Báo cáo toán học: "Two new criteria for comparison in the Bruhat order" pot

... transpositions, then the poly- nomial (1) is equal to a sum of polynomials of the form (2) and again is TNN. (⇐) Suppose that π is not less than or equal to σ in the Bruhat order. By Theorem 1 we ... transpositions, then the evaluation of (3) at A is equal to a sum of polynomials of the form (4) and again (3) is SNN. (⇐) Suppose that π is not less than or equal to σ in the...

Ngày tải lên: 07/08/2014, 08:20

... verifying that the corresponding face of the dominant chamber is confined to a single face of H. We omit the proof, since a stronger result for affine Weyl groups will be given later in the proof of Theorem ... assignment of coordinates for the Bruhat ordering of any parabolic quotient W J (including the full group W in the case J = ∅) may be produced once we have coordin...

Ngày tải lên: 07/08/2014, 08:22

... during multiple natural disasters in the past 2 decades, including the earthquake in Armenia in 1988 [35], Wenchuan, China, in 2008 [36], and Haiti in 2010 [37], and the tsunami in Indonesia in ... article as they were all involved in the literature search, evaluation of the literature, writing and editing process. All authors read and approved the final manusc...

Ngày tải lên: 20/06/2014, 21:20

... than (1) for m ≥ 8. So the Bollobas conjecture fails for k ≥ 10. The idea of the above construction which improves on products of H 3 can be applied to products of other families as well. For example, ... starting with products of H k for any k>3 as well. Or we can start with the families F constructed above. This will allow a very slight improvement in the lower bound...

Ngày tải lên: 07/08/2014, 06:20

... containing  (f,f, ···,f):f ∈ S  , I is a two-sided ideal in G,andJ is a closed right ideal in G. By Theorem 2.9, (θ, ···,θ) is a minimal idempotent in G, therefore I,being a two-sided ideal in ... because the T m ’s contain all the words we are looking for and they are all contained in C z . 3. Four open problems. In this section we discuss a few further extensions of the...

Ngày tải lên: 07/08/2014, 06:20

... maintained by revising the state of the nodes in the logical structure. In other words, the valid/invalid state of the nodes in this network corresponds to the In/ Out state of the nodes in the ... increasing living standards and corporate profits. The design of a product lifecycle includes the steps of modeling the lifecycle itself, evaluating it from variou...

Ngày tải lên: 20/06/2014, 21:20

... below). For information about publishing your research in Journal of Inequalities and Applications go to http://www.journalofinequalitiesandapplications.com/authors/instructions/ For information ... (2.30) Competing interests The authors declare that they have no competing interests. Authors’ contributions QZ carried out the theoretical proof and drafted the manuscript. XH partici...

Ngày tải lên: 20/06/2014, 21:20

... optimal in their general setting, and at the same time, are not very far from the best estimates for particular hypergraphs, when we apply the general setting for them. For example, for any fixed ... from the van der Waerden inequality for the permanent, provided the lower bound for the asymptotic formula. Our goal now is to show (13) from Lemma 3 for k = o(n 1/2...

Ngày tải lên: 07/08/2014, 15:23

... Kronecker products including simple proofs of some basic results of the theory. The experts in symmetric function theory may skip this section. In the fourth section we use the pairing s µ →q µ to ... Our point of departure, as in Macdonald ( [Ma]), is the Frobenius formula, equation I.1, in the vari ables x 0 , x 1 , . . ., x n which for λ = (n − k, µ) with µ ⊢ k may be...

Ngày tải lên: 08/08/2014, 01:20

... an embedding of u in ¯w with the n in position i + ℓk for each i ∈ η(w) and these are the only embeddings. These embeddings exist because there is a pseudo-embedding of v into w with the n in position ... (directed) path in ∆ starting at α, we construct a word in P ∗ by concatenating the elements on the arcs on the path in the order in which they are encountered....

Ngày tải lên: 08/08/2014, 01:20