... possible situations are illustrated
in Fig. 9.
For i ∈ {1, 2}, let N
i
and k
i
be the numbers of vertices and holes of the respective
polygons, R
i
the sets of basic rectangles, I
i
the sets of ... isolated chord as indicated in the
left hand side of Fig. 13. Then f is not a source for any of the rectangles A
1
and A
2
. The
right hand side of the same figure show...
... g
m
(ζ))
b
a+deg
z,∞
a
r
m
{b
a+deg
z,∞
a
r
m
1
m
2
qk−p(r)
m
ρ
m
}
m
1
m
2
qk−p(r)
M
r
[g
m
](ζ).
(3.11)
11
3. Proof of the results
Proof of Theorem 1.4 Suppose that the conclusion of theorem is not true, then
there exists an entire solution w(z) satisfies the equation [Q(w(z))]
n
= P [w]. such
that
λ ... (HTML) versions will be made available soon.
Further results of the esti...
... will solve this problem in the case of r =1andr = 2. Then the other cases
follow by the same method.
2. Notations and Premilinaries
Throughout this paper, the following notations will be used: ... studied the sheaves of differential forms on finite r-jet prolonga-
tions J
r
Y . Then he constructed the sequence of quotient sheaves Ω
k
r
/Θ
k
r
.This
quotient sequence is calle...
... 17].
The authors have used there the notion of admissible sets instead of convex sets
in vector spaces.
In Sec. 3 of this paper, we show that in all these results, the notion of ad-
missible sets ... theorems,
minimax theorems, using the notion of sub-admissible sets instead of admissible sets
as usual.
1. Introduction
After Khamsi s paper [8] on the KKM-maps principle...
... b
k
has no solutions.
Theorem 2.1 (Necessary conditions for lower semicontinuity). If the multifunc-
tion S( ·) is lower semicontinuous at (c, b), then the system Ax ≥ b is regular
and the set S( c, ... i.e., there exists
¯x ∈ R
n
such that A¯x>b. It is easily seen that if the system Ax ≥ b is irregular
then there exists a sequence {b
k
}⊂R
m
converging to b such that, for each k...
... for some r .The
components of λ are called the parts of λ. The integer n, the sum of all the parts of
λ, is called the norm of λ and is denoted by n(λ). The (ordinary) Ferrers diagram of
λ is an ... indicate the hook of the cell
(2, 1). The hook of a cell ρ of the shifted Ferrers diagram of λ again includes all cells
that are either in the same row a...
... study of the limit cases —in which the derived bounds
are attained— has revealed the presence of high levels of structure in the considered
graphs. See, for instance, the papers of Haemers and ... Godsil [24] , we say that the graph
Γ
i
is the i-th class of the scheme, and so we indistinctly use the words “graph” or
“class” to mean the same thing.
2 The Proper...