Gherda, M., M. Boushaba.
Availability of a repairable koutofn: G system with repair
times arbitrarily distributed
(pp. 161−182)
A B S T R A C T S
LIMIT OF THREEPOINT GREEN FUNCTIONS: THE DEGENERATE CASE
Duong Quang Hai
quanghai@math.univtoulouse.fr,
Pascal J. Thomas
pascal.thomas@math.univtoulouse.fr
2010 Mathematics Subject Classification:
32U35, 32A27.
Key words:
pluricomplex Green function, complex MongeAmpère equation, ideals of holomorphic functions.
We investigate the limits of the ideals of holomorphic functions
vanishing on three points in C^{2} when all three points tend to the
origin, and what happens to the associated pluricomplex Green functions.
This is a continuation of the work of Magnusson, Rashkovskii, Sigurdsson
and Thomas, where those questions were settled in a generic case.
SCHURSZEGÖ COMPOSITION OF SMALL DEGREE POLYNOMIALS
Vladimir Petrov Kostov
kostov@math.unice.fr
2010 Mathematics Subject Classification:
12D10.
Key words:
real polynomial, composition of SchurSzegö, real (positive/negative) root.
We consider real polynomials in one variable without root at 0
and without multiple roots. Given the numbers
of the positive, negative and complex roots of two such polynomials,
what can be these numbers
for their composition of
SchurSzegö? We give the exhaustive answer to the question for degree
2, 3 and 4 polynomials and also in the case when the degree is
arbitrary, the composed polynomials being with all roots real,
and one of the polynomials having all roots but one of the same sign.
NEW OSCILLATION CRITERIA FOR THIRD ORDER
NONLINEAR NEUTRAL DELAY DIFFERENCE EQUATIONS WITH
DISTRIBUTED DEVIATING ARGUMENTS
E. M. Elabbasy
emelabbasy@mans.edu.eg,
M. Y. Barsom,
F. S. ALdheleai
faisalsaleh69@yahoo.com
2010 Mathematics Subject Classification:
39A10, 39A12.
Key words:
oscillatory solutions, third order, neutral, deviating arguments, difference equation.
This paper will study the oscillatory behavior of third order nonlinear difference equation with distributed deviating arguments of the form
Δ(a(n)Δ(b(n)Δ(x(n)+p(n)xτ(τ(n)))))+
∑^{m}_{ξ=m0}q(n,ξ)f(x(g(n,ξ)))=0,


where m_{0}, m (>m_{0}) be integers. We establish some new sufficient conditions which insure that every solution of this equation either oscillates or converges to zero. Our results improve and extend some known results in the literature. Examples are given to illustrate the importance of the results.
AVAILABILITY OF A REPAIRABLE kOUTOFn: G SYSTEM WITH REPAIR
TIMES ARBITRARILY DISTRIBUTED
Mebrouk Gherda
mgherda@yahoo.fr,
Mahmoud Boushaba
mboushaba@umc.edu.dz
2010 Mathematics Subject Classification:
90B25, 60K10.
Key words:
Availability, system, koutofn, repairable.
An koutofn: G system is a system that consists of n components
and works if and only if k components among the n work
simultaneously. The system and each of its components can be in only
one of two states: working or failed. When a component fails it
is put under repair and the other components stay in the ``working''
state with adjusted rates of failure. After repair, a component
works as new and its actual lifetime is the same as initially. If
the failed component is repaired before another component fails,
the (n−1) components recover their initial lifetime. The lifetime
and time of repair are independent. In this paper, we propose a
technique to calculate the mean time of repair, the probability of
various states of the system and its availability by using the
theory of distribution.
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