To Honor the Poet: A Festschrift for Shirley Geok-lin Lim

Editor's Introductio

Characterization of the generalized Chebyshev-type polynomials of first kind

Orthogonal polynomials have very useful properties in the solution of mathematical problems, so recent years have seen a great deal in the field of approximation theory using orthogonal polynomials. In this paper, we characterize the generalized Chebyshev-type polynomials of the first kind $\mathscr{T}_{n}^{(M,N)}(x),$ then we provide a closed form of the constructed polynomials in term of the Bernstein polynomials $B_{k}^{n}(x).$ We conclude the paper with some results on the integration of the weighted generalized Chebyshev-type with the Bernstein polynomials.Comment: Modified the title, One reference added, few additions, change in tex

Generalized Chebyshev polynomials of the second kind

We characterize the generalized Chebyshev polynomials of the second kind (Chebyshev-II), and then we provide a closed form of the generalized Chebyshev-II polynomials using the Bernstein basis. These polynomials can be used to describe the approximation of continuous functions by Chebyshev interpolation and Chebyshev series and how to efficiently compute such approximations. We conclude the paper with some results concerning integrals of the generalized Chebyshev-II and Bernstein polynomials.Comment: Change the title (Tschebyscheff to Chebyshev), and adding few comments. Adding the Journal reference

On divisibility graph for simple Zassenhaus groups

The divisibility graph $D(G)$ for a finite group $G$ is a graph with vertex set $cs~(G)\setminus\{1\}$ where $cs~(G)$ is the set of conjugacy class sizes of $G$. Two vertices $a$ and $b$ are adjacent whenever $a$ divides $b$ or $b$ divides $a$. In this paper we will find $D(G)$ where $G$ is a simple Zassenhaus group

A framework for introducing the private finance initiative in Brunei Darussalam construction industry.

The Private Finance Initiative (PFI) is a common, and sometimes preferred, approach to funding public projects without immediate recourse to the public purse, in the construction industry in developed countries throughout the world. It is, also, increasingly gaining popularity among developing countries. Brunei Darussalam is a developing country located on the northern coast of the island of Borneo in South East Asia with an interest in exploring how it can effectively employ the PFI approach to project finance in its construction industry. Against this background, a comprehensive desk study was undertaken together with an analysis of the relevant processes of government in Brunei Darussalam and a framework developed to facilitate the smooth introduction of PFI in the country’s construction industry. The framework was built around four main dimensions: organisation, training, participation and implementation. The framework was evaluated through a survey of managerial level civil servants in Brunei Darussalam’s Ministry of Development. The framework was found to be easy to understand, comprehensive, consistent with government processes and acceptable at all relevant Ministry levels. The framework provides a useful starting point on Brunei Darussalam’s journey towards effective implementation of PFI in its construction industry