Báo cáo toán học: "Spectral saturation: inverting the spectral Tur´n theorem a" pot
Báo cáo toán học: "Threshold Functions for the Bipartite Tur´n Property a" potx
... 5,
µ
2
∆
≥
n
t
4
p
2t
2
t
2
n
t
2
p
2t
2
ϕ(1, 1)
10
the electronic journal of combinatorics 4 (1997), #R18 6
2. PROOFS
Proof of the Theorem:
We have already provided a proof of the second part of the theorem using nothing
more ... = o(n
1/3
); in the last two lines of the above calculation, the notation f g means that
f ≥ Kg for some positive constant K. This prove...
Báo cáo toán học: "Combinatorial Identities from the Spectral Theory of Quantum Graph" potx
... orbits. In the present case a family
is completely specified by the integer q ≡ q
1
which counts the traversals of the loop 1,
i.e., the number of letters 1 in the code word. Each of these q letters ... δ
2π
denotes the 2π periodic delta function. The first
term on the r.h.s. is the average density
d =
2B
2π
. The coefficients of the oscillatory
part
s
n
=trS
n
will play a...
Báo cáo toán học: " Weak compactness and the Eisenfeld-Lakshmikantham measure of nonconvexity" potx
... convex subsets of the bounded and convex set coC,
then µ(C
n
) = 0 (n ∈ N), and therefore C
∞
= ∅. Appealing again to the
ˇ
Smulian theorem [6, Theorem V.6.2] we find that the convex set coC ... A
∞
=
∞
n=1
A
n
is nonempty.
Theorem 1.4 ([2, Theorem 2.5]). For a Banach space X, the following
statements are equivalent:
(i) X is reflexive.
(ii) The E-L measure of nonconvexity...
Báo cáo toán học: "Conjectured Statistics for the Higher q, t-Catalan Sequences" potx
... path from the southwest corner to the northeast corner of
the rectangle R
a,b
, we can keep track of both the area in R
a,b
below the path and the area
in R
a,b
above the path by making the indicated ... s
,thepowerofy does not
change in the passage from D
to D.Thepowerofw does not change either, since there
are the same number of extra cells left of the last vertica...
Báo cáo toán học: "Lower Bound for the Size of Maximal Nontraceable Graphs." pot
... finite graphs G and denote the vertex set, the edge set, the order
and the size of G by V (G), E(G), v(G)ande(G), respectively. The open neighbourhood
of a vertex v in G is the set N
G
(v)={x ∈ V ... need to prove that the sum of the degrees of the vertices of G is at least 3n − 2.
In view of Theorem 8, we let
M = {v ∈ V (G) | d(v) = 2 and no neighbour of v has degree 2}....
Báo cáo toán học: "Indecomposable tilings of the integers with exponentially long periods" potx
... under the map given by the Chinese Remainder Theorem (whereby the
coefficient of x
n
becomes the value of the entry (n mod 2,n mod 3,n mod 5)). Thus the
a
a
a
a
a
a
Figure 8: A 2 ×3 × 5 inflate of the ... tilings with long periods therefore leads us to ask
whether there exist minimal non-periodic C1 arrays. Unfortunately, the following theorem
puts an end to such hopes:
Theo...
Báo cáo toán hoc:" Properties determined by the Ihara zeta function of a Graph " docx
... equal if and only if they have the same spectrum [5]. Theorem 2 is a
strengthening of this result.
The proof of the previous two theorems rely on a theorem of Bass’ in [1]. In the case
that G is ... whether G is bipartite or not and whether it is
cyclic or not can be determined from Z
G
(u). Then Theorem 7 can be applied to obtain
d. Equation (4) then becomes the formula given...
Báo cáo toán học: "Promotion operator on rigged configurations of type A" potx
... ρ-sequence of rc
s
.
The hypothesis we want to carry across inductive steps is the logical disjunction of the
following two sufficient conditions for the commutativity of above diagram:
Hypothesis 6.1 (Simplified ... be viewed as a “cube”, the large outside square being the front face and
the small inside square being the back face, the four trapezoids between these two square...
Báo cáo toán học: "Spectral saturation: inverting the spectral Tur´n theorem a" pot
... . . . s, t) ;
- The stability conditions ( b ) in Theorems 4, 5, and 6 are stronger than the conditions
in the stability theorems of [6], [19] and [11]. Indeed, in all these theorems, condition
(b) ... all the vertices of G;
- The exponents 1 −
√
c and 1 −2
√
c in Theorems 2 and 5 are far from the best ones,
but are simple.
The next section contains notation and results needed t...
