finsler manifold of negative flag curvature, then ([( M)\tilde], [( d)\tilde]){(\widetilde M, \widetilde d)} is an asymmetric δ-hyperbolic space in the sense of Gromov. 相似文献
18.
A theorem of Douady says that the absolute Galois group of a rational function field F( x) in one variable over an algebraically closed field F of characteristic 0 is a free profinite group. A new method is proposed to extend Douady’s theorem from the case of the complex
number field F = ℂ to the case of an arbitrary field. 相似文献
19.
Like the classical Gram-Schmidt theorem for symplectic vector spaces, the sheaf-theoretic version (in which the coefficient
algebra sheaf A is appropriately chosen) shows that symplectic A-morphisms on free A-modules of finite rank, defined on a topological space X, induce canonical bases (Theorem 1.1), called symplectic bases. Moreover (Theorem 2.1), if (ℰ, φ) is an A-module (with respect to a ℂ-algebra sheaf A without zero divisors) equipped with an orthosymmetric A-morphism, we show, like in the classical situation, that “ componentwise” φ is either symmetric (the (local) geometry is orthogonal) or skew-symmetric (the (local) geometry is symplectic). Theorem 2.1 reduces to the classical
case for any free A-module of finite rank. 相似文献
20.
In this paper we prove that if an affine algebraic group (in characteristic zero) has all its conjugacy classes closed, then it is nilpotent. A classical result (called sometimes the Kostant-Rosenlicht Theorem) guarantees that if an affine algebraic group G is unipotent, then all its orbits on affine varieties are closed. We prove the converse of that theorem in arbitrary characteristics. 相似文献
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