Báo cáo toán học: "An addition theorem on the cyclic group Zpαqβ" pptx

... Therefore k  j=1 a (1) j ∈ A 1 + A 2 + ···+ A k , the electronic journal of combinatorics 13 (2006), #N9 2 An addition theorem on the cyclic group Z p α q β Hui-Qin Cao Department of Applied Mathematics Nanjing Audit ... Proof of Theorem 1 For any subset A of an abelian group G let H(A) denote the maximal subgroup of G such that A + H(A)=A. What we state below is a classi...

Ngày tải lên: 07/08/2014, 13:21

... (1) The second ingredient of our proof is the following result of Stiebitz. Lemma 3 ([5]) Let G be a k-critical graph containing at least one vertex of degree k − 1. Then the number of connected ... components of its high-vertex subgraph H(G) does not exceed the number of connected components of its low-vertex subgraph L(G). Proof of Theorem 1. Let L(G) and H(G) be the low-vertex...

Ngày tải lên: 07/08/2014, 06:22

... v t−1 v t v 1 , v t v 1 v 2 }. On the other hand, C 4 , C 6 and C 10 do not admit k-partite representations for any k. The importance of these considerations lies in the following theorem. Theorem 1.1 Le t ... Theorem 2.1 and the fact that the 2-partite representation of C 2t is the graph C t . The one additional ingredient necessary to complete the proof is the Bondy...

Ngày tải lên: 08/08/2014, 12:22

... k) ≤  v d(v)  k=1 1 d(v) log(k) =  v log(d(v)!) 1/d(v) . 3 A proof of the Kahn-Lov´asz theorem The entropy proof of the Kahn-Lov´asz theorem is complicated by the fact that there can be edges of the graph (and a fixed matching) amongst the neighbors ... and conditional entropy are a lways non-negative. One can think of the term log(1/P(X = x)) appearing in the definition...

Ngày tải lên: 08/08/2014, 12:23

... [18] proved the weak convergence theorem of the iteration process (1.3) in uniformly convex Banach spaces that satisfy Opial’s condition. The concept of asymptotical ly nonexpansive in the intermediate ... prove the following theorem. Theorem 3.2 Let C be a nonempty close d conve x subset of uniformly conve x Banach space X which satisfies the Opial’s condition or whose dual...

Ngày tải lên: 20/06/2014, 21:20

... central limit theorem with µ n =  n 2  /2andσ 2 n = n(n − 1)(2n +5)/72 (see [2; Theorem 1]). Bender [2; p. 109] remarks that the theorems of Section 4 do not apply” to the b(n, k). He then shows ... expansion of the integral. Among the consequences, we have a complete asymptotic expansion for b(n, k)/n!fora range of k including the maximum of the b(n, k)/n!. AMS Subject Class...

Ngày tải lên: 07/08/2014, 06:20

... were constructed in [9] by F¨uredi, Seress, and the authors. The fact that the orders of these constructions actually meet the upper bound in (2) for q odd follows from [13]. The constructions ... by these constructions are not as good as the ones given in Theorem A, they are better than the bounds in (1) for all k ≥ 7 and g ≥ 11 when g is odd, and g ≥ 8 when g is even. With s...

Ngày tải lên: 07/08/2014, 06:22

... = τ(G), then we say that G is τ-partitionable. The following conjecture is known as the Path Partition Conjecture (or the PPC, for short). Conjecture 1 Every graph is τ-partitionable. The PPC ... If H consists of k ≥ 1 components, then |N P (H)|≤ τ (G)−1 2 +  k 2  . (b) Let C be a longest cycle in a nonhamiltonian graph G and H = G − V (C). If H consists of k ≥ 1 components, then |N...

Ngày tải lên: 07/08/2014, 13:21

... differences from the other rodents. The purpose of the present study was to clarify the regional distribution and relative fre- quency of endocrine cells in the pancreatic islets of the Mongolian gerbil, ... also demonstrated in the mantle zones. Glucagon-immunore- active cells were mainly restricted to the mantle zones. However, rare examples were found in the peripheral re...

Ngày tải lên: 07/08/2014, 14:23

... subdivided into two regions (epithelial and connective tissue regions). In the pancreatic islet portions, although some cells w ere also demonstrated in the mantle regions, m ost of insulin-immunoreactive ... were demonstrated in the pancreatic islets of C57BL/6 mouse. In the pancreatic duct portions, rare glucagon-immunoreactive cells w ere situated in the epithelial regions. Cell...

Ngày tải lên: 07/08/2014, 15:20