Navaei, L.
On special case of multiple hypotheses optimal testing for three differently distributed random variables
(pp. 79−86)
A B S T R A C T S
ON DIFFERENTIAL INCLUSIONS WITH UNBOUNDED RIGHT-HAND SIDE
S. Benahmed
sfyabenahmed@yahoo.fr
2000 Mathematics Subject Classification:
58C06, 47H10, 34A60.
Key words:
Fixed point, differential inclusin, multifunction, measurable selection, pseudo-Lipchitzness.
The classical Filippov's Theorem on existence of a local trajectory of the
differential inclusion [\dot x](t) Î F(t,x(t)) requires the right-hand side
F(·,·) to be Lipschitzian with respect to the Hausdorff distance and
then to be bounded-valued. We give an extension of the quoted result under a weaker
assumption, used by Ioffe in [J. Convex Anal. 13 (2006), 353-362], allowing unbounded right-hand side.
THE DIRECT AND INVERSE SPECTRAL PROBLEMS FOR SOME BANDED MATRICES
S. M. Zagorodnyuk
Sergey.M.Zagorodnyuk@univer.kharkov.ua
2000 Mathematics Subject Classification:
15A29.
Key words:
banded matrix, spectral function, polynomials.
In this paper we introduced a notion of the generalized spectral function for a matrix J = (g_{k,l})_{k,l = 0}^{ ¥}, g_{k,l} Î C, such that g_{k,l} = 0, if |k-l
| >
N; g_{k,k+N} = 1, and g_{k,k-N} ¹ 0. Here N is a fixed positive integer. The direct and inverse spectral problems for such matrices are stated and solved. An integral representation for the generalized spectral function is obtained.
FREE BICOMMUTATIVE ALGEBRAS
A. S. Dzhumadil'daev
dzhuma@hotmail.com,
N. A. Ismailov
ismail_nurlan@mail.ru,
K. M. Tulenbaev
kaysart@mail.ru
2000 Mathematics Subject Classification:
Primary 17A50, Secondary 16R10, 17A30, 17D25, 17C50.
Key words:
Cocharacters sequence, polynomial identities, growth of a variety, bicommutative algebras.
Algebras with identities a(bc)=b(ac), (ab)c=(ac)b is called bicommutative.
Bases and the cocharacter sequence for free bicommutative algebras are found. It is shown that the exponent of the variety of bicommutaive algebras is equal to 2.
BAYESIAN AND FREQUENTIST TWO-SAMPLE PREDICTIONS OF THE INVERSE
WEIBULL MODEL BASED ON GENERALIZED ORDER STATISTICS
A. H. Abd Ellah
ahmed.abdelah@science.sohag.edu.eg
2000 Mathematics Subject Classification:
62E16,62F15, 62H12, 62M20.
Key words:
Prediction, inverse Wiebull, generalized order statistics,
record values, progressive Type II censored, symmetric and asymmetric loss
functions.
This paper is concerned with the problem of deriving Bayesian
prediction bounds for the future observations (two-sample prediction) from
the inverse Weibull distribution based on generalized order statistics
(GOS). Study the two side interval Bayesian prediction, point prediction
under symmetric and asymmetric loss functions and the maximum
likelihood (ML) prediction using "plug-in" procedure for future
observations from the inverse Weibull distribution based on GOS. Study the
problem of predicting future records based on observed progressive type II
censored data and observed order statistics from the inverse Weibull
distribution. Finally, a numerical example using real data are used to
illustrate the procedure.
CONTACT CR-SUBMANIFOLDS OF KENMOTSU MANIFOLDS
Mehmet Atçeken
matceken@gop.edu.tr
2000 Mathematics Subject Classification:
53C15, 53C42.
Key words:
Kenmotsu manifold, contact CR-submanifold and
contact CR-product.
In this paper, we research some fundamental properties of contact
CR-Submanifolds of a Kenmotsu manifold. We show that the
anti-invariant distribution is always integrable and give a
necessary and sufficient condition for the invariant distribution to
be integrable. After then, properties of the induced structures on
submanifold by almost contact metric structure on the ambient
manifold are categorized. Finally, we give some results for contact
CR-product and totally umbilical contact CR-submanifold in a
Kenmotsu manifold and Kenmotsu space form.
ON SPECIAL CASE OF MULTIPLE HYPOTHESES OPTIMAL TESTING FOR THREE DIFFERENTLY DISTRIBUTED RANDOM VARIABLES
Leader Navaei
leadernavaei@yahoo.com
2000 Mathematics Subject Classification:
62P30.
Key words:
Optimal testing, error
probability, three differently distributed, type.
In this paper by using theory of large deviation techniques (LDT),
the problem of hypotheses testing for three random variables having
different distributions from three possible distributions is solved.
Hypotheses identification for two objects having different
distributions from two given probability distributions was examined
by Ahlswewde and Haroutunian. We noticed Sanov's theorem and its
applications in hypotheses testing.
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