Volume 38, Number 4, 2012
Serdica Mathematical Journal
Volume 38, Number 4, 2012
C O N T E N T S
Articles

Cauty, R.
Approximation par des morphismes
de chaînes et points fixes des applications multivoques
(pp. 523538)

Duong, A. T.
Resonances of twodimensional Schrödinger operators with strong magnetic fields
(pp. 539574)

Mejjaoli, H.
Generalized homogeneous Besov spaces and their applications
(pp. 575614)

Dangovski, R.
On selfavoiding walks on certain grids and the connective constant
(pp. 615632)

Ksir, B., S. Bouhadjar.
An estimation method for the reliability of "consecutivekoutofn system"
(pp. 633644)
A B S T R A C T S
A SURVEY ON THE KISSING NUMBERS
Peter Boyvalenkov
peter@moi.math.bas.bg
Oleg Musin
oleg.musin@utb.edu
2010 Mathematics Subject Classification:
52C17, 94B65.
Key words:
Sphere packing, kissing numbers, bounds for codes, linear
programming.
The maximum possible number of nonoverlapping unit spheres that can touch a unit sphere in n dimensions is called kissing number. The problem for finding kissing numbers is closely connected to the more general problems of finding bounds for spherical codes and sphere packings. We survey old and recent results on the kissing numbers keeping the generality of spherical codes.
APPROXIMATION PAR DES MORPHISMES
DE CHAÎNES ET POINTS FIXES DES APPLICATIONS MULTIVOQUES
Robert Cauty
cauty@math.jussieu.fr
2010 Mathematics Subject Classification:
54C60, 54H25.
Key words:
chain morphism, fixed point, weighted map.
In this paper, we consider u.s.c. multivalued maps with compact point images. We develop a notion of approximation of such maps by chain mappings between the singular chain complexes of the spaces, and use this notion to prove fixed point theorems.
RESONANCES OF TWODIMENSIONAL SCHRÖDINGER OPERATORS WITH STRONG MAGNETIC FIELDS
Anh Tuan Duong
duongat@math.univparis13.fr
2010 Mathematics Subject Classification:
81Q20 (35P25, 81V10).
Key words:
Schrödinger operator, strong magnetic field, Resonances, resonance width.
The purpose of this paper is to study the Schrödinger operator
P(B,w) = (D_{x}By)^{2}+D_{y}^{2}+w^{2}x^{2}+V(x,y), (x,y) Î R^{2},
with the magnetic field B large enough and the constant w ¹ 0 is fixed and proportional to the strength of the electric field. Under certain assumptions on the potential V, we prove the existence of resonances near Landau levels as B®¥. Moreover, we show that the width of resonances is of size O(B^{¥}).
GENERALIZED HOMOGENEOUS BESOV SPACES AND THEIR APPLICATIONS
Hatem Mejjaoli
hmejjaoli@kfu.edu.sa,
hatem.mejjaoli@ipest.rnu.tn
2010 Mathematics Subject Classification:
Primary 35L05. Secondary 46E35, 35J25, 22E30.
Key words:
Dunkl operators, homogeneous LittlewoodPaley
decomposition, homogeneous DunklBesov space, paraproduct operator,
differentialdifference equations.
In this paper we define the homogeneous Besov spaces associated with the Dunkl operators on R^{d}, and we give a complete analysis on these spaces and same applications.
ON SELFAVOIDING WALKS ON CERTAIN GRIDS
AND THE CONNECTIVE CONSTANT
Rumen Dangovski
dangovski@gmail.com
2010 Mathematics Subject Classification:
Primary: 05C81. Secondary: 60G50.
Key words:
Selfavoiding walks.
We consider selfavoiding walks on the square grid graph. More precisely
we investigate the number of walks of a fixed length on Z×{1,0,1}. Using combinatorial arguments we derive the related generating function. We present the asymptotic estimates of the number of walks in consideration, as well as important connective constants.
AN ESTIMATION METHOD FOR THE RELIABILITY OF "CONSECUTIVEkOUTOFn SYSTEM"
Brahim Ksir
ksirbrahim@yahoo.com,
Slimane Bouhadjar
s.bouhadjar@yahoo.fr
2010 Mathematics Subject Classification:
60K10, 60K20, 60J10, 60J20, 62G02, 62G05, 68M15, 62N05, 68M15.
Key words:
Consecutivekoutofn system, Likelihood estimation, Markov chains.
This paper is concerned with consecutivekoutofn system in which all the components have the same q lifetime probability, so, it's possible to estimate q from a sample by using the maximum likelihood principle. In the reliability formula of the consecutivekoutofn system appears the term q^{k}. The goal in this work is to propose a direct estimation of q^{k} to avoid the accumulated errors owed to the power. More precisely, we establish a new method based on the Markov chains to calculate and estimate the reliability of the system.
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