... improved product construction for large sets of Kirkman triple
systems, Discrete Math. 260(20 03) 307-313.
[22] J. Zhou, Y. Chang, Tripling construction for large sets of resolvable directed triple
systems, ... ng.
the electronic journal of combinatorics 16 (2009), #R114 4
Another product construction for large sets of
resolvable directed tripl...
... a family of subsets of a n
2
-
set, S
2
. WedefinetheproductF
1
× F
2
to be the family of subsets of the (n
1
+ n
2
)-set,
S
1
∪ S
2
, whose members consist of the union of any element of F
1
with ... than (1) for m ≥ 8. So the Bollobas conjecture fails for
k ≥ 10.
The idea of the above construction which improves on products of H
3
can be applied
to products of other...
... Any directed edge of G
∗
0
can be
moved to a directed edge of DE(∆) or to its reverse. So, there are at most 6 orbits of
directed edges. Any directed edge can be moved using L and R to a directed ... l) of integers an element of this moving group,
which we call (k,l) -product of basic permutations, and which encodes the lengths of the
ZC-circuits of GC
k,l
(G
0
)....
... strongly
affects the subset of significant DoFs, N
eff
≤ M, called effective DoFs (EDoFs).
3 SNR optimization in opportunistic beamforming systems
The idea of opportunistic beamforming has shown that ... of the wireless channel. Opportunistic beamforming will therefore
improve the performance of wireless channels having a strong line -of- sight (LoS) component
(i.e., Rician channels), by...
... below).
For information about publishing your research in Journal of Inequalities and Applications go to
http://www.journalofinequalitiesandapplications.com/authors/instructions/
For information ... inequalities for a class of
even-order differential equations
Qi-Ming Zhang
∗1
and Xiaofei He
2
1
College of Science, Hunan University of Technology, Zhuzhou,
Hunan 412000, P.R. China...
... giving a complete asymptotic
expansion of I(n, x) can be immediately read out of its proof.
the electronic journal of combinatorics 7 (2000), #R50 4
and, hence, for all n ≥ 9andallrealnumbersx,
|I(n, ... asymptotic expansion for b(n, k)/n!fora
range of k including the maximum of the b(n, k)/n!.
AMS Subject Classification: 05A16, 05A15, 05A10
A permutation σ =(σ(1), ,σ(n)) of [n...
... Acknowledgment
The author thanks Prof. Yair Caro and Raphael Yuster for sending reference [7]. The
author also thanks Prof. Cheng Zhao for his advice.
References
[1] J.A. Bondy and ... result.
Theorem. Let t = 27720r + 169 (r ≥ 1), then
f(n) ≥ n +32t −1
for n ≥
6911
16
t
2
+
514441
8
t −
3309665
16
.
2 Proof of Theorem
Proof. Let t = 27720r + 169,r ≥ 1,n
t
=
6911
16
t
2
+
514441
8
t ....
... transition counts of which
are all the same power of two, or are two successive powers of two. A proof for the
existence of exponentially balanced Gray codes is derived. The proof is much sim-
pler ... e(i)=e(j) for all i, j.
In [11], Wagner and West conjectured that exponentially balanced Gray codes exist
for all length n. By extending the method of Robinson and Cohn for th...
... New upper bound for a class of vertex Folkman
numbers
N. Kolev
Department of Algebra
Faculty of Mathematics and Informatics
“St. Kl. Ohridski” University of Sofia
5 J. Bourchier blvd, ... have
cl(G
i
)=a
i
− 1 for i =1, 2. (14)
From (13), (14) and Lemma 1 we conclude that
The number of the vertices of each connected
component of
¯
G
1
is an even number;
(15)
and
the number o...
... their sets of k-deletions.
We are now ready to prove our main result.
Proof of Theorem 1. Suppose that we are given a positive integer k and a set ∆ of k-
deletions of some (unknown) partition λ of ... the cell (k, k + 1) and that no k-deletion of λ
can contain the cell (k + 1, k). Therefore every k-deletion of µ and of λ is actually a
(k − 1)-deletion of
µ ∧ λ = (k + 1, ....