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Open covering and metric regularity are properties playing a crucial role in several topics of modern variational analysis. Here their stability behaviour in the presence of perturbations is investigated in a purely metric setting. Some results in this sense are obtained, which lead to extend the known Milyutin theorem, and then to expand the concept of radius of regularity, a quantitative measure of the open covering stability. Estimations for the latter in terms of covering moduli are provided.  相似文献   

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In this note I shall prove that if L is a finite-dimensionalLie algebra over a field F of characteristic zero which is generatedas an algebra by a set of elements {e1, e2,...,ek}, then theuniversal enveloping algebra U(L) of L is linearly generatedby monomials spanned by the elements {ei} of an a priori boundedwidth. As an application, a criterion of Kostant for a leftideal of U(L) to be of finite codimension is proved by purelyalgebraic means.  相似文献   

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Let D be a bounded domain in C n (n>1) with a connected smooth boundary D and let f be a continuous function on D. We consider conditions (generalizing those of the Hartogs–Bochner theorem) for holomorphic extendability of f to D. As a corollary we derive some boundary analog of Morera's theorem claiming that if the integrals of f vanish over the intersection of the boundary of the domain with complex curves in some class then f extends holomorphically to the domain.  相似文献   

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Heinz König 《Positivity》2008,12(1):105-118
The traditional representation theorems after Daniell-Stone and Riesz were in a kind of separate existence until Pollard-Topsøe 1975 and Topsøe 1976 were the first to put them under common roofs. In the same spirit the present article wants to obtain a unified representation theorem in the context of the author’s work in measure and integration. It is an inner theorem like the previous ones. The basis is the recent comprehensive inner Daniell-Stone theorem, so that in particular there are no a priori assumptions on the additive behaviour of the data.  相似文献   

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Hall's theorem for bipartite graphs gives a necessary and sufficientcondition for the existence of a matching in a given bipartitegraph. Aharoni and Ziv have generalized the notion of matchabilityto a pair of possibly infinite matroids on the same set andgiven a condition that is sufficient for the matchability ofa given pair (M, W) of finitary matroids, where the matroidM is SCF (a sum of countably many matroids of finite rank).The condition of Aharoni and Ziv is not necessary for matchability.The paper gives a condition that is necessary for the existenceof a matching for any pair of matroids (not necessarily finitary)and is sufficient for any pair (M, W) of finitary matroids,where the matroid M is SCF.  相似文献   

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本文得出一个一般形式的拓扑型的极大极小定理,它包含的主要结果为特例,而且回答了[3]中提出的一个未解决问题。  相似文献   

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《代数通讯》2013,41(7):2723-2732
Abstract

Let L be a line bundle on a smooth curve C, which defines a birational morphism onto Φ(C) ? P r . We prove that, under suitable assumptions on L, which are satisfied by Castelnuovo's curves, a generic section in H 0(C, L 2) can be written as α2 + β2 + γ2, with α, β, γ ∈ H 0(C, L). If there are no quadrics of rank 3 containing Φ(C), this is true for any section. For canonical curves, this gives a non linear version of Noether's Theorem.  相似文献   

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A theorem due to de Bruijn and Post states that if a real valued function f defined on [0, 1] is not Riemann-integrable, then there exists a uniformly distributed sequence { xi} such that the averages do not admit a limit. In this paper we will prove a quantitative version of this result and we will extend it to functions with values in ℝd.  相似文献   

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Dedicated to the memory of Paul Erdős Schur's partition theorem states that the number of partitions of n into distinct parts (mod 3) equals the number of partitions of n into parts which differ by 3, where the inequality is strict if a part is a multiple of 3. We establish a double bounded refined version of this theorem by imposing one bound on the parts (mod 3) and another on the parts (mod 3), and by keeping track of the number of parts in each of the residue classes (mod 3). Despite the long history of Schur's theorem, our result is new, and extends earlier work of Andrews, Alladi-Gordon and Bressoud. We give combinatorial and q-theoretic proofs of our result. The special case L=M leads to a representation of the generating function of the underlying partitions in terms of the q-trinomial coefficients extending a similar previous representation of Andrews. Received November 18, 1999 Research of the first author supported in part by NSF Grant DMS-0088975.  相似文献   

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Our objective in this paper is to prove an Implicit Function Theorem for general topological spaces. As a consequence, we show that, under certain conditions, the set of the invertible elements of a topological monoid X is an open topological group in X and we use the classical topological group theory to conclude that this set is a Lie group.  相似文献   

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We prove that if all the rank-one bounded operators on a Banachspace X attain their numerical radii, then X must be reflexive,but the converse does not hold. In fact, every reflexive spacewith basis can be renormed in such a way that there is a rank-oneoperator not attaining the numerical radius. 1991 MathematicsSubject Classification 47A12, 46B10.  相似文献   

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Let N be a normal subgroup of a finite group G. Let ϕ be an irreducible Brauer character of N. Assume π is a set of primes and χ(1)/ϕ(1) is a π′-number of any χ∈IBr p (G/ϕ). If p∤|G:N|, and N is p-solvable, then G/N has an abelian-by-metabelian Hall-π subgroup; If p∉π then G/N has a metabelian Hall-π subgroup. Received February 22, 2000, Accepted May 9, 2001  相似文献   

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Suppose that G is a finite group and f is a complex-valued function on G. f induces a (left) convolution operator from L 2(G) to L 2(G) by g ? f *g{g \mapsto f \ast g} where
f *g(z) : = \mathbbExy=zf(x)g(y)  for  all  z ? G.f \ast g(z) := \mathbb{E}_{xy=z}f(x)g(y)\,\, {\rm for\,\,all} \, z \in G.  相似文献   

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In this paper,we initiate a study of S-fuzzy ideal(filter) of a lattice where S stands for a meet semilattice.A S-fuzzy prime ideal(filter) of a lattice is defined and it is proved that a S-fuzzy ideal(filter) of a lattice is S-fuzzy prime ideal(filter) if and only if any non-empty α-cut of it is a prime ideal(filter).Stone's theorem for a distributive lattice is extended by considering S-fuzzy ideals(filters).  相似文献   

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Guédon  Olivier 《Positivity》1997,1(1):1-5
Using Gordon's inequalities, we give a short proof of the existence of an embedding T:l2k to ln such that ||T||||T-1|| c k/ln(1+n/k). In the same way, we give a new proof of a theorem of Milman and Schechtman (1995).  相似文献   

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The aim of the paper is to prove a monogenic version of classical M. Riesz theorem on harmonic conjugates in the framework of quaternionic analysis in \({\mathbb{R}^{4}}\) . Our proof is subharmonic and somewhat simpler than that for less general Riesz-Stein-Weiss systems of harmonic conjugate functions.  相似文献   

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