Petrogradsky, V. M.
Exponents of subvarieties of upper triangular matrices
over arbitrary fields are integral
(pp. 167176)
A B S T R A C T S
ON AVERAGING NULL SEQUENCES OF REALVALUED FUNCTIONS
P. Ch. Kiriakouli
kyriak@hol.gr
2000 Mathematics Subject Classification: 46B20.
Key words:
partition theorems, uniform convergence,
repeated averages of realvalued functions, convergence index, oscillation
index.
If x is a countable ordinal and (f_{k}) a sequence of
realvalued functions we define the repeated averages of order
x of (f_{k}). By using a partition theorem of
NashWilliams for families of finite subsets of positive integers it is proved that
if x is a countable ordinal then every sequence (f_{k})
of realvalued functions has a subsequence (f¢_{k})
such that either every sequence of repeated averages of order x
of (f_{k}¢) converges uniformly to zero or no sequence
of repeated averages of order x of
(f¢_{k}) converges uniformly to zero.
By the aid of this result we obtain some results stronger than Mazur's
theorem.
PRIMITIVE IDEALS AND SYMPLECTIC LEAVES OF QUANTUM MATRICES
V. G. Mosin
bacha11@mail.ru
2000 Mathematics Subject Classification: 17B37.
Key words:
twisted algebra, Poisson algebra, primitive ideals, symplectic leaves.
It is proved that there exists a bijection between the primitive ideals
of the algebra of regular functions on quantum m×nmatrices
and the symplectic leaves of associated Poisson structure.
ON MINIMIZING  S(AXXB)
_{p}^{p}
Salah Mecheri
mecherisalah@hotmail.com
2000 Mathematics Subject Classification: Primary 47B47, 47A30; Secondary 47B10.
Key words:
Generalized Derivation,
Orthogonality, von NeumannSchatten class, Putnam Fuglede's property.
In this paper, we minimize the map F_{p}(X) =
S(AXXB)_{p}^{p},
where the pair (A,B) has the property (FP)_{Cp}, S
Î C_{p}, X varies such that AXXB
Î C_{p} and C_{p} denotes the von
NeumannSchatten class.
STRICHARTZ TYPE ESTIMATES FOR OSCILLATORY PROBLEMS FOR
SEMILINEAR WAVE EQUATION
Stefania Di Pomponio
dipompon@univaq.it
2000 Mathematics Subject Classification:
35B37, 35L05, 35L70.
Key words:
Semilinear wave equation, Strichartz estimate.
We treat the oscillatory problem for semilinear wave equation.
The oscillatory initial data are of the type



h(x) +
e^{s+
1} e^{il(x)/e} b_{0}
(e,x) 
 

e^{s}
e^{il(x)/e} b_{1}
(e,x). 

  
By using suitable variants of Strichartz estimate we extend the results
from [6] on a priori estimates of the approximations
of geometric optics. The main improvement is the fact that we can
obtain a priori estimates for the case s = 1, while in
[6] we could treat only the case s >
^{n}/_{2}1.
ASYMPTOTIC BEHAVIOUR OF COLENGTH OF VARIETIES OF LIE ALGEBRAS
S. P. Mishchenko
msp@mishch.ulsu.ru ,
M. V. Zaicev
zaicev@mech.math.msu.su
2000 Mathematics Subject Classification:
Primary 17B01, 17B30, 16R10, Secondary 20C30.
Key words:
Lie algebras with
polynomial identities, varieties of Lie algebras, codimensions, colength.
We study the asymptotic behaviour of numerical characteristics of
polynomial identities of Lie algebras over a field
of characteristic 0. In particular we investigate the
colength for the cocharacters of polynilpotent varieties
of Lie algebras. We prove that there exist
polynilpotent Lie varieties with exponential and overexponential
colength growth. We give the exact asymptotics for the colength
of a product of two nilpotent varieties.
ON A NEW APPROACH TO WILLIAMSON'S GENERALIZATION
OF PÓLYA'S ENUMERATION THEOREM
Valentin Vankov Iliev
viliev@math.bas.bg ,
viliev@nws.aubg.bg
2000 Mathematics Subject Classification:
05A15, 20C30.
Key words:
induced monomial representations of the symmetric
group, enumeration.
Pólya's fundamental enumeration theorem and some results from
Williamson's generalized setup of it are proved in terms of
SchurMacdonald's theory (SMT) of ``invariant matrices''.
Given a permutation group W £ S_{d}
and a onedimensional character c
of W, the polynomial functor F_{c}
corresponding via SMT to the induced monomial representation
U_{c} =
ind_{W}^{Sd}(c)
of S_{d}, is studied.
It turns out that the characteristic ch(F_{c})
is the weighted inventory of some set J(c) of Worbits in
the integervalued hypercube [0,¥)^{d}. The
elements of J(c) can be distinguished among all
Worbits by a maximum property. The identity
ch(F_{c} ) = ch(U_{c})
of both characteristics is a consequence of SMT, and is equivalent to a result of
Williamson. Pólya's theorem can be obtained from the above identity by the
specialization c = 1_{W}, where 1_{W}
is the unit character of W.
EXPONENTS OF SUBVARIETIES OF UPPER TRIANGULAR MATRICES
OVER ARBITRARY FIELDS ARE INTEGRAL
V. M. Petrogradsky
vmp@mmf.ulsu.ru
2000 Mathematics Subject Classification:
16R10.
Key words:
associative algebras with polynomial identities,
growth of codimensions.
Let U_{c} be the variety of associative algebras generated
by the algebra of all upper triangular matrices, the field being arbitrary.
We prove that the upper exponent of any subvariety
V Ì U_{c}
coincides with the lower exponent and is an integer.
Back