... assume that there exists a sequence of triangulations of the unit square
starting with T
n
0
and satisfying the conditions (i)−(iii) of Theorem 2.7, then, analogously
to the proof of Theorem 2.7, ... ≥
1
k
j
·
A
1
n
′
i
−
A
2
n
′′
i
.
the electronic journal of combinatorics 18 (2011), #P137 10
On the area discrepancy of triangulations
of squares...
... τ
−1
((T
)) and
T
is one of the two components of T − e. (This is well defined since, for T
being the
other component of T − e,thesets(T
),(T
) form a partition of (T ).) The width of
the ... branch-decomposition (T,τ) is the maximum of the widths of the edges of T ,andthe
branch-width of M is the minimal width over all branch-decompositions...
... proof is
the main focus of the present work:
Theorem. The number of ASMs of size n with the 1 of the first row in the (i + 1)
st
position and the 1 of last row in the (j + 1)
st
position is the ... number of ASMs of size n is the same as
the number of TSSCPPs of size 2n:
A
n
= A
n
(1) = U
0
n
(1)
4 The proof
4.1 ASM counting as the partition functi...
... analysis of Breaker’s random strategy described in the
proof of Theorem 4 leaves a lot of room for improvement. For the sake of simplicity and
clarity of the presentation, in Claim 9 and Lemma ... contradiction.
4 Proof of Theorem 4
As Maker and Breaker claim their edges during the game, they are building two edge-
disjoint subgraphs of K
n
, denoted by G
M
and G...
... only the spacing between the grid lines and not their actual
position. We choose the position of the rightmost vertical line randomly and uniformly in
the interval [n −, n), and the slope of the ... trapezoid. The position of
the slanting dividing line is chosen such that the measure of balanced α above the line and
inside the sector equals the measu...
... statistical analysis of the capacity of N∗Nakagami-m
channels. Specifically, we have studied the influence of the severity of fading and the
number of hops on the PDF, CDF, LCR, and ADF of the channel capacity. ... as
the numb er of hops N in N∗Nakagami-m channels increases, the mean channel capacity
decreases. The influence of the severity of fading an...
... R
+
, 0 ≤ j ≤ n and p ∈ (0, 1).
The following result provides a necessary and sufficient condition for the boundedness of the solution of
(4.4) and (4.5). The necessary part of the next theorem was ... 2.3). Thus, the conditions of Theorem 3.1 hold, and the initial vector x
0
belongs to S,
and hence the solution x(n; x
0
) of (1.1) and (1.2) is bounded.
We...
... Figure 4 . The peaked-
ness of the out -of- band signal exceeds the peakedness of
the in-band signal by over an order of magnitude.
The lower panel of Figure 5 shows, for the same
examples, the total ... ndlimited mixture of a thermal
(Gaussian) and a white impulsive noises, with the total
noise peakedness of 8.8 dBc. The signal-to-noise ratio in
the baseband...