... explicitly derived the equation at hand from the
elementary Miura transformations of D
(1)
5
. Further, we have clarified these relations from
the point of view of Weyl group theory and of rational surfaces.
References
[1] ... now, along similar lines, to derive the second equation of the system. First we
6 On the identity of two q-discrete Painlev
´
e equation...
... with the recordings. The experimental
procedures adhered to the recommendations of the Euro-
pean Union and the NIH Guide for Care and Use of Lab-
oratory Animals, and were approved by the Ethical
Committee ... means of
implanted interfaces with the peripheral nerves of the
subject [12]. In the latter case, the choice of the electrode
will make a differen...
... of the
throat."
Then they mixed all the "stuff" together and sprayed 1 cc
of the mixture in each of the nostrils of 10 volunteers, and
"into the throat, while inspiring, and ... was the largest of the studies, illustrative
of the attempts, and remarkable for the courageousness of
the volunteers [52]. In 1919 – in a series of expe...
... existence
results o f solutions of (1.1). The idea of the proof is to transfer the problem of the
existence of solutions for (1.1) into the problem of the existence of a minimizer for
some associated ... weak solutio n
of (1.1).
In order to complete the proof of Theorem 3.2, we will prove the uni queness of the
weak solution.
Let u
1
and u
2
be two weak...
... solutions of the system
of the difference equations
x
n
= A +
1
y
n−
p
, y
n
= A +
y
n−1
x
n−r
y
n−s
.
In [10], Yalcinkaya studied the global asymptotic stability of the system of difference
equations
z
n+1
=
t
n
z
n−1
+ ... EM: On the solutions of a class of difference equations systems. Demonstratio
Mathematica. 41(1), :109–122 (2008)
32. Elsayed, EM: On the so...
... d (2.5) of Theorem 2.3 have been used only in the choice of the
constant C (see (2.11)) and in the proof of Step 1. Hence, we now present only the
proof of this part, the rest being the same.
Cupini ... with the
exception of (2.2), and with (2.5) replaced by
lim
y→+∞
θ(y)
y
=0
.
(2:17)
Then, the assertion of Theorem 2.3 follows.
Proof. The proof is quite simi...
... -1)[14].In
the case of the Binary tree, the number of branches is
doubled as the matrix size n increases, being the
increasing number of nodes equal to 2
n+1
-1[15].On
the other hand and conversely, the ... than.
Acknowledgements
The authors would like to thank the anonymous reviewers for their helpful
comments, as well as to the Technical University of Catalon...
... notations and the
formulation of the problem. In Section 3 we present the results on the unique exis-
tence and the regularity in time of the generalized solution. The global regularity of
the solution ... 2γ
1
.
(3:12)
From now to the end of the present proof, we fix such constants ε
1
, ε
2
, ε
3
and r. Let
|||u
N
(·, τ )
2
||
|
stand for the left-hand...
... visiting the research Institute of Mathematics, Seoul National University.
Author details
1
Department of Mathematics, Hanyang University, Seoul 133-791, Republic of Korea
2
Department of Mathematics,
University ... Mathematics,
University of Ulsan, Ulsan 680-749, Republic of Korea
3
Department of Mathematics, Daejin University, Kyeonggi 487-
711, Republic of Korea
4
Departm...
... the
description of our database and the results of the experi-
ments. Section 5 has the discussion and the conclusions
on the limitations of the TTT early prediction of out-
come from the parameters in the ... even
questioned the actual predictive value of some of the
formerly proposed parameters [17].
Therefore, the aim of this study was twofo ld. Fi...