Báo cáo toán học: "Bounding the partition function of spin-systems" ppsx
Báo cáo toán học: "Bounding the partition function of spin-systems" ppsx
... product over the vertices of G of the weights of the spins times the product over the edges
of G of the weights of the spin-pairs. In this language Z
W
(G) is the partition function of the
the electronic ... all of the edge-weights are either
0 or 1,andtherˆole of these weights is to exclude certain configurations from contributing to the
partition...
Báo cáo toán học: " On a Partition Function of Richard Stanley" pptx
... replaced by N +1.
Proof of Theorem 1. We let τ
2N
(q, z,y) denote the numerator on the right-hand side of
(3) and τ
2N+1
(q, z,y) denote the numerator on the right-hand side of (4). If we can show
that ... sequence may well be zero; the non-zero entries
make up the parts of π
. However in light of the fact that 0 is even, we see that O(π
)is
the number of odd e...
Báo cáo toán học: "On the first occurrence of strings" ppsx
... of all cases, and the proof of the lemma.
Lemma 12 With all the hypothesis of the previous lemma except that l
n
(τ
) = 2, P (T
τ
=
N
3
) > 1/3.
Proof: By direct computation, we verify the ... τ ≥ 2
n
+ 2
n−4
. Then c is the fourth character of σ
2
, the fifth character of σ
2
equals
the first character of σ
2
, the sixth character equals the second, and so...
Báo cáo toán học: "Bounding the number of edges in permutation graphs" pdf
... upper bound on
the size of such graphs. The last section of the paper contains some concluding remarks.
the electronic journal of combinatorics 13 (2006), #R44 3
On the other hand, if the insertion ... that of π
s,m
n
then the configuration of the first type
in Figure 2 will not occur for most pairs of vertices. Then we would not need the region
E in the proof, a...
Báo cáo toán học: "On the Asymptotic Distribution of the Bootstrap Estimate with Random Resample Size" ppsx
... > 0), which completes the
proof.
Proof of Theorem 2.1.
If EX
2
< ∞ then s
2
n
→ σ
2
a.s. Therefore, the theorem follows if we show that
the conditional distribution of Y
∗
nN
n
converges ... replacing the unknown distribution by the empirical
distribution of the data in the definition of the statistical function, and then
resampling the data to obtain a Monte...
Báo cáo toán học: "Maximizing the Stability Radius of Discrete-Time Linear Positive Systems by Linear Feedbacks" ppsx
... given matrices defining the structure of the
perturbations and Δ ∈ R
l×q
is unknown disturbance matrix. Then the stability
radius of the matrix A with respect to perturbations of the structure (D, ... <
1. If the compact basis V
b
of the polyhedron V = {F : A − BF ≥ 0} consists of
only one point F
∗
then either F
0
=0or F
∗
is the unique optimal solution for
Proble...
Báo cáo toán học: "On the Asymptotic Behavior of Solutions of a Nonlinear Difference Equation with Bounded Multiple Delay" pptx
... =min
1ir
m
i
, ˆm =
1
r
r
i=1
m
i
.
The proofs of the following theorems can be obtained similarly as the proofs
of Theorem 6.20.1, Theorem 6.20.2 in [1], so we omit them here.
Theorem 2. Assume that
xF ... further that
lim sup
x,y→∞
H(x, y)
x
< 1 − λ
∗
, (2.2)
Then every solution {x
n
}
∞
n=−m
of (2.1) is bounded.
Proof. The proof follows from applying the mean value t...
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