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Creative Mathematics
and Informatics

Print Edition: ISSN 1584 - 286X
Online Edition: ISSN 1843 - 441X

Creative Math. and Inf. is a category B+ journal in the CNCSIS classification

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Mathematical Reviews
Zentralblatt MATH

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Vol. 17 (2008), No. 1,
Two dimensional divided differences revisited
Author: Dan Bărbosu
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.
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About Simpson-type and Hermite-type inequalities
Author: Mihaly Bencze / Zhao Changjian
Abstract: In this paperwe introduce newmeans and prove newrelations between classical means based on the Simpson formula and Hermite integral inequality.
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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.
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A formula involving the Bernstein fundamental polynomials
Author: Mircea D. Farcaș
Abstract: In this article we want to determinate a relation between the Bernstein fundamental multivariate polinomyals.
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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.
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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.
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An approximate fixed point proof of the Browder-G¨ ohde-Kirk fixed point theorem
Author: Mădălina Păcurar
Abstract: The theorem known in literature as the Theorem of Browder-G¨ ohde-Kirk is proven by using approximate fixed point terminology and results.
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Operators of Bernstein type
Author: Ovidiu T. Pop
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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.
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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.
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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.
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ARIMA models for unemployment
Author: Alina Bărbulescu
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.
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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.
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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.
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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.
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The shape of Earth-type planets
Author: Istvan Huba Attila Sass
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.
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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.
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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.
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A note on the Nagel and Gergonne points
Author: Dorin Andrica / Khos Lu Nguyen
Abstract: In this note, we study some special properties of the Nagel point, Gergonne point, and their adjoints.
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A category of new inequalities
Author: Mihaly Bencze
Abstract: In this paper we present a category of new inequalities generated by weighted AM - GM - HM inequalities.
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Some separations results by inversion
Author: Dan Brânzei / Cristinel Mortici
Abstract: In this paper we solve and extend a separation problem given at the Swedish Mathe- matical Olympiad in 1984, using the inversion method.
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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
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A new weighted Erdos-Mordell type inequality
Author: Wei-Dong Jiang
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.
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