Báo cáo toán học: "On the most Weight w Vectors in a Dimension k Binary Code" potx

... weight w in a k- dimensional subspace of F n . Ahlswede, Aydinian, and Khachatrian found a formula for M R [1]. Theorem 1 (Ahlswede, Aydinian, and Khachatrian). Given n, k, w ∈ N, M R (n, k, w) ... M R (n, k, w) . Furthermore, for k, w ∈ N with k  2w and w odd, we have m (k, k, w) = m (k + 1, k, w) = m (k + 2, k, w) =  k w  = M R (k, k, w) = M R (...

Ngày tải lên: 08/08/2014, 12:22

... 3 j where k  0, j  1 . 2 The number of matchings in a tree In t his section, we turn to the number of matchings in a graph. This is a lso known as the Hosoya index, or the Z-index in mathematical ... i  k − 1, a} ⊂ B. In particular, (i, k) ∈ B for all 0  i  k − 1. Now as (1, −1) ⊙ (i, k) = (k, i − k) , applying Proposition 7, we get that (i − k, k) ∈ B....

Ngày tải lên: 08/08/2014, 11:20

... 16 2k 5 − 32 4k 5 a 2 + 37 8k 4 a 2 − 18 9k 4 − 32 4k 4 a 3 + 10 8k 4 a − 83 7k 4 a 4 − 72ak 3 + 72 a 2 k 3 + 64 8a 3 k 3 + 165 6a 4 k 3 + 72 a 2 k 2 − 62 4a 3 k 2 − 151 2a 4 k 2 + 48 0a 3 k + 60 8a 4 k − ... odd. Acknowledgement The first author is a recipient of an APART-fellowship of the Austrian Academy of Sci- ences at the University of W...

Ngày tải lên: 07/08/2014, 21:21

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Ngày tải lên: 05/08/2014, 09:46

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Ngày tải lên: 05/08/2014, 15:21

... (x)= a x ,a& gt;0,x∈ (0, +∞) then Theorem 7 is applied, i.e. (2.7), (2.8) always have at least one positive periodic solution. Acknowledgement. The author would like to thank Prof. Pham Ky Anh, ... Global attraction in a delay difference equation, Nonlin. Anal. 17 (1991) 473–479. 5. G. Karakostas, Ch. G. Philos, and Y. G. Sficas, The dynamics of some discrete population models, Nonli...

Ngày tải lên: 06/08/2014, 05:20

... meets in nitely many K n ,thenx ∈ K. We define lim inf K n as the largest set satisfying (1), and lim sup K n as the smallest set satisfying (2). Then K n → K is equivalent to lim sup K n = lim inf ... every ray lands at some point in J c 0 . Vietnam Journal of Mathematics 33:3 (2005) 283–289 On the Continuity of Julia Sets and Hausdorff Dimension of Polynomials Zhuang...

Ngày tải lên: 06/08/2014, 05:20

... A  then again it is easy to show that A  =2B + l −3whenk =2andk = 5. In these two cases the constructed surfaces are obtained by joining l tubes between two surfaces each having genus B − 1, and therefore ... Class B subinterval is not empty. The value of g A is called the breaking point of the interval [γ (K m )+1,γ (K m+1 )]. We now show that if we knew the complete an...

Ngày tải lên: 07/08/2014, 07:21

... visit at the Erwin Schr¨odinger International Institute for Mathematical Physics. The author would like to thank the ESI for hospitality and financial support during his visit. References [1] N. Alon ... showed that if a subset of the d-dimensional vector space over a finite field is large enough, then it contains many k- tuples of mutually orthogonal vectors. In this note, we pr...

Ngày tải lên: 07/08/2014, 15:22

... inf l→∞ |E(G (l) )| l 2 can be for an in nite graph G (∞) , which does not contain an increasing path I k with k + 1 vertices. We will show that for sufficiently large k there are I k –free in nite graphs with 1 4 + 1 200 < ... = 1 6 . The following was stated in [1] as a question and in [2, 3] as a conjecture. Conjecture 1.1 ([1, 2, 3]) For any k ≥ 2 the following ho...

Ngày tải lên: 07/08/2014, 15:23