Abstract: The notion of two dimensional divided difference was introduced by Academician T.
Popoviciu, in 1934, for the case when the number of abscissas is equal with the number of coordinates.
In his famous monograph, D. V. Ionescu recovered the Popoviciu’s definition and proved an integral
representation for the two dimensional divided difference of n-th order.
In a recent monograph, M. Ivan introduced the notion of two dimensional (m, n)-th order divided
difference.
The focus of the present paper is to establish some properties of the two dimensional divided differ-
ence of (m, n)-th order and to give a representation of the bivariate Lagrange interpolation polynomial
in terms of above divided differences.

Abstract: In this paperwe introduce newmeans and prove newrelations between classical means
based on the Simpson formula and Hermite integral inequality.

Theorems of the type of Cutler for abelian p-groups

Author: Peter Danchev

Abstract: Suppose G and H are abelian p-groups. It is shown that if G and H are quasi-
isomorphic then G is (a) summable or (b) ?-summable or (c) p?+m-projective, m ? IN0 = IN ?{0} or
(d) a strong ?-elongation of a totally projective (respectively summable) group by a p?+m-projective
group, m ? IN0 = IN ?{0} or (e) thick if and only if so is H. These ?ve independent claims comple-
mented results of this type due to Cutler (appeared in Pac. J. Math., 1966) and are supplements to our
recent results (published in Proc. Indian Acad. Sci.-Math. Sci., 2004) too.

Anticommutativity in the ring of square matrices of the second order with complex entries

Author: Cristinel Mortici

Abstract: The main purpose of this paper is to solve the equation AB+BA =0 in the ringM2(C)
of square matrices of the second order with complex entries. The discussion is made by considering the
cases when A and B are inversable or singular. The methods used in each case are completely different
and instructive. Considerations about matrices which commutes and ?nally an application are also
given.

Some stability and strong convergence results for the Jungck-Ishikawa iteration process

Author: M. O. Olatinwo

Abstract: In this paper, we shall establish some stability results as well as some strong conver-
gence results for a pair of nonselfmappings using a newly introduced Jungck-Ishikawa iteration pro-
cess and some general contractive conditions. Our results are generalizations and extensions of the
results in some of the references listed in the reference section of this paper as well as of some other
analogous ones in the literature.

The inclusion-exclusion principle and the pingenhole principle on distributive lattices

Author: Vasile Pop

Abstract: We present concrete examples of lattices endowed with ”measures” (related to contest
problems). The corresponding applications of the two principles are illustrated.

A sharp criterion for the univalence of the Libera operator

Author: Robert Szasz

Abstract: Let f be an analytic function of the form f(z)= z + a2z + ... de?ned in the unit
disc U = {z ? C : |z| < 1}. Suitable values of ? have been determined by a number of authors,
so that Re(zf
(x)+ z2
3 f
(z)
> ??, z ? U implies the starlikeness of f. In all these previous
papers the method of differential-subordination has been used. We improve their results using the
method of convolution and obtain the biggest possible value of ? so that the differential inequality
Re(zf
(x)+ z2
3 f
(z)
> ??, z ? U implies the univalence of the function f. The integral version of
the result involving Libera operator is given.

Generalization of classification trees for a poset

Author: Laura Vereș

Abstract: The present article studies directed trees and classification trees defined in a partially
ordered set. In the first chapter we recall the notion of the classification trees for a poset, and the basic
notions for our investigations. In the second chapter we analyse the relations between classification
trees and tolerance classes, we present a new construction of classification trees, and also we discuss
the relation between classification trees and orthogonal systems.

Abstract: In a previous paper it was proved that laws of Okun’s type can not be determined for
Romanian economy, after 1990. In consequence, in this paper we give a description of unemployment
evolution after 1990, using ARIMA models.

Serviceability analysis of the ambulance car fleet and examination of the transport security of an Emergency Aid Centre

Author: Veselina S. Evtimova

Abstract: The paper examines the serviceability of the vehicles and the transport security of the
EAC in Ruse. The aim of the article is to determine the number of vehicles in working order at a certain
rate of breakdowns and if these vehicles can manage to respond to all incoming emergency calls. A
graph shows the possible states of the vehicles. A system of Kolmogorov’s equations is made up to
describe the process. The paper comes to de?nite conclusions about the state of the ambulance car
fleet.

Optimizing the finance of collective consumption using evolutionary computation

Author: Diana Andrana Filip / Rodica Ioana Lung / Simona G. Serbu / Voichița Adriana Cleciu

Abstract: On the market of collective goods, the state is a provider of services and the individuals
are considered to be the beneficiaries. The correct resizing of public expenses for financing indivisi-
ble collective consumption is necessary mostly due to the unproductive character of these costs. The
optimization of the public goods supply must take into account the individuals preferences for pure
collective goods that are expressed as a collective preferences function. This function, together with
the constraints resulting from budgetary equilibrium forms a maximization problem that can be solved
using evolutionary algorithms.

The convergence of some clustering techniques for elements ideally grouped in clusters

Author: Dana Avram Lupșa

Abstract: Depending on the characteristics of the clusters we want to determine, different clus-
tering techniques are employed. Data characterization is usually not perfect, the model suffers and the
clustering results are not always what the user expected. This paper argues that, for elements ideally
grouped in clusters, clustering techniques converges. We propose a characterization of elements ide-
ally grouped in clusters and prove the uniqueness of the optimumclusters for some different clustering
criteria.

Abstract: This paper dealswith the application of the equation of the surface of a rotatingmassive
body for the surface of the Earth-type planets. A contradiction with the present situation appears, but
having a geological explanation.

An evaluation of the multithreading benefits for a network scan application

Author: Ovidiu Cosma

Abstract: The network scanning applications are useful for building the search engines databases,
and for establishing the security level of a computer network. Such an application usually searches for
services through a sequential detection process. This process can be time consuming because each try
is followed by a waiting interval, in which the answer from the server is expected. The process can
be speeded up by shorting this waiting period, or by reducing the number of retries. Both approaches
affect the reliability of the scanning process. This article evaluates a different approach: speeding up
the search process by multithreading.

Impact of modern Web technologies on e-learning platforms

Author: Cezar Toader

Abstract: This paper presents a consistent overview of the evolution of Web 2.0 relevant tech-
nologies in order to sustain the connection with e-learning 2.0 concepts. Relevant changes in Web
application presentation layer are discussed, and the actual trends in Web programming are taken into
account. Web browsers drawbacks and HTML transformation are emphasized, rich clients advantages
are presented, and programming frameworks are discussed. Also, several Web technologies for Web
learning, used at North University of Baia Mare, are presented.

About generalization in mathematics (III). On the inclusion and exclusion principle

Author: Gheorghe Miclăuș

Abstract: Let A1,A2, ...,An be finite sets and m(Ai) denote the number of elements of the set
Ai. In this paper we obtain a formula of type ”the inclusion and exclusion principle” (Boole-Sylvester)
for finding out the number of elements of the set A1?A2?...?An where A?B =(A\B) ? (B\A) is
”the symmetric difference of the sets A and B”:
m(A1?A2?...?An)=
=
n
i=1
m(Ai) ? 2
1?i

Abstract: A new weighted Erdos-Mordell type inequality involving interior point of a triangle is
established. By it's application, some interesting geometric inequalities are derived.