Serdica Mathematical Journal
Volume 42, Number 1, 2016
C O N T E N T S
·
Cabello, J. C.
On Martindale's lemma for nonassociative algebras
(pp. 1−20)
·
Elabbasy, E. M., Sh. R. Elzeiny, T. S. Hassan.
Note on a paper of Elabbasy and Hassan
(pp. 21−26)
·
Kostadinova, K. Y., L. D. Minkova.
Type II family of bivariate inflated-parameter generalized power series
distributions
(pp. 27−42)
·
Assel, R., M. B. Salah.
Bound states of a quantum waveguide with an arbitrary shaped window
(pp. 43−58)
·
Godefroy, G.
James boundaries and Martin's axiom
(pp. 59−64)
·
Glakousakis, E., S. Mercourakis.
Some notes on Morita equivalence of operator algebras
(pp. 65−88)
A B S T R A C T S
ON MARTINDALE'S LEMMA FOR NONASSOCIATIVE ALGEBRAS
J. C. Cabello
jcabello@ugr.es
2010 Mathematics Subject Classification:
Primary 17A60; Secondary 16R60.
Key words:
Semiprime algebra, extended centroid, central closure,
nonassociative algebra, multiplicatively semiprime algebra.
We give a nonassociative version of Martindale's lemma, and as a
consequence, we obtain a semiprime GPI-theorem: if A is a multiplicatively semiprime algebra, M(A) is its multiplication
algebra and C is its extended centroid, then the following are equavalent: (1) CM(A) has a finite rank operator over C; (2) M(A) is GPI; (3) there are Fi, Gi, Hj, Kj∈ CM(A) and pi, qj
∈ A with F_iXGiY(pi)≠ 0 for some i, and such that
∑i=1n FiXGiY(pi) = ∑j=1mHjYKjX(qj)
(for all X, Y ∈ M(A)); (4) there exists F ∈ M(A) and a ∈
A such that the FMC(Q)F(a)) is C-finitely generated.
NOTE ON A PAPER OF ELABBASY AND HASSAN
E. M. Elabbasy
emelabbasy@mans.edu.eg,
Sh. R. Elzeiny
shrelzeiny@yahoo.com,
T. S. Hassan
tshassan@mans.edu.eg
2010 Mathematics Subject Classification:
34K15, 34C10.
Key words:
Oscillations, first order, neutral delay differential
equations.
We give a correction to the proof of Theorem 2.3 in the paper of E. M.
Elabbasy and T. S. Hassan, Serdica Math. J. 34 (2008), 531−542.
TYPE II FAMILY OF BIVARIATE INFLATED-PARAMETER GENERALIZED POWER SERIES
DISTRIBUTIONS
Krasimira Y. Kostadinova
kostadinova@shu-bg.net,
Leda D. Minkova
leda@fmi.uni-sofia.bg
2010 Mathematics Subject Classification:
60E05, 62P05.
Key words:
Compound distributions, bivariate
geometric distribution, inflated-parameter distributions.
The family of Inflated--parameter Generalized Power Series
distributions (IGPSD) was introduced by Minkova in 2002 as a
compound Generalized Power Series distributions (GPSD) with
geometric compounding distribution. In this paper we introduce a
family of compound GPSDs with bivariate geometric compounding
distribution. The probability mass function, recursion formulas,
conditional distributions and some properties are given. A member of
this family is a Type II bivariate Pólya-Aeppli distribution,
introduced by Minkova and Balakrishanan [Type II bivariate
Pólya-Aeppli distribution. Stat. Probab. Lett. 88 (2014), 40−49]. In this paper the
particular cases of bivariate compound binomial, negative binomial
and logarithmic series distributions are analyzed in detail and
compared by the bivariate Fisher index of dispersion.
BOUND STATES OF A QUANTUM WAVEGUIDE WITH AN ARBITRARY SHAPED WINDOW
Rachid Assel
rachid.assel@gmail.com,
Mounir Ben Salah
mounir.bensalah@fsb.rnu.tn
2010 Mathematics Subject Classification:
35P15, 35Q40, 58C40, 81Q10.
Key words:
waveguide, potential window, bound states.
In this paper we prove the existence of isolated eigenvalues of finite multiplicity below the essential spectrum of a straight waveguide with a curved potential window in the three dimensional space. We give also some asymptotic results for these eigenvalues and their counting function. We illustrate our results by some numerical computations.
JAMES BOUNDARIES AND MARTIN'S AXIOM
Gilles Godefroy
gilles.godefroy@imj-prg.fr
2010 Mathematics Subject Classification:
Primary 46B20, Secondary 46A50.
Key words:
James boundary, uncountable $l_1$-bases, Martin’s axiom.
Let X be a separable Banach space, and B a subset of the dual unit ball BX* such that every x ∈ X attains its norm on B. Under Martins's axiom and the negation of continuum hypothesis, it is shown that one of the following statements is true: (a) the dual unit ball BX* is the norm-closed convex hull of B; (b) the set B contains a subset Γ which has the cardinality of the continuum, and is equivalent to the canonical basis of l1(Γ). Several consequences of this optimal result are spelled out.
EXAMPLES OF INFINITE DIMENSIONAL BANACH SPACES WITHOUT~INFINITE EQUILATERAL SETS
E. Glakousakis
e.glakousakis@gmail.com,
S. Mercourakis
smercour@math.uoa.gr
2010 Mathematics Subject Classification:
Primary 46B20; Secondary 46B04.
Key words:
equilateral set.
An example of an infinite dimensional and separable Banach space is given, that is not isomorphic to a subspace of
$l_1$ with no infinite equilateral sets.
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