共查询到20条相似文献,搜索用时 31 毫秒
1.
Yakov ALBER Jin Lu LI 《数学学报(英文版)》2007,23(6):1109-1120
In this paper we study the connection between the metric projection operator PK : B →K, where B is a reflexive Banach space with dual space B^* and K is a non-empty closed convex subset of B, and the generalized projection operators ∏K : B → K and πK : B^* → K. We also present some results in non-reflexive Banach spaces. 相似文献
2.
George T. Diderrich 《Israel Journal of Mathematics》1973,14(1):14-22
LetG be an Abelian group written additively,B a finite subset ofG, and lett be a positive integer. Fort≦|B|, letB
t denote the set of sums oft distinct elements overB. Furthermore, letK be a subgroup ofG and let σ denote the canonical homomorphism σ:G→G/K. WriteB
t (modB
t) forB
tσ and writeB
t (modK) forBσ. The following addition theorem in groups is proved. LetG be an Abelian group with no 2-torsion and letB a be finite subset ofG. Ift is a positive integer such thatt<|B| then |B
t (modK)|≧|B (modK)| for any finite subgroupK ofG. 相似文献
3.
Let K ? L be a field extension. Given K-subspaces A, B of L, we study the subspace ?AB? spanned by the product set AB = {ab∣ a ∈ A, b ∈ B}. We obtain some lower bounds on dim K ?AB? and dim K ?B n ? in terms of dim K A, dim K B and n. This is achieved by establishing linear versions of constructions and results in additive number theory mainly due to Kemperman and Olson. 相似文献
4.
In this paper, we investigate the characteristics of the metric projection operator P K : B → K, where B is a Banach space with dual space B?, and K is a nonempty closed convex subset of B. Then we apply its properties to study the existence of solutions of variational inequalities in uniformly convex and uniformly smooth Banach spaces. 相似文献
5.
Let B3(K) = {v:? an S(3,K,v)}. For K = {4} or {4,6}, B3(K) has been determined by Hanani, and for K = {4, 5} by a previous paper of the author. In this paper, we investigate the case of K = {4,5,6}. It is easy to see that if v ∈ B3 ({4, 5, 6}), then v ≡ 0, 1, 2 (mod 4). It is known that B3{4, 6}) = {v > 0: v ≡ 0 (mod 2)} ? B3({4,5,6}) by Hanani and that B3({4, 5}) = {v > 0: v ≡ 1, 2, 4, 5, 8, 10 (mod 12) and v ≠ 13} ? B3({4, 5, 6}). We shall focus on the case of v ≡ 9 (mod 12). It is proved that B3({4,5,6}) = {v > 0: v ≡ 0, 1, 2 (mod 4) and v ≠ 9, 13}. © 2003 Wiley Periodicals, Inc. 相似文献
6.
Using a combinatorial approach that avoids geometry, this paper studies the structure of KT(G/B), the T-equivariant K-theory of the generalized flag variety G/B. This ring has a natural basis
(the double Grothendieck polynomials), where
is the structure sheaf of the Schubert variety Xw. For rank two cases we compute the corresponding structure constants of the ring KT(G/B) and, based on this data, make a positivity conjecture for general G which generalizes the theorems of M. Brion (for K(G/B)) and W. Graham (for HT*(G/B)). Let [Xλ]KT(G/B) be the class of the homogeneous line bundle on G/B corresponding to the character of T indexed by λ. For general G we prove “Pieri–Chevalley formulas” for the products
,
,
, and
, where λ is dominant. By using the Chern character and comparing lowest degree terms the products which are computed in this paper also give results for the Grothendieck polynomials, double Schubert polynomials, and ordinary Schubert polynomials in, respectively K(G/B), HT*(G/B) and H*(G/B). 相似文献
7.
Mohamed Krir 《manuscripta mathematica》1998,96(1):9-16
Let R be a complete discrete valuation ring with mixed characteristic. Denote by K its field of fractions and by k its residue field. Let 0 →A
K
→B
K
→C
K
→ 0 be an exact sequence of abelian varieties over K and consider the corresponding complex of Nérons models 0 →A→B→C→ 0, over R. We assume that the identity component B
k
0 of the special fibre B
k
of B is a torus and we study the defect of exactmess at B in this last sequence.
Re?u: 4 décembre 1997/ Version revisée: 15 décembre 1997 相似文献
8.
ComplexK-theory ofBSL3(Z) andBSt3(Z) are computed. We first study a Brown-Peterson (BP) version of Soulé's arguments. Then we consider complexK-theory by using a Conner-Floyd type theorem. 相似文献
9.
Dan Pritikin 《Journal of Graph Theory》1985,9(4):497-502
Let B be a bipartite graph with edge set E and vertex bipartition M, N. The bichromaticity β(B) is defined as the maximum number β such that a complete bipartite graph on β vertices is obtainable from B by a sequence of identifications of vertices of M or vertices of N. Let μ = max{∣M∣, ∣N∣}. Harary, Hsu, and Miller proved that β(B) ≥ μ + 1 and that β(T) = μ + 1 for T an arbitrary tree. We prove that β(B) ≤ μ + ∣E∣/μ yielding a simpler proof that β(T) = μ + 1. We also characterize graphs for which Kμ, 2 is obtainable by such identifications. For QK. the graph of the K-dimensional cube, we obtain the inequality 2K?1 + 2 ≤ β(QK) ≤ 2K?1 + K, the upper bound attainable iff K is a power of 2. 相似文献
10.
Karolina Mroczyńska 《代数通讯》2013,41(3):916-934
The paper investigates the following problem. Let bimodules N, M yield a stable equivalence of Morita type between self-injective K-algebras A and E. Further, let bimodules S, T yield a stable equivalence of Morita type between self-injective K-algebras B and F. Then we want to know whether the functor M ? A ? ? B S: mod(A ? K B op ) → mod(E ? K F op ) induces a stable equivalence between A ? K B op and E ? K F op . There is given a reduction of this problem to some smaller subcategories for self-injective algebras. Moreover, new invariants of stable equivalences of Morita type are constructed in a general case of arbitrary finite-dimensional algebras over a field. 相似文献
11.
Let K be a field of characteristic zero and V a vector space of dimension m>1 with a nondegenerate symmetric bilinear form f:V×V→K. The Jordan algebra Bm = K⊕V of the form f is a ?2-graded algebra with this decomposition. We prove that the ideal of all the ?2-graded identities of Bm satisfies the Specht property and we compute the ?2-graded cocharacter sequence of Bm. 相似文献
12.
Chuan Ming Zong 《Geometriae Dedicata》1997,65(2):135-145
This article discusses the relation between the translative kissing numbers of convex bodies K
1, K
2 and K
1 K
2. As an application of the main theorem, we find that the translative kissing number of B Q, where B is a 24-dimensional ball and Q is a two-dimensional non-parallelogram convex domain, is 1375926. 相似文献
13.
David G Wagner 《Advances in Applied Mathematics》1998,21(4):644-684
We define a contravariant functorKfrom the category of finite graphs and graph morphisms to the category of finitely generated graded abelian groups and homomorphisms. For a graphX, an abelian groupB, and a nonnegative integerj, an element of Hom(Kj(X), B) is a coherent family ofB-valued flows on the set of all graphs obtained by contracting some (j − 1)-set of edges ofX; in particular, Hom(K1(X),
) is the familiar (real) “cycle-space” ofX. We show thatK · (X) is torsion-free and that its Poincaré polynomial is the specializationtn − kTX(1/t, 1 + t) of the Tutte polynomial ofX(hereXhasnvertices andkcomponents). Functoriality ofK · induces a functorial coalgebra structure onK · (X); dualizing, for any ringBwe obtain a functorialB-algebra structure on Hom(K · (X), B). WhenBis commutative we present this algebra as a quotient of a divided power algebra, leading to some interesting inequalities on the coefficients of the above Poincaré polynomial. We also provide a formula for the theta function of the lattice of integer-valued flows inX, and conclude with 10 open problems. 相似文献
14.
《代数通讯》2013,41(5):2357-2379
Abstract Restrictions of irreducible representations of classical algebraic groups to root A 1-subgroups, i.e., subgroups of type A 1 generated by root subgroups associated with two opposite roots, are studied. Composition factors of such restrictions are found in the following cases: for groups of types A n with n > 2 and D n , for groups of type B n , n > 2, and long root subgroups, for groups of type C n , n > 2, and short root subgroups, and for p-restricted representations of A 2(K), C 2(K) (recall that B 2(K) ? C 2(K)), and of B n (K), n > 2, and short root subgroups. Here we assume that p > 2 for G = B n (K) or C n (K). 相似文献
15.
The Derived Picard Group is a Locally Algebraic Group 总被引:1,自引:0,他引:1
Amnon Yekutieli 《Algebras and Representation Theory》2004,7(1):53-57
Let A be a finite-dimensional algebra over an algebraically closed field K. The derived Picard group DPic
K
(A) is the group of two-sided tilting complexes over A modulo isomorphism. We prove that DPic
K
(A) is a locally algebraic group, and its identity component is Out0
K
(A). If B is a derived Morita equivalent algebra then DPic
K
(A)DPic
K
(B) as locally algebraic groups. Our results extend, and are based on, work of Huisgen-Zimmermann, Saorín and Rouquier. 相似文献
16.
Let v, k be positive integers and k ≥ 3, then Kk = : {v: v ≥ k} is a 3‐BD closed set. Two finite generating sets of 3‐BD closed sets K4 and K5 are obtained by H. Hanani [5] and Qiurong Wu [12] respectively. In this article we show that if v ≥ 6, then v ∈ B3(K,1), where K = {6,7,…,41,45,46,47,51,52,53,83,84}\{22,26}; that is, we show that K is a generating set for K6. Finally we show that v ∈ B3(6,20) for all v ∈ K\{35,39,40,45}. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 128–136, 2008 相似文献
17.
This paper merges some classifications of G-M-type Banach spaces simplifically, discusses the condition of K
0(B(X)) = 0 for operator algebra B(X) on a Banach space X, and obtains a result to improve Laustsen's sufficient condition, gives an example to show that X ≈ X
2 is not a sufficient condition of K
0(B(X)) = 0. 相似文献
18.
19.
Kyriakos Keremedis 《Mathematical Logic Quarterly》1999,45(1):95-104
We find topological characterizations of the pseudointersection number ?? and the tower number t of the real line and we show that ?? < t iff there exists a compact separable T2 space X of π-weight < ?? that can be covered by < t nowhere dense sets iff there exists a weak Hausdorff gap of size K < t, i. e., a pair ({A : i ≠ k}, {BJ : j ε K}) C [W]W X [U]W such that A = {Ai : i ε K} is a decreasing tower, B = {Bj : j ε K) is a family of pseudointersections of A, and there is no pseudointersection S of A meeting each member of B in an infinite set. 相似文献
20.
Let A be a central simple algebra over its center F. Define CK1 A = Coker(K1 F → K1 A). We prove that if A and B are F-central simple algebras of coprime degrees, then CK1(A? F B) = CK1 A × CK1 B. 相似文献