Volume 31, Number 3, 2005
PROJECTIVELY NORMAL LINE BUNDLES ON
k-GONAL CURVES AND RATIONAL SURFACES
E. Ballico
ballico@science.unitn.it,
C. Keem
ckeem@math.snu.ac.kr
2000 Mathematics Subject Classification:
14H50.
Key words:
plane curve, singular curve, gonality, scrollar invariants.
RECURSIVE METHODS FOR CONSTRUCTION OF BALANCED
n-ARY BLOCK DESIGNS
Z. Ghéribi-Aoulmi
gheribiz@yahoo.fr,
M. Bousseboua
2000 Mathematics Subject Classification:
Primary 05B05; secondary 62K10.
Key words:
Balanced incomplete binary blocks, n-ary designs, finite
projective geometry, finite linear sub-variety.
This method is based on the analogy between a balanced incomplete binary block design (B.I.E.B) and the set of all distinct linear sub-varieties of the same dimension extracted from a finite projective geometry. If V_{1} is the first B.I.E.B resulting from this projective geometry, then by regarding any block of V_{1} as a projective geometry, we obtain another system of B.I.E.B. Then, by reproducing this operation a finite number of times, we get a family of blocks made up of all obtained B.I.E.B blocks. The family being partially ordered, we can obtain an n-ary design in which the blocks are consisted by the juxtaposition of all binary blocks completely nested. These n-ary designs are balanced and have well defined parameters. Moreover, a particular balanced n-ary class is deduced with an appreciable reduction of the number of blocks.
ON ROOT ARRANGEMENTS OF POLYNOMIAL-LIKE FUNCTIONS
AND THEIR DERIVATIVES
Vladimir Petrov Kostov
kostov@math.unice.fr
2000 Mathematics Subject Classification:
12D10.
Key words:
hyperbolic polynomial; root arrangement; configuration vector.
QUATERNION EXTENSIONS OF ORDER 16
Ivo M. Michailov
ivo_michailov@yahoo.com
2000 Mathematics Subject Classification:
12F12.
Key words:
embedding problem, extension, Galois,
quaternion.
A GEOMETRICAL CONSTRUCTION FOR THE POLYNOMIAL INVARIANTS
OF SOME REFLECTION GROUPS
Alessandra Sarti
sarti@mathematik.uni-mainz.de
2000 Mathematics Subject Classification:
Primary 20F55, 13F20; Secondary 14L30.
Key words:
Polynomial invariants, Reflection and Coxeter groups,
Group actions on varieties.
ROBUST PARAMETRIC ESTIMATION OF BRANCHING PROCESSES WITH A RANDOM
NUMBER OF ANCESTORS
Vessela Stoimenova
stoimenova@fmi.uni-sofia.bg
2000 Mathematics Subject Classification:
60J80.
Key words:
Branching processes, random number of
ancestors, power series distribution,
parametric estimation, robustness, d-fullness.