Báo cáo toán học: "An extremal theorem in the hypercube" pps
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...
Báo cáo toán học: "An addition theorem on the cyclic group Zpαqβ" pptx
... 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...
Báo cáo toán học: "An Extremal Characterization of Projective Planes" pps
... 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...
Báo cáo toán học: " Weak convergence theorem for the three-step iterations of non-Lipschitzian nonself mappings in Banach spaces" pptx
... 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...
Báo cáo toán học: "Two Extremal Problems in Graph Theory" pot
... 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...
Báo cáo toán học: "An improved bound on the minimal number of edges in color-critical graphs" pot
... (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...
Báo cáo toán học: "An Extremal Doubly Even Self-Dual Code of Length 112" pdf
... 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...
Báo cáo toán học: "An Extremal Property of Tur´n Graphs a" potx
... 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...
Báo cáo toán học: "An entropy proof of the Kahn-Lov´sz theorem a" ppsx
... 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...
Tài liệu Báo cáo khoa học: An alternative isomerohydrolase in the retinal Muller cells of a cone-dominant species doc
... 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...
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