Serdica Mathematical Journal
Volume 31, Numbers 12, 2005
C O N T E N T S
A B S T R A C T S
AN INVITATION TO ADDITIVE PRIME NUMBER THEORY
A. V. Kumchev
kumchev@math.utexas.edu,
D. I. Tolev
dtolev@pu.acad.bg
2000 Mathematics Subject Classification:
11D75, 11D85, 11L20, 11N05, 11N35, 11N36, 11P05, 11P32, 11P55.
Key words:
Goldbach problems, additive problems, circle method, sieve methods,
prime numbers.
The main purpose of this survey is to introduce the inexperienced reader to
additive prime number theory and some related branches of analytic number theory.
We state the main problems in the field, sketch their history and the basic
machinery used to study them, and try to give a representative sample of the
directions of current research.
WEAK COMPATIBILITY AND COMMON FIXED POINT THEOREMS FOR
ACONTRACTIVE AND EEXPANSIVE MAPS IN UNIFORM SPACES
M. Aamri, D. El Moutawakil
d.elmoutawakil@math.net
2000 Mathematics Subject Classification:
47H10, 54E15.
Key words:
Uniform spaces, common fixed point, contractive maps,
expansive maps, compatible maps, weakly compatible maps.
The purpose of this paper is to define the
notion of Adistance and Edistance in uniform
spaces and give several new common fixed point
results for weakly compatible contractive or
expansive selfmappings of uniform spaces.
ON THE CONVERGENCE OF (0, 1, 2) INTERPOLATION
Y. E. Muneer
muneeralnour@yahoo.co.uk
2000 Mathematics Subject Classification:
41A05.
Key words:
Zeros, modulus of continuity, interpolation process, approximation.
For the Hermite interpolation polynomial, H_{m} (x)
we prove for any function f Î C^{(2q)}([1,1]) and any
s = 0,1,2,¼, q, where q is a fixed integer
that
 H_{m}^{(s)} (x)  f^{(s)}(x) = O(1)w( 
1
m

,f^{(2q)}) 
logn
n^{2q  2s}

. 

Here m is defined by m = 3n1.
If f Î C^{(q)}([1,1]), then
 H_{m}^{(s)}  f^{(s)}(x) = O(1)w( 
1
m

,f^{(q)}) 
logn
(1  x^{2})^{q / 2}



for x Î (1, 1).
TRIANGULAR MODELS AND ASYMPTOTICS OF CONTINUOUS
CURVES WITH BOUNDED AND UNBOUNDED SEMIGROUP GENERATORS
Kiril P. Kirchev
kpkirchev@abv.bg,
Galina S. Borisova
g.borisova@fmi.shubg.net
2000 Mathematics Subject Classification:
Primary 47A48, Secondary 60G12.
Key words:
Unbounded operator,
operator colligation, characteristic function, nondissipative
curve, correlation function, wave operator, scattering operator.
In this paper classes of K^{r}operators are considered 
the classes of bounded and unbounded operators A with equal
domains of A and A^{*}, finite dimensional imaginary parts and
presented as a coupling of a dissipative operator and an
antidissipative one with real absolutely continuous spectra and
the class of unbounded dissipative K^{r}operators A with
different domains of A and A^{*} and with real absolutely
continuous spectra. Their triangular models are presented. The
asymptotics of the corresponding continuous curves with generators
from these classes are obtained in an explicit form. With the help
of the obtained asymptotics the scattering theory for the couples
(A^{*},A) when A belongs to the introduced classes is
constructed.
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