Volume 30, Number 4, 2004
DIRECT AND INVERSE SPECTRAL PROBLEMS FOR (2N+1)-DIAGONAL,
COMPLEX, SYMMETRIC, NON-HERMITIAN MATRICES
S. M. Zagorodnyuk
Sergey.M.Zagorodnyuk@univer.kharkov.ua
2000 Mathematics Subject Classification: 42C05. Key words: inverse problems, difference equation.
å_{i = 1}^{N} ( a_{k-i,i} y_{k-i} + a_{k,i}y_{k+i} ) + a_{k,0} y_{k} = l^{N} y_{k}, k = 0,1,2,... ,
where a_{i,j} Î C: a_{i,N} ¹ 0, l is a complex parameter, (y_{0}, y_{1}, ..., y_{k}, ...) = [y^{®}]^{T} is a vector solution, N is a fixed integer. It can be written in the following matrix form: J [y^{®}] = l^{N} [y^{®}], where J is a (2N+1)-diagonal, symmetric matrix. We give an easy procedure for solving of the direct and the inverse spectral problems for the equation. Guseynov used a procedure of the Gelfand-Levitan type for the case N = 1. We use another procedure and this procedure is more easy and transparent.
A NOTE ON THE ASYMPTOTIC BEHAVIOUR OF A PERIODIC
MULTITYPE GALTON-WATSON BRANCHING PROCESS
M. González
mvelasco@unex.es
R. Martínez
rmartinez@unex.es
M. Mota
mota@unex.es
2000 Mathematics Subject Classification: 60J80. Key words: Periodic Multitype Galton-Watson Branching Process, almost sure convergence, cycle.
SYMMETRIC AND ASYMMETRIC GAPS IN SOME
FIELDS OF FORMAL POWER SERIES
N. Yu. Galanova
natagyi@mail2000.ru
2000 Mathematics Subject Classification: 03E04, 12J15, 12J25. Key words: Non-archimedean real closed fields, super-real fields, h_{1}-fields, semi-h_{1}-fields, fields of formal power series, symmetric gaps.
ESSENTIAL COVER AND CLOSURE
R. R. Andruszkiewicz
randrusz@math.uwb.edu.pl
2000 Mathematics Subject Classification: 16N80, 16S70, 16D25, 13G05. Key words: essential extension, essential cover, essential closure, accessible subring.
INFORMATION MATRIX FOR BETA DISTRIBUTIONS
Gokarna Aryal
Saralees Nadarajah
snadaraj@math.iupui.edu
2000 Mathematics Subject Classification: 33C90, 62E99. Key words: Beta distributions, Beta function, Hypergeometric function.
REGULAR AVERAGING AND REGULAR EXTENSION OPERATORS IN
WEAKLY COMPACT SUBSETS OF HILBERT SPACES
Spiros A. Argyros
sargyros@math.ntua.gr
Alexander D. Arvanitakis
aarva@math.ntua.gr
2000 Mathematics Subject Classification: Primary 46E15, 54C55; Secondary 28B20. Key words: C(K) spaces, Weakly compact sets, Regular averaging operators, Regular extension operators.
A NOTE ON ELEMENTARY DERIVATIONS
Joseph Khoury
jkhoury@matrix.cc.uottawa.ca
2000 Mathematics Subject Classification: Primary: 14R10. Secondary: 14R20, 13N15. Key words: Derivations, Hilbert fourteenth problem.