The Fifth Vasil Popov Prize awarded to Mauro Maggioni of Duke
University
A B S T R A C T S
GROUPS OF ORDER 32 AS GALOIS GROUPS
Ivo M. Michailov
i.michailov@fmi.shu-bg.net
2000 Mathematics Subject Classification:
12F12.
Key words:
embedding problem, Galois extension, quaternion algebra, obstruction.
We find the obstructions to realizability of groups of order 32
as Galois groups over arbitrary field of characteristic not 2.
We discuss explicit extensions and automatic realizations as well.
OLIGOPOLY MODEL OF A DEBIT CARD NETWORK
Peter Manchev
manchev.p@bnbank.org
JEL Classification:
G21, L13.
Key words:
debit card, payment networks, switch fees, access
pricing.
The paper builds an oligopoly model of a debit card network. It
examines the competition between debit card issuers. We show that
there is an optimal pricing for the debit card network, which
maximizes all issuer's revenues. The paper also shows that
establishing a link between debit card networks averages the costs
provided that there is no growth in the customer's usage of the
networks, resulting from the link.
THE ASYMPTOTIC BEHAVIOUR OF THE FIRST EIGENVALUE
OF LINEAR SECOND-ORDER ELLIPTIC EQUATIONS IN DIVERGENCE FORM
Alexander Fabricant
Nikolai Kutev
Tsviatko Rangelov
rangelov@math.bas.bg
2000 Mathematics Subject Classification:
35J70, 35P15.
Key words:
linear elliptic equations, eigenvalue
problem, asymptotic behavior, dynamical systems.
The asymptotic of the first eigenvalue for linear second order
elliptic equations in divergence form with large drift is studied. A
necessary and a sufficient condition for the maximum possible rate
of the first eigenvalue is proved.
A NEW CHARACTERIZATION OF WEIGHTED PEETRE K-FUNCTIONALS
Borislav R. Draganov
bdraganov@fmi.uni-sofia.bg
Kamen G. Ivanov
kamen@math.bas.bg
2000 Mathematics Subject Classification:
46B70, 41A25, 41A17, 26D10.
Key words:
K-functional, modulus of smoothness, linear operator, fractional integral.
Certain types of weighted Peetre K-functionals are characterized
by means of the classical moduli of smoothness taken on a proper
linear transforms of the function. The weights with power-type
asymptotic at the ends of the interval with arbitrary real
exponents are considered. This paper extends the method and results
presented in [3].
ON SOME EXTREMAL PROBLEMS OF LANDAU
Szilárd Révész
revesz@renyi.hu,
revesz@ihp.jussieu.fr
2000 Mathematics Subject Classification:
Primary: 42A05. Secondary: 42A82, 11N05.
Key words:
Prime number
formula, positive trigonometric polynomials, positive definite
functions, extremal problems, Borel measures, convexity, duality.
The prime number theorem with error term presents itself as
&pi'(x) = ∫_{2}^{x} [dt/ logt] + O ( x e^{- K logL x}). In 1909, Edmund Landau provided a systematic analysis of
the proof seeking better values of L and K. At a key point of
his 1899 proof de la Vallée Poussin made use of the nonnegative
trigonometric polynomial
^{2}/_{3} (1+cos x)^{2} = 1+^{4}/_{3} cosx +^{1}/_{3} cos2x. Landau considered more general positive definite
nonnegative cosine polynomials
1+a_{1}cos x+… + a_{n}cos nx ≥ 0, with a_{1}> 1,a_{k} ≥ 0 (k = 1,…,n), and deduced the above
error term with L = 1/2 and any K< 1/(2V(a))^{½}, where
V(a): = (a_{1}+a_{2}+…+ a_{n})/(( (a_{1})^{½}-1)^{2}). Thus the
extremal problem of finding V: = minV(a) over all admissible
coefficients, i.e. polynomials, arises.
The question was further studied by Landau and later on by many
other eminent mathematicians. The present work surveys these works
as well as current questions and ramifications of the theme,
starting with a long unnoticed, but rather valuable Bulgarian
publication of Lubomir Chakalov.
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