Volume 60 , issue 4 ( 2008 ) | back |

Growth and oscillation theory of solutions of some linear differential equations | 233$-$246 |

**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.

**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 graphs | 247$-$253 |

**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 $\Sigma_{v\in V(G)} f(v)$ 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~$G$.

**Keywords:** Roman domination number, diameter, girth.

**MSC:** 05C69, 05C05

On bitopological paracompactness | 255$-$259 |

**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.

**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 spaces | 261$-$268 |

**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.

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

**MSC:** 47H10, 54H25

On weakly conformally symmetric manifolds | 269$-$284 |

**Abstract**

The object of the present paper is to study {\it 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.

**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 conditions | 285$-$294 |

**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.

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

**MSC:** 34L20, 47E05

Multiplicities of compact Lie group representations via Berezin quantization | 295$-$309 |

**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 $\pi$.

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

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