Báo cáo tin học: "Nonexistence of triples of nonisomorphic connected graphs with isomorphic connected P3-graphs" pot

... triple of mutually nonisomorphic connected graphs with an isomorphic connected P 3 -graph. Proof. Assume, to the contrary, that there exists a triple of mutually nonisomorphic connected graphs ... ϕ −1 i , where the electronic journal of combinatorics 15 (2008), #R31 4 Nonexistence of triples of nonisomorphic connected graphs with isomorphic connected...

Ngày tải lên: 07/08/2014, 15:23

... check positive definiteness of (millions of) potential leading principal submatrices of minimal idempotents E i for assocation schemes with the requested parameters. For ease of notation we will denote ... again end up with a matrix ¯ A whose rank cannot be larger than the rank of A. In each of these cases it is of course possible that the rank of ¯ A is strictly smaller th...

Ngày tải lên: 07/08/2014, 15:23

... choice of ε and δ, we have 2δ = 2ε  µ −1 +  −1  ≤ 1 4 µ( + µ) ≤ 1 4 . This concludes the proof of Lemma 10. 3 Proofs of Theorems 7 and 8 We present the proof of Theorem 7 in Section 3.1 and of ... cycle of length at least (1 −κ)k. Let us continue with the proof of the lower bound in Theorem 8. Let α > 0 be as given in that theorem and let β > 0 be fixed. By an applica...

Ngày tải lên: 07/08/2014, 15:23

... where |V (Γ)| is the number of vertices of Γ. The generating set D n of Γ n is a union of conjugacy classes, because a derangement is just a permutation with no cycles of length one, and cycle type ... result also follows with a little work from the properties of derangement numbers given in Lemma 4.1 and a result of Okazaki ([15]; see [20], Exercise 7.63, p. 469). 7 Proof...

Ngày tải lên: 07/08/2014, 15:23

... 1.2. The proofs will be given in Section 2. In Section 3, we construct several interesting Dyson style constant term identities. 2 Proof of Theorem 1.2 and Theorem 1.3 Good’s proof [4] of the Dyson ... conditions (2.4). 2.4 The Proof Now we can prove Theorems 1.2 and 1.3. Without loss of generality, we may assume r = 1, s = 2 and t = 3 in Theorems 1.2 and 1.3. Proof of Theorems 1.2 an...

Ngày tải lên: 07/08/2014, 15:23

... integrating an SLD with an SOA, is fabricated. A high power (500 mW) with a broad emission of 86 nm is obtained. By properly controlling the current injection in the two sections of the QD-SLD ... with a two-section ES1 emission of QDs is achieved at I SLD = 200 and 100 mA for a given I SOA of 8.5 and 9.5 A, respectively. With I SOA fixed at 8.5 A, when the SLD section...

Ngày tải lên: 18/06/2014, 22:20

... graph with |V | < 2∆ and let F be an edge cut of H with |F | < ∆. Then F cuts off one vertex of H, i.e., H − F has two components and one of them consists of exactly one vertex. Proof. Let ... induced ∆-overfull subgraphs of G with more than |V (ker(G))|−∆(G) vertices. The second phase consists of finding a certain edge cut F of ker(G )with| F |≤∆(G) − 2. Let H be an i...

Ngày tải lên: 07/08/2014, 06:22

... approximation of the number of cliques in random intersection graphs. Journal of Applied Probability 47 (3), 826–840, 2010. [17] Singer-Cohen, K. B. Random intersection graphs. PhD thesis, Department of Mathematical ... G ∗ (n, M ′ ) . The proof of the next fact is analogous to the proof of Fact 2 in [15]. Fact 2. Let (G i ) i=1, ,m and (G ′ i ) i=1, ,m be sequences of indepen...

Ngày tải lên: 08/08/2014, 12:23

... (2006) Nonexistence of positive solutions of an integral system with weights Zhengce Zhang School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China Email ... monotonic- ity of the positive solutions for a class of integral systems with weights. We use a new type of moving plane method introduced by Chen–Li–Ou. Our new ingredi...

Ngày tải lên: 20/06/2014, 21:20

... questions on nonexistence and symmetry of positive solutions of the equation with weights as (1.1) in the rest range of p, q, ξ, and η. It is an interesting research subject in the future. 16 [3] ... complete. Nonexistence of positive solutions of an integral system with weights Zhengce Zhang School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, Peopl...

Ngày tải lên: 20/06/2014, 21:20