Abstract: This paper presents an important new technique for studying a particular compact semigroup, $\mathbb{N}\cup \{\infty\}$, the one-point compactification of positive integers with usual addition, which is an important semigroup. Indeed, the semigroup $\mathbb{N}\cup \{\infty\}$ is constructed as the quotient semigroup of a particular compact right topological semigroup. In the study of such a semigroup, a major role is played by the substructures called standard oids. For instance, some of the already known results on the structure of $\mathbb{N}\cup \{\infty\}$ are obtained as immediate consequences.
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The Voronovskaja-type formula for the Bleimann, Butzer and Hahn operators

Author: Dan Bărbosu / Ana Maria Acu / Florin D. Sofonea

Abstract: We present a short and simple proof to the Voronovskaja-type formula for the Bleimann, Butzer and Hahn operators. The proof is essentially based on the relationship between the Bleimann, Butzer and Hahn operators and the Stancu operators.
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No. of downloads: 187

Some applications of Shisha-Mond theorem

Author: Dan Bărbosu

Abstract: A result due to Shisha, O. and Mond, B., is recalled and some applications in the evaluation of approximation order by linear positive operator are presented.
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Abstract: We introduce an inversion diagram and use it to describe a simple bijection between $312$--avoiding permutations and Dyck paths that sends inversion statistic to area statistic. We define Tamari and Dyck lattice using inversion tables. Our unified approach allows to understand the connections between these lattices better. We present a simple bijection between pairs of $312$--avoiding permutations and perfect matchings of ordered graphs that avoid the pattern $abccab$.
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Controlling autonomous scalar discrete dynamical systems generated by non self Lipschitzian functions

Author: Vasile Berinde / Gabriella Kovacics

Abstract: We apply fixed point techniques of Krasnoselskij type for stabilizing autonomous scalar discrete dynamical systems in the case of Lipschitzian functions.
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No. of downloads: 160

Comparing the molecular graph degeneracy of Wiener, Harary, Balaban, RandiÄ‡ and ZEP topological indices

Author: Zoița Mărioara Berinde

Abstract: The aim of this paper is to show that the ZEP topological index has better discrimination power than four well known topological indices in molecular chemistry: Balaban index, Harary index, RandiÄ‡ index, and Wiener index.
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No. of downloads: 188

The recurrence theorem of Frenet formulae

Author: Abel Cavași

Abstract: In this paper we generalize Frenet trihedron and we provide some other classes of trihedrons, called Frenet trihedrons of order $n$, $n\geq 1.$ Moreover we prove that those trihedrons can be defined recurrently and we emphasize their role in the study of the generalized helices of order $n$. As practical applications we present the influence of the recurrence theorem in some interdisciplinary domains like physics, chemistry and biology.
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No. of downloads: 225

Developing an ontology for automated scene creation

Abstract: This article presents an ontology meant to be used by algorithms for automated creation of scenes. At any time and in any place we encounter scenes: in plays, in paintings, in film frames, at hospitals, at police stations, at schools, at restaurants, at stores, everywhere. Depending on where it is located, a scene can contain more types of elements: backgrounds, objects, characters connected through their spatial relationships. Our intention is to offer the posibility of realizing many combinations of the chosen elements in order to obtain the wated scene. In practice is difficult to obtain such a result, that is why we intend to design an automatic system, which will automatically generate the scenes. The possible elements of scenes together with their relationships are grouped in an ontology which is presented in this article.
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No. of downloads: 147

The crossing numbers of products of paths with 7--vertex trees

Author: EmÃlia DraÅ¾enskÃ¡

Abstract: The crossing numbers of Cartesian products of paths with all graphs of order at most five are given. The crossing numbers of Cartesian products of paths with several graphs on six vertices are known.
We extend these results by giving the exact values or upper bound of crossing numbers of Cartesian products $G \, \Box\, P_n$ for every tree $G$ on seven vertices.
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No. of downloads: 151

Comparing performance of a speaker recognition system for Dynamic Time Warping and Vector Quantization models

Author: Marieta Gâta

Abstract: This paper analyzes Dynamic Time Warping $(DTW)$ and Vector Quantization $(VQ)$ technique for speaker recognition showing performance of each model. Text independent $(TI)$ experiments are realized with $VQ$ and text dependent $(TD)$ experiments are realized with $VQ$ and $DTW$.
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No. of downloads: 140

On some properties of $\gamma$-semi-$R_{0}$ spaces

Author: Sabir Hussain

Abstract: The purpose of this paper is to introduce $\gamma$-semi-$R_{0}$ spaces in terms of $\gamma$-semi-open sets which contains the $\gamma$-semi-closure of each of its singletons. Some properties of $\gamma$-semi-$R_{0}$ spaces are also discussed and explored.
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No. of downloads: 150

The estimation of solution of Fredholm integral equation in three variables

Author: Monica Lauran

Abstract: The aim of the present paper is to establish an existence result (Theorem 2.1) as well as an estimation result (Theorem 2.2) for a functional equation in three variables.
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No. of downloads: 144

Existence and behaviour of parameter classes of solutions of a system of quasilinear differential equations

Author: Alma Omerspahic

Abstract: The paper presents some results on the existence and behaviour of parameter classes of solutions for system of quasilinear
differential equations. Behaviour of integral curves in neighborhood of an arbitrary or a certain curve is considered. The
obtained results contain the answer to the question on stability as well as approximation of solutions whose existence is
established. The errors of the approximation are defined by the functions that can be sufficiently small. To obtain our main results, the theory of qualitative analysis of differential equations and topological retraction method are used.
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Abstract: The aim of this paper is to extend the Kannan fixed point theorem from single-valued self mappings $T: X \rightarrow X$ to mappings $F: X^{3} \rightarrow X$ satisfying a PreÅ¡iÄ‡-Kannan type contractive condition:
$$
d\left(F\left(x,y,z\right),F\left(y,z,u\right)\right) \leq \frac{k}{8}[d\left(x,F(x,y,z)\right) + d\left(y,F(y,x,y)\right) +
$$
$$
+d\left(z,F(z,y,x)\right)+d\left(y,F(y,z,u)\right) + d\left(z,F(z,y,z)\right) + d\left(u,F(u,z,y)\right)],
$$
or a PreÅ¡iÄ‡-Chatterjea type contractive condition:
$$
d\left(F\left(x,y,z\right),F\left(y,z,u\right)\right) \leq \frac{k}{8}[d\left(x,F(y,z,u)\right) + d\left(y,F(z,y,z)\right) +
$$
$$
+d\left(z,F(u,z,y)\right)+d\left(y,F(x,y,z)\right) + d\left(z,F(y,x,y)\right) + d\left(u,F(z,y,x)\right)].
$$
The obtained tripled fixed point theorems extend and unify several related results in literature.
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No. of downloads: 173

Some properties of idempotents of $(n,m)$-semirings

Author: Adina Pop

Abstract: In this paper, we investigate some properties of the additive and multiplicative idempotents of an $(n,m)-$semiring. In particular, the research is focused on differences between $(n,m)-$semirings, $n,m\geq 3$ and usual semirings.
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No. of downloads: 158

Heuristic introduction to weakly Picard operator theory

Author: Ioan A. Rus

Abstract: In this paper we study the impact of weakly Picard operator theory, [see I. A. Rus, Picard operators and applications}, Sc. Math. Japonicae, 58(2003), No. 1, 191--219] on the following problem: what can we do in order to find conditions under which a given operator is a weakly Picard operator?
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No. of downloads: 148

On some inequalities for $s$-logarithmically convex functions in the second sense via fractional integrals

Abstract: In this paper, the authors establish some new Hadamard type inequalities for $s$-logarithmically convex functions in the second sense via fractional integrals by using Lemma 1.1 which has been proved by SarÄ±kaya et al.
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