Serdica Mathematical Journal
Volume 25, Number 3, 1999
C O N T E N T S
A B S T R A C T S
NEW BINARY EXTREMAL SELF-DUAL CODES OF LENGTHS 50 AND 52
Stefka Buyuklieva
1991 Mathematics Subject Classification: 05A05.
Key words:
self-dual codes.
New extremal binary self-dual codes of lengths 50 and 52 are constructed.
Some of them are the first known codes with such weight enumerators. The
structure of their automorphisms groups are shown.
ON THE UNIFORM DECAY OF THE LOCAL ENERGY
Georgi Vodev
vodev@math.univ-nantes.fr
1991 Mathematics Subject Classification: 35P25, 35J15, 47F05.
Key words:
cutoff resolvent, local energy decay.
It is proved in [1], [2] that in odd dimensional spaces any uniform
decay of the local energy implies that it must decay exponentially.
We extend this to even dimensional spaces and to more general
perturbations (including the transmission problem) showing that any
uniform decay of the local energy implies that it must decay like
O(t^{-2n}), t >> 1 being the
time and n being the space dimension.
THE GENERAL DIFFERENTlAL OPERATORS GENERATED BY A QUASI-DIFFERENTIAL
EXPRESSIONS WITH THEIR INTERIOR SINGULAR POINTS
Sobhy El-sayed Ibrahim
1991 Mathematics Subject Classification: 34A05, 34B25, 34C11,
34E15, 34G10, 47E05.
Key words:
quasi-differential
expressions, regular and singular end-points, regularly solvable
operators, Hilbert space, boundary conditions.
The general ordinary quasi-differential expression M of n-th order with
complex coefficients and its formal adjoint M^{+}
are considered over a regoin (a,b) on the real line,
-¥ £ a
< b £
¥, on which the operator may have a
finite number of singular points. By considering M over various subintervals
on which singularities occur only at the ends, restrictions of the maximal
operator generated by M in L^{2}_{w} (a,b)
which are regularly solvable with respect to the minimal
operators T_{0}(M) and T_{0}(M^{+}).
In addition to direct sums of regularly solvable operators defined on the
separate subintervals, there are other regularly solvable restrications of
the maximal operator which involve linking the various intervals together
in interface like style.
GEOMETRIC STABLE LAWS THROUGH SERIES REPRESENTATIONS
Tomasz J. Kozubowski
tkozubow@cecasun.utc.edu
Krzysztof Podgórski
kpodgorski@math.iupui.edu
1991 Mathematics Subject Classification:
60E07, 60F05, 60F15, 60F17, 60G50, 60H05.
Key words:
Geometric compound,
invariance principle, Linnik distribution, Mittag-Leffler distribution,
random sum, stable distribution, stochastic integral.
Let (X_{i}) be a sequence of i.i.d. random variables, and let N
be a geometric random variable independent of (X_{i}). Geometric
stable distributions are weak limits of (normalized) geometric compounds,
S_{N} = X_{1}+¼+X_{N}, when
the mean of N converges to infinity. By an appropriate representation of the
individual summands in S_{N} we obtain series representation of the
limiting geometric stable distribution. In addition, we study the asymptotic
behavior of the partial sum process
S_{N}(t) = å_{i =
1}^{[Nt]} X_{i}, and derive series representations of
the limiting geometric stable process and the corresponding stochastic
integral. We also obtain strong invariance principles for stable and
geometric stable laws.
A REMARK ON S.M. BATES' THEOREM
Petr Hájek
1991 Mathematics Subject Classification:
58C25.
Key words:
Separable Banach space, smooth surjection, homogeneous
polynomial surjection, noncompact operator.
In his paper [1], Bates investigates the existence of nonlinear,
but highly smooth, surjective operators between various classes
of Banach spaces. Modifying his basic method, he obtains the following
striking results.
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