Báo cáo toán học: "An extremal theorem in the hypercube" pps

... have an embedding of H in G, completing the proof. ✷ To complete the proof o f Theorem 1.1, we only need to apply the f ollowing classi- cal result of Erd˝os [10] regarding the extremal number ... 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. T...

Ngày tải lên: 08/08/2014, 12:22

... Erd˝os-Ginzburg-Ziv [1] proved the following theorem. EGZ Theorem If S is a sequence of elements from Z n of length 2n− 1, then 0 ∈  n S. The inverse problem to EGZ Theorem is how to describe the structure of ... a (1) j into A j for 1 ≤ j ≤ l and a (1) j ,a (2) j into A j for l<j≤ k. Then the other terms of S are put into A 1 ,A 2 , ··· ,A k such that each A i does not incl...

Ngày tải lên: 07/08/2014, 13:21

... the only ones with the property that • D is the first or the second point, • the first point is collinear with the second point, • the second point is collinear with the third point. Clearly, these ... of Theorem 1 We begin by tightening the aforementioned result from [7] concerning the average degree. This will allow us to obtain the lower bound of 157 on n in Theore...

Ngày tải lên: 07/08/2014, 21:21

... Theorem 3.1 extends the main results in [4,16,18,20]to the case of asymptotically nonexpansive in the intermediate sense mappings and it seems to be new even in the case that the space has a Fréchet ... norm. In the end, to illustrate our theorem, we give a nonself mapping which is asymptotically nonexpansive in the intermediate sense but not asymptotical ly nonexpa...

Ngày tải lên: 20/06/2014, 21:20

... bisectable. The graphs for t odd given in the statement of the theorem have t + 4 edges, do not contain an independent set of size t and are not bisectable. This proves the first assertion of the theorem ... neither K t nor K t,t as a subgraph. If n<2t, then Problem 1 is equivalent to Tur´an’s theorem. The case n =2t is settled in the next theorem. If G and H are gr...

Ngày tải lên: 07/08/2014, 06:20

... (we follow the terminology of [4]). If G =(V,E)isak-critical graph, then the low-vertex subgraph of G, denoted by L(G), is the subgraph of G, induced by all vertices of degree k − 1. The high-vertex ... we denote by H(G), is the subgraph of G induced by all vertices of degree at least k in G. Brooks’ theorem implies that if k ≥ 4 and G = K k , then H(G) = ∅. A maximal by inclu...

Ngày tải lên: 07/08/2014, 06:22

... C 112 has minimum weight 20 (the minimum weight is also verified by Magma [1]). Therefore C 112 is an extremal doubly even self-dual code and we have the following: Theorem 1. There is an extremal ... 0), (1, 1) in the coordinates and deleting the coordinates) from C 112 . The codes S C 112 (i, j) are self-dual codes of length 110 and minimum weight 18 or 20. Let M = (m ij ) b...

Ngày tải lên: 07/08/2014, 15:22

... therefore there are 2 |V i | −2 ways of coloring it with the chosen two colors. Finally, there are (r − 1)! ways to color the remaining (r − 1) V j ’s with the remaining (r − 1) colors. So, there ... V i into 2 subsets, therefore there are 2 |V i | − 2 ways of coloring it with the chosen two colors. Finally, there are (r − 1)! ways to color the remaining (r − 1) V j ’s with the re...

Ngày tải lên: 08/08/2014, 12:23

... present the entropy proof of Theorem 1 due to R adhakrishnan. The proof proceeds by applying the randomized chain rule above with respect to orderings of the vertices in L. For a fixed matching, then, ... a lways non-negative. One can think of the term log(1/P(X = x)) appearing in the definition of the entropy as measuring the surprise involved in discovering that the...

Ngày tải lên: 08/08/2014, 12:23

... GS staining (B3), and 4¢,6-diamidino-2-phenylindole (DAPI) staining (B4), respectively. (B5-8) High magnification images of the boxed area in (B4) showing RPE65c staining (B5), GS staining (B6), ... contribute to providing chromophore to melanopsin to maintain their light sensitivities. The expression and function of RPE65c in other cell types in the retina remains to be investigat...

Ngày tải lên: 14/02/2014, 14:20