Let a net
be given in the space A_{N} with an affine connectedness
G_{ab}^{s}, without a torsion . If the covectors
are defined such that

v
a

^{s} 
b v

_{s} = d_{a}^{b}, 

then the affinor
a_{a}^{b} = 
v
1

^{b} 
1 v

_{a}+ 
v
2

^{b} 
2 v

_{a} + ¼+ 
v
n

^{b} 
n v

_{a} 
v
n+1

^{b} 
n+1 v

_{a}¼ 
v
N

^{b} 
N v

_{a} 

is uniquely determinate by the net.
Since
a_{a}^{b} a_{b}^{s} = d_{a}^{s},
then a_{a}^{b} defines a composition
(X_{n} ×X_{m}) in A_{N}, i.e. the net
defines a composition.
Special nets which characterize Cartesian, geodesic, Chebyshevian,
geodesic Chebyshevian and
Chebysheviangeodesic compositions are introduced.
Conditions for the coefficients of the connectedness in the parameters of
these special nets are found.
The following three affinors are considered : a_{a}^{b},
b_{a}^{b} = 
v
1

^{b} 
1 v

_{a}+ 
v
2

^{b} 
2 v

_{a} + ¼+ 
v
k

^{b} 
k v

_{a} 
v
k+1

^{b} 
k+1 v

_{a} ¼ 
v
N

^{b} 
N v

_{a}, c_{a}^{b} = 

= 
v
1

^{b} 
1 v

_{a}+ 
v
2

^{b} 
2 v

_{a} + ¼+ 
v
k

^{b} 
k v

_{a} 
v
k+1

^{b} 
k+1 v

_{a} ¼ 
v
n

^{b} 
n v

_{a}+ 
v
n+1

^{b} 
n+1 v

_{a}+¼+ 
v
N

^{b} 
N v

_{a} . 

These affinors define a three interrelated compositions and satisfy
a_{a}^{b} b_{b}^{s} = c_{a}^{s}, b_{a}^{b} c_{b}^{s} = a_{a}^{s}, c_{a}^{b} a_{b}^{s} = b_{a}^{s}.
It is proved that
if two of the three interrelated compositions are Cartesian (Chebyshevian),
then the third one is Cartesian (Chebyshevian) too.
CARACTÉRISATION DES ESPACES 1MATRICIELLEMENT NORMÉS
Christian Le Merdy
lemerdy@math.univfcomte.fr,
Lahcène Mezrag
lmezrag@caramail.com
2000 Mathematics Subject Classification:46B28, 46B32, 46M05.
Key words:
Espace d'opérateurs, espace pmatriciellement normé, opérateur
complètement borné.
Let X be a closed subspace of B(H) for some Hilbert space H. In [9],
Pisier introduced S_{p}[ X] (1 £ p £ +¥) by
setting S_{p}[ X] = (S_{¥}[ X] ,S_{1}[ X] )_{q}, (where
q = ^{1}/_{p},
S_{¥}[ X] = S_{¥} 
Ä
min

X 

and
and showed that there are pmatricially normed spaces. In this paper we prove that conversely, if X is
a pmatricially normed space with p = 1, then there is an operator
structure on X, such that M_{n}^{1}( X) = S_{1}^{n}[ X] where S_{1}^{n}[ X] is the finite dimentional
version of S_{1}[ X] . For p ¹ 1, we have no answer.
USING MONTE CARLO METHODS TO EVALUATE SUBOPTIMAL EXERCISE POLICIES
FOR AMERICAN OPTIONS
Ghada Alobaidi
alobaidi@math.uregina.ca,
Roland Mallier
2000 Mathematics Subject Classification:91B28, 65C05.
Key words:
American options, Monte Carlo Method.
In this paper we use a Monte Carlo scheme to find the
returns that an uninformed investor
might expect from an American option
if he followed one of several naïve
exercise strategies rather than the optimal
exercise strategy.
We consider several such strategies that an illadvised
investor might follow.
We also consider how the expected return is affected by
how often the
investor checks to see if his exercise criteria have been met.
ON A CLASS OF VERTEX FOLKMAN NUMBERS
Nedyalko Dimov Nenov
nenov@fmi.unisofia.bg
2000 Mathematics Subject Classification:
05C55.
Key words:
vertex Folkman graph, vertex Folkman number.
Let a_{1}, ..., a_{r} be positive integers, m = å_{i = 1}^{r} (a_{i}1)+1 and
p = max{a_{1},¼,a_{r}}. For a graph G the symbol G ® (a_{1},¼,a_{r})
means that in every
rcoloring of the vertices of G there exists a monochromatic a_{i}clique
of color i for some i Î {1,¼, r}. In this paper we consider the
vertex Folkman numbers
F(a_{1},¼,a_{r}; m1) = 
min
 
ì í
î

V(G): G ®(a_{1},¼,a_{r}) and K_{m1}Ë G 
ü ý
þ



We prove that F(a_{1},¼,a_{r};m1) = m+6, if p = 3 and m ³ 6 (Theorem 3)
and
F(a_{1},¼,a_{r};m1) = m+7, if p = 4 and m ³ 6 (Theorem 4).
ON THE STABILIZATION OF THE WAVE EQUATION BY THE
BOUNDARY
Fernando Cardoso
fernando@dmat.ufpe.br,
Georgi Vodev
vodev@math.univnantes.fr
2000 Mathematics Subject Classification:
35B37, 35J15, 47F05.
Key words:
complex eigenvalues, energy decay.
We study the distribution of the (complex) eigenvalues
for interior boundary value problems with dissipative boundary conditions
in the case of C^{1}smooth boundary under some natural assumption
on the behaviour of the geodesics. As a consequence we obtain
energy decay estimates of the solutions of the corresponding wave equation.
GROUPS WITH RESTRICTED CONJUGACY CLASSES
F. de Giovanni
degiova@matna2.dma.unina.it,
A. Russo
alessio.russo@unile.it,
G. Vincenzi
gvincenzi@unisa.it
2000 Mathematics Subject Classification:
20F24.
Key words:
conjugacy class, nilpotent group.
Let FC^{0} be the class of all finite groups, and for each nonnegative
integer n define by induction the group class FC^{n+1} consisting of
all groups G such that for every element x the factor group
G/C_{G}(x^{G}) has the property FC^{n}.
Thus FC^{1}groups are
precisely groups with finite conjugacy classes, and the class FC^{n}
obviously contains all finite groups and all nilpotent groups with
class at most n. In this paper the known theory of FCgroups
is taken as a model, and it is shown that many properties of FCgroups
have an analogue in the class of FC^{n}groups.
THE AUTOMORPHISM GROUP OF THE FREE ALGEBRA OF RANK TWO
P. M. Cohn
pmc@math.ucl.ac.uk
2000 Mathematics Subject Classification:
16W20.
Key words:
free algebra, free product with amalgamation, affine
automorphism, linear automorphism, bipolar structure.
The theorem of Czerniakiewicz and MakarLimanov, that all the automorphisms
of a free algebra of rank two are tame is proved here by showing that the
group of these automorphisms is the free product of two groups
(amalgamating their intersection), the group of all affine automorphisms
and the group of all triangular automorphisms. The method consists in
finding a bipolar structure. As a consequence every finite subgroup of
automorphisms (in characteristic zero) is shown to be conjugate to a group
of linear automorphisms.
RELIABILITY FOR BETA MODELS
Saralees Nadarajah
snadaraj@chumal.cas.usf.edu
2000 Mathematics Subject Classification:
33C90, 62E99.
Key words:
Beta distributions, Hypergeometric functions,
Incomplete beta function, Reliability.
In the area of stressstrength models there has been a large amount of work
as regards estimation of the reliability R = Pr(X_{2} < X_{1})
when X_{1} and X_{2} are independent random variables belonging to the
same univariate family of distributions.
The algebraic form for R = Pr(X_{2} < X_{1}) has been worked out for the majority
of the wellknown distributions including Normal, uniform, exponential, gamma,
weibull and pareto.
However, there are still many other distributions for which the form of R is not known.
We have identified at least some 30 distributions with no known form for R.
In this paper we consider some of these distributions and derive
the corresponding forms for the reliability R.
The calculations involve the use of various special functions.
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