Báo cáo toán học: "A note on exponents vs root heights for complex simple Lie algebras" pot

... Macdonald-Cherednik theory). For completeness sake, we first quickly recall [2] how one can use proposition 1 to deduce the classical fact concerning exponents and heights of roots. Let P denote ... form on the dual of the Cartan subalgebra and let s j ∈ W (j = 1 · · · n) be the simple reflection correponding to α j . We will prove proposition 1 by induction on ht β. If ht β = 1, β...

Ngày tải lên: 07/08/2014, 13:21

... to Sponsor Teams for Innovation in the Construction of Talent Highlands in Guangxi Institutions of Higher Learning ([2011]47), and the support program of Key Laboratory of Spatial Information and ... ∞, where N denotes the standard normal random variable. This implies that for any g(x) which is a non-negative, bounded Lipschitz function 6 A note on the almost sure limit theorem for...

Ngày tải lên: 20/06/2014, 21:20

Ngày tải lên: 05/08/2014, 10:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:21

... question for all k ≥ 4 and to the second question for all k ≥ 5. We would like to note that there is an interesting discussion about the Burkard–Hammer condition in [9]. Concerning the hamiltonian ... a necessary condition for a split graph G = S(I ∪K, E)with|I| < |K| to be hamiltonian [2] (see Sec. 2 for more detail). We will call this condition the Burkard–Hammer condition. Als...

Ngày tải lên: 06/08/2014, 05:20

... denoted by |w|. Thus |banana| = 6, for example. The language consisting of all words over Σ is denoted by Σ ∗ . If x, y ∈ Σ ∗ , the concatenation of x and y, written xy, is simply the string consisting ... encounter m j since m j is longer than m i . Suppose, for the sake of a contradiction, that m j encounters m i . Say that m j = αf(m i )β where f is a non-erasing substitution. If α =...

Ngày tải lên: 07/08/2014, 06:20

... Bounds on D(n) Our basic strategy for computing upper bounds for dim F n is to write all of the generating functions f λ (q) as rational functions over a common denominator; then the dimension of ... of nonnegative integer solutions to the equation λ 1 x 1 + ···+ λ k x k = N.Consequently, one easily verifies that f λ (q) is the generating function for the entries of the column correspo...

Ngày tải lên: 07/08/2014, 06:20

... n/n for a constant κ<2/3, then it outputs a cover graph whp. Note that the output graph will have whp girth equal to 4. On a related note we point to [8] which surveys constructions of non ... electronic journal of combinatorics 7 (2000), #R19 9 [8] O. Pretzel, Orientations and Edge Functions on Graphs, in: A.D.Keedwell (ed.), Surveys in Combinatorics, London Math. Soc. Lecture N...

Ngày tải lên: 07/08/2014, 06:20

... value for r =2.495 and (α, β, x, y) ∈D. For that purpose we used a Maple (see [12] for information on Maple) implementation of the downhill simplex function optimization method (see [13] for a ... will now consider an arbitrary term of the double sum that appears in (7) and examine for which values of r it converges to 0. If we find a condition on r that forces such a term to con...

Ngày tải lên: 07/08/2014, 06:20