Résumé: In the present paper, a new characterization of the orthogonality of a monic polynomials sequence {Qn}n≥0 is obtained. This is defined as a linear combination of another monic orthogonal polynomials sequence {Pn}n≥0 such as Qn(x)+rnQn−1(x) = Pn(x)+snPn−1(x)+tnPn−2 (x)+vnPn−3 (x)+wnPn−4(x), n ≥ 0 where wnrn 6= 0, for every n ≥ 5. Futhermore, the relation between the corresponding linear functionals is showed . Finally, an illustration using special case of the above type relation is given

Résumé: n this paper, we present a simple approach in order to build up recursively the connection coefficients between a sequence of polynomials {Qn}n≥0 and an orthogonal polynomials sequence {Pn}n≥0 when Pn(x) = Qn(x) +rnQn−1(x), n≥0. This yields the relation between the parameters of the corresponding recurrence relations. Some special cases are developed. More specifically, assuming that {Pn}n≥0 is a discrete classical orthogonal polynomials sequence.

Résumé: In this paper, we characterize the four derived sequences obtained by the symbolic approach to the quadratic decomposition of Appll sequences. Moreover, we prove that the two monic polynomial sequences associated to such quadratic decomposition are also Appell sequences.

Résumé: n this paper, we are interested in the following inverse problem. We assume that {Pn}n≥0 is a monic orthogonal polynomials sequence with respect to a quasi-definite linear functional u and we analyze the existence of a sequence of orthogonal polynomials {Qn}n≥0 such that we have a following decomposition Qn(x)+rnQn-1(x)=Pn(x)+snPn-1(x)+tnPn-2(x)+vnPn-3(x), n≥0, when vnrn≠0, for every n≥4. Moreover, we show that the orthogonality of the sequence {Qn}n≥0 can be also characterized by the existence of sequences depending on the parameters rn, sn, tn, vn and the recurrence coefficients which remain constants. Furthermore, we show that the relation between the corresponding linear functionals is k(x-c)u=(x3+ax2+bx+d)v, where c,a,b,d∈C and k∈C∖{0}. We also study some subcases in which the parameters rn, sn, tn and vn can be computed more easily. We end by giving an illustration for a special example of the above type relation.

Résumé: A new zero-truncated distribution called zero-truncated Poisson-Pseudo Lindley distribution is introduced. Its statistical properties including general expression of probabilities, moments, cumulative function and the quantile function were examined. Different statistical properties of moment method, maximum likelihood estimation and the quantile function are identified. The parameters estimation of the zero-truncated Poisson-Pseudo Lindley distribution is explained by estimation methods and, to recommend its performance, a simulation is proposed. The model distribution to real-life data is presented and measured with the goodness of fit got by well-known one and two parameters distributions.

Résumé: The purpose of this paper is to present a new interpretation of Darboux transforms in the context of 2-orthogonal polynomials and find conditions in order for any Darboux transforms to yield a new set of 2-orthogonal polynomials. We also introduce the LU and UL factorizations of the monic Jacobi matrix J associated with a quasi-definite linear functional gamma defined on the linear space of polynomials with real coefficients, as well as the Darboux transforms without parameters. Index Terms: 2- orthogonal polynomials, linear functional, Jacobi matrix, Darboux transforms.

Résumé: As a primary data mining method for knowledge discovery, clustering is a technique of classifying a dataset into groups of similar objects. The most popular method for data clustering K-means suffers from the drawbacks of requiring the number of clusters and their initial centers, which should be provided by the user. In the literature, several methods have proposed in a form of k-means variants, genetic algorithms, or combinations between them for calculating the number of clusters and finding proper clusters centers. However, none of these solutions has provided satisfactory results and determining the number of clusters and the initial centers are still the main challenge in clustering processes. In this paper we present an approach to automatically generate such parameters to achieve optimal clusters using a modified genetic algorithm operating on varied individual structures and using a new crossover operator. Experimental results show that our modified genetic algorithm is a better efficient alternative to the existing approaches.

Résumé: In this paper, the construction of the kernel polynomial of 2-orthogonal polynomials is given. Properties of this polynomial are invertigated. We prove in particular that this polynomial conserves the 2-orthogonality, the strictly 2-quasi-orthogonality, the 2-weakly-orthogonality. On the other hand we prove that it also preserves the classical 2-orthogonality properties under some conditions.