Pascal k-eliminated functional matrix and its property

Generalized Pascal k-eliminated functional matrix with 2n variables

-Riordan array for q -Pascal matrix and its inverse matrix

In this paper, we prove the q -analogue of the fundamental theorem of Riordan arrays. In particular, by defining two new binary operations ∗q and ∗1/q , we obtain a q -analogue of the Riordan representation of the q -Pascal matrix. In addition, by aid of the q -Lagrange expansion formula we get q -Riordan representation for its inverse matrix.

An involutory Pascal matrix

An involutory upper triangular Pascal matrix Un is investigated. Eigenvectors of Un and of UT n are considered. A characterization of Un is obtained, and it is shown how the results can be extended to matrices over a commutative ring with unity. © 2004 Elsevier Inc. All rights reserved.

the effect of functional/notional approach on the proficiency level of efl learners and its evaluation through functional test

in fact, this study focused on the following questions: 1. is there any difference between the effect of functional/notional approach and the structural approaches to language teaching on the proficiency test of efl learners? 2. can a rather innovative language test referred to as "functional test" ge devised so so to measure the proficiency test of efl learners, and thus be as much reliable an...

Fast and Stable Pascal Matrix Algorithms

In this paper, we derive a family of fast and stable algorithms for multiplying and inverting n × n Pascal matrices that run in O(n log n) time and are closely related to De Casteljau’s algorithm for Bézier curve evaluation. These algorithms use a recursive factorization of the triangular Pascal matrices and improve upon the cripplingly unstable O(n log n) fast Fourier transform-based algorithm...