Volume 29, Number 1, 2003
CHARACTERIZATIONS OF THE SOLUTION SETS OF GENERALIZED
CONVEX MINIMIZATION PROBLEMS
Vsevolod I. Ivanov
vsevolodivanov@yahoo.com
2000 Mathematics Subject Classification: 90C26, 90C20, 49J52, 47H05, 47J20. Key words: generalized convexity, pseudoconvex function, quasiconvex quadratic function, solution set, variational inequality.
A PVT-TYPE ALGORITHM FOR MINIMIZING A NONSMOOTH CONVEX FUNCTION
Li-Ping Pang
lipingpang@163.com,
Zun-Quan Xia
zqxiazhh@dlut.edu.cn
zqxia@mail.dlptt.ln.cn
2000 Mathematics Subject Classification: 90C25, 68W10, 49M37. Key words: Parallel algorithm, synchronous parallel, convex minimization, Moreau-Yosida regularization, strong convexity, descent condition, forced function.
SYLOW p-SUBGROUPS OF ABELIAN GROUP RINGS
P. V. Danchev
2000 Mathematics Subject Classification: Primary 20C07, 20K10, 20K20, 20K21; Secondary 16U60, 16S34. Key words: unit groups. direct factors, basic subgroups, direct sums of cyclics.
Suppose K is a first kind field with respect to p in char K ¹ p and A is an abelian p-group. In the present work, the p-primary components U_{p}(KA) and S(KA) of the group of units U(KA) and V(KA) in the semisimple abelian group ring KA are studied when they belong to some central classes of abelian groups. The established criteria extend results obtained by us in Compt. rend. Acad. bulg. Sci. (1993). Moreover, the question for the isomorphic type of the basic subgroup of S(KA) is also settled. As a final result, it is proved that if A is a direct sum of cyclics, the group of all normed p-units S(KA) modulo A, that is, S(KA)/A, is a direct sum of cyclics too. Thus A is a direct factor of S(KA) with a direct sum of cyclics complementary factor provided s_{p}(K) Ê N. This generalizes a result due to T. Mollov in Pliska Stud. Math. Bulgar. (1986).
ACCELERATION OF CONVERGENCE IN DONTCHEV'S
ITERATIVE METHOD FOR SOLVING VARIATIONAL INCLUSIONS
M. Geoffroy
michel.geoffroy@univ-ag.fr,
S. Hilout,
A. Pietrus
alain.pietrus@univ-ag.fr
2000 Mathematics Subject Classification: 47H04, 65K10. Key words: Multiapplication, Aubin Continuity, Cubic Convergence.
ADEQUATE COMPACTA WHICH ARE GUL'KO OR TALAGRAND
Petr Cízek, Marián Fabian
fabian@math.cas.cz
2000 Mathematics Subject Classification: 54H05, 03E15, 46B26 Key words: K-analytic space, K-countably determined space, analytic set, coanalytic set, adequate family, ill-founded tree, well-founded tree, Mercourakis space.
ON ARRANGEMENTS OF REAL ROOTS OF A REAL POLYNOMIAL AND ITS DERIVATIVES
Vladimir Petrov Kostov
kostov@math.unice.fr
2000 Mathematics Subject Classification: 12D10. Key words: arrangement of roots.
ON THE TRANSFORMATIONS OF SYMPLECTIC EXPANSIONS AND THE RESPECTIVE
BÄCKLUND TRANSFORMATION FOR THE KDV EQUATION
E. Kh. Khristov
hristov@fmi.uni-sofia.bg
2000 Mathematics Subject Classification: Primary: 34B40; secondary: 35Q51, 35Q53. Key words: Symplectic expantion, KdV equation, Bäcklund transformation.