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831.
Brualdi et al. [Codes with a poset metric, Discrete Math. 147 (1995) 57-72] introduced the concept of poset codes, and gave an example of poset structure which admits the extended binary Golay code to be a 4-error-correcting perfect P-code. In this paper we classify all of the poset structures which admit the extended binary Golay code to be a 4-error-correcting perfect P-code, and show that there are no posets which admit the extended binary Golay code to be a 5-error-correcting perfect P-code. 相似文献
832.
Wensong Lin 《Discrete Mathematics》2008,308(16):3565-3573
The generalized Mycielskians of graphs (also known as cones over graphs) are the natural generalization of the Mycielskians of graphs (which were first introduced by Mycielski in 1955). Given a graph G and any integer p?0, one can transform G into a new graph μp(G), the p-Mycielskian of G. In this paper, we study the kth chromatic numbers χk of Mycielskians and generalized Mycielskians of graphs. We show that χk(G)+1?χk(μ(G))?χk(G)+k, where both upper and lower bounds are attainable. We then investigate the kth chromatic number of Mycielskians of cycles and determine the kth chromatic number of p-Mycielskian of a complete graph Kn for any integers k?1, p?0 and n?2. Finally, we prove that if a graph G is a/b-colorable then the p-Mycielskian of G, μp(G), is (at+bp+1)/bt-colorable, where . And thus obtain graphs G with m(G) grows exponentially with the order of G, where m(G) is the minimal denominator of a a/b-coloring of G with χf(G)=a/b. 相似文献
833.
Matthew Elder 《Discrete Mathematics》2008,308(16):3479-3490
A path bundle is a set of 2a paths in an n-cube, denoted Qn, such that every path has the same length, the paths partition the vertices of Qn, the endpoints of the paths induce two subcubes of Qn, and the endpoints of each path are complements. This paper shows that a path bundle exists if and only if n>0 is odd and 0?a?n-⌈log2(n+1)⌉. 相似文献
834.
Néstor E. Aguilera 《Discrete Mathematics》2008,308(11):2167-2174
Using results by McKee and Woodall on binary matroids, we show that the set of postman sets has odd cardinality, generalizing a result by Toida on the cardinality of cycles in Eulerian graphs. We study the relationship between T-joins and blocks of the underlying graph, obtaining a decomposition of postman sets in terms of blocks. We conclude by giving several characterizations of T-joins which are postman sets. 相似文献
835.
Imed Zaguia 《Discrete Mathematics》2008,308(23):5727-5734
We prove that a prime interval order, not necessarily finite, has no prime upper cover if and only if it has width two. On the other hand, we prove that every finite prime N-free order has at least one prime upper cover. 相似文献
836.
Tuomas Hytönen 《Journal of Functional Analysis》2008,254(3):675-726
Let L be an elliptic differential operator with bounded measurable coefficients, acting in Bochner spaces Lp(Rn;X) of X -valued functions on Rn. We characterize Kato's square root estimates and the H∞-functional calculus of L in terms of R-boundedness properties of the resolvent of L, when X is a Banach function lattice with the UMD property, or a noncommutative Lp space. To do so, we develop various vector-valued analogues of classical objects in Harmonic Analysis, including a maximal function for Bochner spaces. In the special case X=C, we get a new approach to the Lp theory of square roots of elliptic operators, as well as an Lp version of Carleson's inequality. 相似文献
837.
The standard C∗-algebraic version of the algebra of canonical commutation relations, the Weyl algebra, frequently causes difficulties in applications since it neither admits the formulation of physically interesting dynamical laws nor does it incorporate pertinent physical observables such as (bounded functions of) the Hamiltonian. Here a novel C∗-algebra of the canonical commutation relations is presented which does not suffer from such problems. It is based on the resolvents of the canonical operators and their algebraic relations. The resulting C∗-algebra, the resolvent algebra, is shown to have many desirable analytic properties and the regularity structure of its representations is surprisingly simple. Moreover, the resolvent algebra is a convenient framework for applications to interacting and to constrained quantum systems, as we demonstrate by several examples. 相似文献
838.
Ying Hu 《Journal of Functional Analysis》2008,254(5):1282-1306
We prove maximal ergodic inequalities for a sequence of operators and for their averages in the noncommutative Lp-space. We also obtain the corresponding individual ergodic theorems. Applying these results to actions of a free group on a von Neumann algebra, we get noncommutative analogues of maximal ergodic inequalities and pointwise ergodic theorems of Nevo-Stein. 相似文献
839.
Turdebek N. Bekjan 《Journal of Functional Analysis》2008,254(9):2401-2418
Let M be a von Neumann algebra equipped with a normal semifinite faithful trace τ. Let T be a positive linear contraction on M such that τ○T?τ and such that the numerical range of T as an operator on L2(M) is contained in a Stoltz region with vertex 1. We show that Junge and Xu's noncommutative Stein maximal ergodic inequality holds for the powers of T on Lp(M), 1<p?∞. We apply this result to obtain the noncommutative analogue of a recent result of Cohen concerning the iterates of the product of a finite number of conditional expectations. 相似文献
840.
The representation of dual spaces of EM(μ,X), owing to its extensive application, is given in this paper. Using the representation, we get the sufficient and necessary conditions of LM(μ,X) possessing drop property, and extend the result of Hudzik and Wang [H. Hudzik, B. Wang, Approximative compactness in Orlicz spaces, J. Approx. Theory 95 (1998) 82-89]. Simultaneously, under some conditions, the weak∗ drop property in LM(μ,X∗) and LM∗(μ,X) is discussed. 相似文献