共查询到20条相似文献,搜索用时 31 毫秒
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Constantin Bacuta Victor Nistor Ludmil T. Zikatanov 《Numerical Functional Analysis & Optimization》2013,34(6):613-639
ABSTRACT Let 𝒯 k be a sequence of triangulations of a polyhedron Ω ? ? n and let S k be the associated finite element space of continuous, piecewise polynomials of degree m. Let u k ∈ S k be the finite element approximation of the solution u of a second-order, strongly elliptic system Pu = f with zero Dirichlet boundary conditions. We show that a weak approximation property of the sequence S k ensures optimal rates of convergence for the sequence u k . The method relies on certain a priori estimates in weighted Sobolev spaces for the system Pu = 0 that we establish. The weight is the distance to the set of singular boundary points. We obtain similar results for the Poisson problem with mixed Dirichlet–Neumann boundary conditions on a polygon. 相似文献
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《代数通讯》2013,41(10):4765-4774
Abstract For vector spaces V and W over a field F, L F (V, W) denotes the set of all linear transformations α : V → W, and for a cardinal number k > 0, let L F (V, W, k) be the set of all α ∈ L F (V, W) of rank less than k. For θ ∈ L F (W, V), let (L F (V, W, k), θ) denote the semigroup L F (V, W, k) under the operation ? defined by α ? β = αθβ for all α, β ∈ L F (V, W, k). In this paper, all 0-minimal quasi-ideals of the semigroup (L F (V, W, k), θ) are completely characterized. It is also shown from this characterization that every nonzero semigroup (L F (V, W, k), θ) always has a 0-minimal quasi-ideal. 相似文献
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Let Φ be a Drinfeld A-module over an A-field K of generic characteristic. We will prove the following two results which are analogous to ones in number fields. Case 1. Φ is of rank one. Suppose that P and Q are two nontorsion points in Φ(K). If for any element a ? A and almost all prime ideals 𝒫 in one has that Φ a (P) ≡ 0 (mod 𝒫) ? Φ a (Q) ≡ 0 (mod 𝒫), then Q = Φ m (P) for some m ? A. Case 2. Φ is of general rank ≥ 1. Let x, y ? Φ(K) be two K-rational points. Denote = End K (Φ) which is commutative and Λ = · y which is a cyclic -module. Let red v :Φ(K) → Φ(k v ) be the reduction map at a place v of K with residue field k v . If red v (x) ? red v (Λ) for almost all places v of K. Then f(x) = g(y), for some nonzero elements f and g in . 相似文献
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《代数通讯》2013,41(1):379-389
Abstract Let d 1 : k[X] → k[X] and d 2 : k[Y] → k[Y] be k-derivations, where k[X] ? k[x 1,…,x n ], k[Y] ? k[y 1,…,y m ] are polynomial algebras over a field k of characteristic zero. Denote by d 1 ⊕ d 2 the unique k-derivation of k[X, Y] such that d| k[X] = d 1 and d| k[Y] = d 2. We prove that if d 1 and d 2 are positively homogeneous and if d 1 has no nontrivial Darboux polynomials, then every Darboux polynomial of d 1 ⊕ d 2 belongs to k[Y] and is a Darboux polynomial of d 2. We prove a similar fact for the algebra of constants of d 1 ⊕ d 2 and present several applications of our results. 相似文献
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László Fuchs 《代数通讯》2013,41(5):2311-2318
Abstract We classify the C 2 × C 2-gradings on M 2(k), k an arbitrary field. If char(k) ≠ 2 our approach relies on the duality between gradings and actions for finite abelian groups, and if k is algebraically closed we find precisely one isomorphism type of grading which is not isomorphic to a grading with all the matrix units being homogeneous elements. If char(k) = 2 we use a computational approach and we find that any C 2 × C 2-grading is induced by a C 2-grading. 相似文献
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Xianglin Du 《代数通讯》2013,41(4):1345-1359
ABSTRACT Let k(G) be the number of conjugacy classes of finite groups G and π e (G) be the set of the orders of elements in G. Then there exists a non-negative integer k such that k(G) = |π e (G)| + k. We call such groups to be co(k) groups. This article classifies all finite co(1) groups. They are isomorphic to one of the following groups: A 5, L 2(7), S 5, Z 3, Z 4, S 4, A 4, D 10, Hol(Z 5), or Z 3 ? Z 4. 相似文献
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Silvia Montarani 《代数通讯》2013,41(5):1449-1467
Let Γ N : = S N ? Γ N be the wreath product of Γ, a finite subgroup of SL(2,C), by the symmetric group of degree N. In this article we classify all the irreducible representations of S N ? Γ N that can be extended to a representation of the associated symplectic reflection algebra H 1,k,c (Γ N ) (where k is a complex number and c a class function on the nontrivial elements of Γ) for nonzero values of k. 相似文献
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A set of permutations 𝒮 on a finite linearly ordered set Ω is said to be k-min-wise independent, k-MWI for short, if Pr (min (π(X)) = π(x)) = 1/|X| for every X ? Ω such that |X| ≤ k and for every x ∈ X. (Here π(x) and π(X) denote the image of the element x or subset X of Ω under the permutation π, and Pr refers to a probability distribution on 𝒮, which we take to be the uniform distribution.) We are concerned with sets of permutations which are k-MWI families for any linear order. Indeed, we characterize such families in a way that does not involve the underlying order. As an application of this result, and using the Classification of Finite Simple Groups, we deduce a complete classification of the k-MWI families that are groups, for k ≥ 3. 相似文献
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ABSTRACT In this article, we first consider n × n upper-triangular matrices with entries in a given semiring k. Matrices of this form with invertible diagonal entries form a monoid B n (k). We show that B n (k) splits as a semidirect product of the monoid of unitriangular matrices U n (k) by the group of diagonal matrices. When the semiring is a field, B n (k) is actually a group and we recover a well-known result from the theory of groups and Lie algebras. Pursuing the analogy with the group case, we show that U n (k) is the ordered set product of n(n ? 1)/2 commutative monoids (the root subgroups in the group case). Finally, we give two different presentations of the Schützenberger product of n groups G 1,…, G n , given a monoid presentation ?A i | R i ? of each group G i . We also obtain as a special case presentations for the monoid of all n × n unitriangular Boolean matrices. 相似文献
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In the maximal ring O of octonion integers (“octavians”), let O m be the set of elements of norm m. Motivated by a question of H. P. Rehm, we ask whether, for a given positive rational integer m, there exists a set {α i } of norm-m octavians such that O m is partitioned by cosets O 1α i . For the case when m = 2, we characterize all possible intersections O 1α ∩ O 1α′, where α and α′ are any norm-2 octavians, and we show that all norm-2 partitioning sets are equivalent under the automorphisms of the underlying E 8 lattice mod 2. We then provide conditions sufficient to ensure that certain collections of one-sided cosets of O 1 partition O m , leading to partitioning sets in the new cases m = 4, 8, and 2 k, k odd. 相似文献
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Jaka Cimprič 《代数通讯》2013,41(11):4035-4041
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In this article we prove that a set of points B of PG(n, 2) is a minimal blocking set if and only if ?B? = PG(d, 2) with d odd and B is a set of d + 2 points of PG(d, 2) no d + 1 of them in the same hyperplane. As a corollary to the latter result we show that if G is a finite 2-group and n is a positive integer, then G admits a ? n+1-cover if and only if n is even and G? (C 2) n , where by a ? m -cover for a group H we mean a set 𝒞 of size m of maximal subgroups of H whose set-theoretic union is the whole H and no proper subset of 𝒞 has the latter property and the intersection of the maximal subgroups is core-free. Also for all n < 10 we find all pairs (m,p) (m > 0 an integer and p a prime number) for which there is a blocking set B of size n in PG(m,p) such that ?B? = PG(m,p). 相似文献
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T. Guédénon 《代数通讯》2013,41(12):4403-4413
ABSTRACT Let k be a field, R an associative k-algebra with identity, Δ a finite set of derivations of R, and R[Θ1, δ1] ··· [Θ n , δ n ] an iterated differential operator k-algebra over R such that δ j (Θ i ) ∈ R[Θ1, δ1] ··· [Θ i?1, δ i?1]; 1 ≤ i < j ≤ n. If R is Noetherian Δ-hypercentral, then every prime ideal P of A is classically localizable. The aim of this article is to show that under some additional hypotheses on the Δ-prime ideals of R, the local ring A P is regular in the sense of Robert Walker. We use this result to study the catenarity of A and to compute the numbers μ i of Bass. Let g be a nilpotent Lie algebra of finite dimension n acting on R by derivations and U(g) the enveloping algebra of g. Then the crossed product of R by U(g) is an iterated differential operator k-algebra as above. In this particular case, our results are known if k has characteristic zero. 相似文献
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《代数通讯》2013,41(3):1485-1497
Abstract We define the lower socle of a semiprime algebra 𝒜 as the sum of all minimal left ideals 𝒜e where e is a minimal idempotent such that the division algebra e𝒜e is finite dimensional. We study the connection between the condition that the elements a k , b k , 1 ≤ k ≤ n, lie in the lower socle of 𝒜 and the condition that the elementary operator x ? a 1 xb 1 + ? + a n xb n has finite rank. As an application we obtain some results on derivations certain of whose powers have finite rank. 相似文献
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D. Caponetti A. Trombetta G. Trombetta 《Numerical Functional Analysis & Optimization》2013,34(9-10):979-986
We present a theorem about calculation of fixed point index for k-ψ-contractive operators with 0 ≤ k < 1 defined on a radial set of a wedge of an infinite-dimensional Banach space. Then, results on the existence of eigenvectors and nonzero fixed points are obtained. 相似文献
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Garrett Johnson 《代数通讯》2013,41(3):1018-1032
We express the double affine Hecke algebra ? associated to the general linear group GL2(k) (here, k is a field with char(k) ≠ 2) as an amalgamated free product of quadratic extensions over the three-dimensional quantum torus 𝒪q((k×)3). With an eye towards proving ring-theoretic results pertaining to ?, a general treatment of amalgamated products of Ore and quadratic extensions is given. We prove an analogue of the Hilbert Basis Theorem for an amalgamated product Q of quadratic extensions and determine conditions for when the one-sided ideals of Q are principal or doubly-generated. Furthermore, we determine sufficient conditions which imply Q is a principal ideal ring. Finally, we construct an explicit isomorphism from ? to the amalgamated free product ring of quadratic extensions over 𝒪q((k×)3), a ring known to be noetherian. Therefore, it follows that ? is noetherian. 相似文献