Volume 2 (2010), Number 2
On the Al-Salam and Verma orthogonal q-polynomials
Author(s): A. BOUANANI, L. KHÉRIJI, AND M. IHSEN. TOUNSI
Abstract: The aim of this paper is to highlight a new integral representation of the Al-Salam and Verma regular form through a true function by investigating the quadratic operator , duality and the -classical character of the Wall form where is the q-difference operator. Some other characterizations are given in the general case and in the symmetric one corresponding to the Al-Salam and Verma polynomials.
DownloadQuaternion interval numbers and a matrix approach to them
Author(s): CENNET BOLAT AND AHMET İPEK
Abstract: This paper is an extension of the work [Quaternions: further contributions to a matrix oriented approach, Linear Alg. and its Appl., 326 (2001), 205,-213.] , in which the representation matrix of a quaternion with real number coefficients is explicitly described, and then investigated properties of the fundamental real matrix associated with a quaternion. In this new paper, we extend the powerful ideas in that study to the quaternions with real interval coefficients. Many number of concepts and techniques that we learned in a standard setting for quaternions with real number coefficients, real intervals and matrices can be carried over to quaternion interval numbers.
DownloadOn a Sharp Inequality for the Medians of a Triangle
Author(s): JIAN LIU
Abstract: In this paper, we prove that the known inequality which involving the upper bounds of median sums for the triangle is sharp. We also prove a stronger conjecture for this inequality, which is equivalent to a inequality posed by H.Y.Yin in [1]. Finally, a similar conjecture checked by the computer is put forward.
DownloadA Note on the Numerical Range of a Complex Tridiagonal Matrix
Author(s): FATMA FEYZA TOPAL AND AHMET İPEK
Abstract: This paper is an extension of the work [Numerical range of a continuant matrix, Appl.Math.Lett., 14 (2001) 213-216.], in which the numerical range of a continuant matrix is explicitly described as an elliptic disc. In this new paper, we improve the results of that work.
DownloadOn Newton's Quadrature Formula for Mappings of Bounded Variation
Author(s): MARIUS NICOLAE HELJIU
Abstract: An estimation of remainder for Newton`s quadrature formula for mappings of bounded variation are given. Also, some applications to special means are given.
DownloadThe Optimization of Simple Regression Models
Author(s): CONSTANTIN ZĂVOIANU AND FELICIA ZĂVOIANU
Abstract: This paper contains an optimization algorithm for simple regression models, which has the purpose of selecting the best regression equation, if, for the same set of statistical data, several statistically valid models exist. Furthermore, the paper presents a method of determining the confidence intervals of the parameters of the non-linear simple regression models by operating, simultaneously, both with the original model as well as with the corresponding linearized model.
DownloadThe Optimization of Linear Multiple Regression Models Through the Method of Forward Selection
Author(s): FELICIA ZĂVOIANU AND CONSTANTIN ZĂVOIANU
Abstract: This article refers to the problem of optimizing linear multiple regression models through the method of forward selection. Therefore, the techniques for selecting the variables that can be inserted into the model are presented and the optimization algorithm is described. The algorithm is implemented on territorial statistical data that partially characterize the labour market.
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