Serdica Mathematical Journal
Volume 21, Number 4, 1995
C O N T E N T S
A B S T R A C T S
OPTIMIZATION OF DISCRETE-TIME, STOCHASTIC SYSTEMS
Nikolaos S. Papageorgiou
1991 Mathematics Subject Classification: 93E20, 49A20, 60H99.
Key words:
Bellman function, dynamic programming, conditional
expectation, measurable selection, induction.
In this paper we study
discrete-time, finite horizon stochastic systems with
multivalued dynamics and obtain a necessary and sufficient
condition for optimality using the dynamic programming
method. Then we examine a nonlinear stochastic discrete-time
system with feedback control constraints and for it, we
derive a necessary and sufficient condition for optimality
which we then use to establish the existence of an optimal
policy.
RADON MEASURES ON BANACH SPACES WITH THEIR WEAK TOPOLOGIES
J. E. Jayne, C. A. Rogers
1991 Mathematics Subject Classification: 28C99, 46B99.
Key words: Banach space, weak topology, Borel measure, Radon measure.
The main concern of this paper is to present some
improvements to results on the existence or non-existence of
countably additive Borel measures that are not Radon
measures on Banach spaces taken with their weak topologies,
on the standard axioms (ZFC) of set-theory. However, to put
the results in perspective we shall need to say something
about consistency results concerning measurable cardinals.
AN ITERATIVE METHOD FOR THE MATRIX PRINCIPAL n-th ROOT
Slobodan Lakic
1991 Mathematics Subject Classification:65F30.
Key words: iterative methods, matrix function.
In this paper we give an iterative method to compute
the principal n-th root and the principal inverse n-th root of a
given matrix. As we shall show this method is locally convergent.
This method is analyzed and its numerical stability is investigated.
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