Abstract: We introduce the bornological ideals of type $\mathcal L\Im$ and
we show that the boundedness of a bornological ideal of type
$\mathcal L\Im$ is unique. PDF | DVI | PS |

Weak forms of open and closed functions via semi-$\theta$-open sets

Author: Miguel Caldas / Saeid Jafari / Govindappa Navalagi

Abstract: In this paper, we introduce and study two new classes of functions by
using the notions of semi-$\theta$-open sets and
semi-$\theta$-closure operator called weakly semi-$\theta$-open
and weakly semi-$\theta$-closed functions. The connections
between these functions and other existing well-known related
functions are investigated. PDF | DVI | PS |

Abstract: In this brief note we give a new algebraic interpretation, which
is also a non-elementary extension, of an assertion due to
Chatzidakis-Pappas appeared in J. Symbolic Logic (2001). PDF |

Abstract: A new counting polynomial, called the
Omega $\Omega(G, x)$ polynomial, is proposed
on the ground of quasi-orthogonal cut
qoc edge strips in a
bipartite lattice. Within a qoc not all cut edges are
necessarily orthogonal, meaning not all are pairwise codistant.
Two topological indices: $CI$ (Cluj-Ilmenau), eventually equal to
the well-known $PI$ index, in planar, bipartite graphs and
$I_\Omega$ are defined on the newly proposed polynomial and
exemplified. Closed analytical formulas for $\Omega(G, x)$ in
polyhex tori are given. PDF |

The SOR method for infinite systems of linear equations (III)

Author: Bela Finta

Abstract: In [3], [4] we presented the extension of the Jacobi and Gauss-Seidel iterative numerical method from the case of finite linear systems to the case of infinite systems.
The purpose of this paper is to extend the classical SOR (successiv over relaxation) method, known for finite linear systems, to infinite systems. PDF |

Successive approximations for the solution of second order advanced

Author: Răzvan V. Gabor

Abstract: For the initial value problem associated with second order advanced differential equation on Banach space, it is constructed a numerical method to approximate the solution. The method uses the sequence of Picard successive approximations and the trapezoidal quadrature rule (adapted for Lipschitzian functions with values in Banach spaces). PDF |

Abstract: We continue our research on the differences of positive linear operators by giving estimates for such differences. Special emphasis is on the Bernstein operators, Beta operators of the second kind as introduced by Lupaş, piecewise linear interpolation at equidistant knots and on certain products of these mappings. PDF |

Superpositions of functions involved in nomography

Author: Maria Mihoc

Abstract: The current paper deals with the conditions by which the functions of more variables, and also the equations which contain such functions, can be represented by the superpositions of functions of fewer variables. We will also give the corresponding nomograms by which these functions are nomographically represented. PDF |

Abstract: We solve a few equations concerning arithmetic functions. The proofs in the last section are based on known (but difficult) inequalities. PDF |

On $p$-cluster sets and their application to $p$-closedness

Author: M. N. Mukherjee / B. Roy

Abstract: In this paper, the study of a new type of cluster sets for functions and multifunctions between topological spaces has been initiated by use of preopen sets of [8]. Such a notion of cluster
sets is characterized and studied to some extent. In the process, a characterization of Hausdorffness is achieved in terms of the
cluster set of a certain class of functions. An important application of the study is exhibited by establishing a characterization of the concept of $p$-closedness of [7] via the
introduced idea of cluster set of multifunctions. PDF |

On the convergence of the Mann iteration in locally convex spaces

Author: J. O. Olaleru

Abstract: The approximation of fixed points of some quasi contractive
operators in arbitrary Banach spaces using the Mann iterative
procedure is generalized to complete metrisable locally convex
spaces. This turns out to be an extension of a result of Berinde
[2] which in turn is an extension of a theorem of Rhoades [12]. PDF | DVI | PS |

A note on the direct limit of a direct system of multialgebras in a subcategory of multialgebras

Author: Cosmin Pelea

Abstract: We will present some properties of the direct limit of a direct
system of multialgebras in a subcategory of the category of
multialgebras obtained by considering as morphisms the ideal
multialgebra homomorphisms. PDF |

At least version of the generalized minimum spanning tree problem

Author: Petrică C. Pop / Andrei Horvat Marc / Corina Pop Sitar

Abstract: We consider the at least version of the Generalized Minimum
Spanning Tree Problem, denoted by L-GMST, which consists in
finding a minimum cost tree spanning at least one node from each
node set of a complete graph with the nodes partitioned into a
given number of node sets. We describe new integer programming
formulations of the L-GMST problem and establish relationships
between the polytopes corresponding to their linear relaxations. PDF |

On a conjecture for weighted interpolation using Chebyshev polynomials of the third and fourth kinds

Author: Simon J. Smith

Abstract: A conjecture for the projection norm (or Lebesgue constant) of a weighted
interpolation method based on the zeros of Chebyshev polynomials of the third and fourth kinds
is resolved. This conjecture was made in a paper by J. C. Mason and G. H. Elliott in 1995.
The proof of the conjecture is achieved by relating the projection norm to that of a weighted
interpolation method based on zeros of Chebyshev polynomials of the second kind. PDF |

Controlling chaos of a dynamical system with feedback control

Author: Gheorghe Țigan

Abstract: The present work is devoted to control chaotic behavior of a
three--dimensional differential system introduced in \cite{tig2}.
We stabilize the chaotic dynamics of the system to the unstable
equilibrium points. The Lyapunov function method is employed.
Using a linear controller, the system is controlled to a stable
state. Numerical illustrations are presented to show the control
process. PDF |

On embedding Fibonacci meshes on Fibonacci cube networks

Author: Ioana Zelina

Abstract: The Fibonacci cube was presented as a new topology for
interconnection networks. Due to his strong recursive structure,
the Fibonacci cube posses many attractive properties. In this
papers we show how two Fibonacci meshes can be simultaneously
embedded in a Fibonacci cube with dilation 1. PDF |