Volume 60 , issue 4 ( 2008 )back
Growth and oscillation theory of solutions of some linear differential equations233$-$246
Benharrat Bela\"ı di Department of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganem, B. P 227 Mostaganem--(Algeria), E-mail: belaidi

Abstract

The basic idea of this paper is to consider fixed points of solutions of the differential equation $f^{\left( k\right) }+A\left( z\right) f=0$, $k\geq 2$, where $A\left( z\right) $ is a transcendental meromorphic function with $\rho \left( A\right) =\rho >0$. Instead of looking at the zeros of $f\left( z\right) -z$, we proceed to a slight generalization by considering zeros of $f\left( z\right) -\varphi \left( z\right) $, where $\varphi $ is a meromorphic function of finite order, while the solution of respective differential equation is of infinite order.

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Keywords: Linear differential equations; Meromorphic solutions; Hyper order; Exponent of convergence of the sequence of distinct zeros; Hyper exponent of convergence of the sequence of distinct zeros.

MSC: 34M10, 30D35

Bounds on Roman domination numbers of graphs247$-$253
B.P. Mobaraky and S.M. Sheikholeslami

Abstract

Roman dominating function of a graph $G$ is a labeling function $f\:V(G)\rightarrow \{0, 1, 2\}$ such that every vertex with label 0 has a neighbor with label 2. The Roman domination number $\gamma_R(G)$ of $G$ is the minimum of $\Sigma_{vın V(G)} f(v)$ over such functions. In this paper, we find lower and upper bounds for Roman domination numbers in terms of the diameter and the girth of~$G$.

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Keywords: Roman domination number, diameter, girth.

MSC: 05C69, 05C05

On bitopological paracompactness255$-$259
M.K. Bose, Arup Roy Choudhury and Ajoy Mukharjee

Abstract

A new definition of pairwise paracompactness is given. Among other results, an analogue of Michael's characterization of regular paracompact spaces is proved. This notion of pairwise paracompactness is more general than the notion of pairwise compactness.

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Keywords: Pairwise Hausdorff; pairwise regular; strongly pairwise regular; pairwise normal; pairwise compact; locally finite; pairwise paracompact.

MSC: 54E55

Common fixed point of self-maps in intuitionistic fuzzy metric spaces261$-$268
Sh. Rezapour

Abstract

Intuitionistic fuzzy metric spaces have been defined by J.H. Park. Although topological structure of an intuitionistic fuzzy metric space $(X,M,N,*,\lozenge)$ coincides with the topological structure of the fuzzy metric space $(X,M,*)$, study of common fixed theory in intuitionistic fuzzy metric (and normed) spaces is interesting. We shall give some results in this field.

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Keywords: Intuitionistic fuzzy metric space; $f$-invariant; fixed point.

MSC: 47H10, 54H25

On weakly conformally symmetric manifolds269$-$284
A. A. Shaikh, M. Hasan Shahid and Shyamal Kumar Hui

Abstract

The object of the present paper is to study {ıt weakly conformally symmetric manifolds}. Among others it is shown that an Einstein weakly conformally symmetric manifold reduces to a weakly symmetric manifold. Also several examples of weakly conformally symmetric manifolds with non-vanishing scalar curvature have been obtained.

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Keywords: Weakly conformally symmetric manifold; conformal curvature tensor; conformal transformation; scalar curvature.

MSC: 53B35, 53B05, 53B05

The dependence of the eigenvalues of the Sturm-Liouville problem on boundary conditions285$-$294
T. N. Harutyunyan

Abstract

We prove a new asymptotic formula for the eigenvalues of Sturm-Liouville problem, which is a generalization of the known formulae and which takes into account the analytic dependence of the eigenvalues on boundary conditions.

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Keywords: Sturm-Liouville problem, eigenvalue, eigenvalues function, boundary conditions.

MSC: 34L20, 47E05

Multiplicities of compact Lie group representations via Berezin quantization295$-$309
Benjamin Cahen

Abstract

Let $G$ be a compact Lie group and $\pi$ be a unitary representation of $G$ on a reproducing kernel Hilbert space. We study some applications of Berezin quantization to the description of the irreducible decomposition of $\pi$.

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Keywords: Decomposition of a unitary representation; Berezin quantization; Berezin symbol; multiplicity; flag manifold; semi-simple compact Lie group.

MSC: 22E46, 43A65, 32M10, 46E22, 81S30