Students often have a difficult time understanding what convolution is. Students can often evaluate the convolution integral (continuous time case), convolution sum (discrete-time case), or perform graphical convolution but may not have a good grasp of what is happening. In other words, students can solve the formula but often do not understand the result or why they get that result. Most engin...

The aim of this article is to study a multiplier family of univalent harmonic meromorphic functions using the sequences {cn} and {dn} of positive real numbers. By specializing {cn} and {dn}, representation theorms, bounds, convolution, geometric convolution, integral convolution and convex combinations for such functions have been determined. The theorems presented, in many cases, confirm or ge...

Chen and Mangasarian (1995) developed smoothing approximations to the plus function built on integral-convolution with density functions. X. Chen (2012) has recently picked up this idea constructing a large class of smoothing functions for nonsmooth minimization through composition with smooth mappings. In this paper, we generalize this idea by substituting the plus function for an arbitrary fi...

which has the following property Fc(f ∗ g)(x) = (Fcf)(x)(Fcg)(x). (3) The theory of integral transforms related to the Fourier and Mellin convolutions is well developed [2, 6, 10, 11, 12, 13, 19] and has many applications. Some other classes of integral transforms, that are not related to any known convolutions, are considered in [14, 15]. In this paper we investigate integral transforms of the...

The Kitware Software Developer's Quarterly Newsletter contains articles related to the development of Kitware projects in addition to a myriad of software updates, news and other content relevant to the open source community. In this issue, Utkarsh Ayachit illustrates the LIC implementations in VTKEdge, VTK and ParaView which will allow users to exploit the processing power provided by modern G...