This article deals with issues related to grammatical structures of the English language used in teaching mathematics. The emphasizes need for knowledge mathematical patterns by native speakers. stated hypotheses are illustrated illustrative examples.

Most illustrative techniques used in non-photorealistic rendering to date apply a rendering style to objects or a scene and alter the appearance of this style by employing illumination or depth cueing. However, for generating high quality illustrations this approach relies almost entirely on smart placement of light sources. In this paper we introduce the concept of illustrative effects to desc...

Fractional calculus has been used to model the physical and engineering processes that have found to be best described by fractional differential equations. For that reason, we need a reliable and efficient technique for the solution of fractional differential equations. The aim of this paper is to present an analytical approximation solution for linear and nonlinear multi-order fractional diff...

I would like to thank the following members of the editorial board who are rotating off the board for their service for the past several years: Heinrich Audebert, Antoni Dávalos, Agnes Flöel, Mikael Mazighi, Majaz Moonis, Patrik Michel, and J Mocco. I would also like to thank Scott Silverman for his contribution to the Illustrative Teaching Cases and Amytis Towfighi for her assistance with the ...

in this paper, an effective direct method to determine the numerical solution of linear and nonlinear fredholm and volterra integral and integro-differential equations is proposed. the method is based on expanding the required approximate solution as the elements of chebyshev cardinal functions. the operational matrices for the integration and product of the chebyshev cardinal functions are des...