Kostov, Vl. P.
Overdetermined strata in general families of polynomials
(pp. 377386)
A B S T R A C T S
APPLICATIONS OF THE FRÉCHET SUBDIFFERENTIAL
M. Durea
durea@uaic.ro
2000 Mathematics Subject Classification: 46A30, 54C60, 90C26.
Key words:
Fréchet subdifferentials,
multifunctions, optimization, metric regularity.
In this paper we prove two results of nonsmooth analysis involving the
Fréchet subdifferential. One of these results provides a necessary
optimality condition for an optimization problem which arise naturally from a
class of wide studied problems. In the second result we establish a sufficient
condition for the metric regularity of a setvalued map without continuity
assumptions.
ON A CLASS OF ELLIPTIC EQUATIONS
FOR THE nLAPLACIAN IN R^{n}
WITH ONESIDED EXPONENTIAL GROWTH
Anna Maria Candela
candela@dm.uniba.it,
Marco Squassina
squassina@mate.polimi.it
2000 Mathematics Subject Classification: 35J40, 49J52, 49J40, 46E30.
Key words:
Nonsmooth analysis, onesided
growth, TrudingerMoser inequality.
By means of a suitable nonsmooth critical point theory
for lower semicontinuous functionals
we prove the existence of infinitely many solutions
for a class of quasilinear Dirichlet problems with
symmetric nonlinearities having a onesided growth condition
of exponential type.
STABILITY AND INSTABILITY OF SOLITARY WAVE SOLUTIONS OF
A NONLINEAR DISPERSIVE SYSTEM OF BENJAMINBONAMAHONY TYPE
Sevdzhan Hakkaev
shakkaev@fmi.shubg.net
2000 Mathematics Subject Classification:
35B35, 35B40, 35Q35, 76B25, 76E30.
Key words:
Dispersive system, solitary waves, stability.
This paper concerns the orbital stability and instability
of solitary waves of the system of coupling equations of
BenjaminBonaMahony type. By applying the abstract results
of Grillakis, Shatah and Strauss and detailed spectral
analysis, we obtain the existence and stability of the
solitary waves.
THE KOEBE DOMAIN FOR CONCAVE UNIVALENT FUNCTIONS
KarlJoachim Wirths
kj.wirths@tubs.de
2000 Mathematics Subject Classification:
30C25, 30C45.
Key words:
Koebe domain, concave univalent functions,
starlike meromorphic functions.
Let D denote the open unit disc and
f:D®[`(C)]
be meromorphic and injective in D. We further assume that
f has a simple pole at the point p Î (0,1)
and an expansion
f(z) = z+ 
¥
å
n = 2

a_{n}(f)z^{n}, 
z < p. 

Especially, we consider f that map D onto a
domain whose complement with respect to [`
(C)] is convex. It is proved that this implies
K: = 
ì í î 
w : 
ê ê ê 
w + 
p(1+p^{2})
(1p^{2})^{2}


ê ê ê 
> 
2p^{2}
(1p^{2})^{2}


ü ý þ  Ì
f(D) 

and that for any c Î [`
(C)]\K there exists a function f satisfying the conditions
mentioned above such that c does not belong to f(D).
This means that K is the exact Koebe domain for the
class of functions considered here.
ON NONADAPTIVE SEARCH PROBLEM
Emil Kolev
emil@moi.math.bas.bg
2000 Mathematics Subject Classification:
91A46, 91A35.
Key words:
search, nonadaptive search.
We consider nonadaptive search problem for an unknown element x from
the set A = {1,2,3,..., 2^{n}}, n ³ 3.
For fixed integer S the questions are of the form: Does x
belong to a subset B of A, where the sum of the elements of B
is equal to S? We wish to find all integers S
for which nonadaptive search with n questions finds x.
We continue our investigation from [4] and
solve the last remaining case n = 2^{k}, k ³ 2.
OVERDETERMINED STRATA IN GENERAL FAMILIES OF POLYNOMIALS
Vladimir Petrov Kostov
kostov@math.unice.fr
2000 Mathematics Subject Classification:
12D10.
Key words:
Overdetermined stratum; hyperbolic polynomial;
Gegenbauer's polynomial.
Denote by Pol_{Cn} the space
of all complex monic degree n polynomials in one variable and by
PP_{n} the product space
Pol_{Cn}×Pol_{Cn1}×¼×Pol_{C1}. Stratify the space PP_{n} according to the
multiplicities of the roots of the n polynomials and the presence of
common roots between any two of them. Define the map
p: Pol_{Cn}\hookrightarrow PP_{n} by
P® (P, P¢/n,P¢¢/n(n1),¼,P^{(n1)}/n!). A stratum
is called overdetermined if its codimension in
PP_{n} is greater
than the codimension of its intersection with p(Pol_{Cn})
in p(Pol_{Cn}). In the paper we give different examples of
overdetermined strata.
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