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1.
For finite subsets A1,…,An of a field, their sumset is given by . In this paper, we study various restricted sumsets of A1,…,An with restrictions of the following forms:
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Hao Pan 《Journal of Combinatorial Theory, Series A》2009,116(8):1374-1381
Let A1,…,An be finite subsets of a field F, and let
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Yevhen Zelenyuk 《Journal of Combinatorial Theory, Series A》2008,115(2):331-339
Let G be an Abelian group and let be infinite. We construct a partition of A such that whenever (xn)n<ω is a one-to-one sequence in A, g∈G and m<ω, one has
(g+FSI((xn)n<ω))∩Am≠∅, 相似文献
6.
Peter Borg 《Discrete Mathematics》2009,309(14):4750-4753
Families A1,…,Ak of sets are said to be cross-intersecting if for any Ai∈Ai and Aj∈Aj, i≠j. A nice result of Hilton that generalises the Erd?s-Ko-Rado (EKR) Theorem says that if r≤n/2 and A1,…,Ak are cross-intersecting sub-families of , then
7.
Hao Pan 《Journal of Number Theory》2006,117(1):216-221
Let k,m,n?2 be integers. Let A be a subset of {0,1,…,n} with 0∈A and the greatest common divisor of all elements of A is 1. Suppose that
8.
Mihály Pituk 《Linear algebra and its applications》2011,434(2):490-500
Let An,n∈N, be a sequence of k×k matrices which converge to a matrix A as n→∞. It is shown that if xn,n∈N, is a sequence of nonnegative nonzero vectors such that
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Ding-Gong Yang 《Applied mathematics and computation》2010,215(9):3473-3481
Let Tn(A,B,α) denote the class of functions of the form:
10.
Let A1,…,AN be complex self-adjoint matrices and let ρ be a density matrix. The Robertson uncertainty principle
11.
Michel Balazard 《Advances in Mathematics》2004,188(1):69-86
Opération fondamentale de l'arithmétique, familière depuis des millénaires, la division euclidienne n'a pas livré tous ses secrets. Ainsi, notons pour k et a entiers positifs, le reste de la division euclidienne de k par a, et imaginons un instant que, par un choix convenable d'un entier n et de réels c2,…,cn, nous sachions rendre arbitrairement petite la quantité
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Zinaida A. Lykova 《Journal of Pure and Applied Algebra》2006,205(3):471-497
We present methods for the computation of the Hochschild and cyclic-type continuous homology and cohomology of some locally convex strict inductive limits of Fréchet algebras Am. In the pure algebraic case it is known that, for the cyclic homology of A, for all n?0 [Cyclic Homology, Springer, Berlin, 1992, E.2.1.1]. We show that, for a locally convex strict inductive system of Fréchet algebras such that
0→Am→Am+1→Am+1/Am→0 相似文献
13.
Yasuo Teranishi 《Discrete Mathematics》2002,257(1):183-189
14.
Let be a sequence of i.i.d. random variables taking values in a real separable Hilbert space (H,‖⋅‖) with covariance operator Σ, and set Sn=X1+?+Xn, n?1. Let . We prove that, for any 1<r<3/2 and a>−d/2,
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Let A=(A1,…,Am) be a sequence of finite subsets from an additive abelian group G. Let Σ?(A) denote the set of all group elements representable as a sum of ? elements from distinct terms of A, and set . Our main theorem is the following lower bound:
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For any given n-by-n matrix A, a specific circulant preconditioner tF(A) introduced by Tyrtyshnikov [E. Tyrtyshnikov, Optimal and super-optimal circulant preconditioners, SIAM J. Matrix Anal. Appl. 13 (1992) 459-473] is defined to be the solution of
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Zhi-Wei Sun 《Journal of Number Theory》2005,111(1):190-196
Let be a finite system of residue classes with the moduli n1,…,nk distinct. By means of algebraic integers we show that the range of the covering function is not contained in any residue class with modulus greater one. In particular, the values of w(x) cannot have the same parity. 相似文献