The concept of strong differential subordinations was introduced in [1], [2] by Antonio and Romaguera and developed in [6,8]. The dual concept of strong differential superordination was introduced in [4] and developed in [5,7]. In this paper, we introduce two new classes of symmetric analytic functions defined by strong differential subordination and superordination. Also we study some properties of these classes.

New strong differential subordination and superordination results are obtained for meromorphic multivalent quasi-convex functions in the punctured unit disk by investigating appropriate classes of admissible functions. Strong differential sandwich results are also obtained.

In this paper we introduce generalized (α, β) derivation on Semirings and extend some results of Oznur Golbasi on prime Semiring. Also, we present some results of commutativity of prime Semiring with these derivation.

Suppose that  is a finite group and  is a non-empty subset of  such that  and . Suppose that  is the Cayley graph whose vertices are all elements of  and two vertices  and  are adjacent if and only if . In this paper, we introduce the generalized Cayley graph denoted by  that  is a graph with vertex set consists of all column matrices  which all components are in  and two vertices  and  are adjacent if and only if , where  is a column matrix that each entry is the inverse of similar entry of  and  is  matrix with all entries in  ,  is the transpose of  and . In this paper, we clarify some basic properties of the new graph and assign the structure of  when  is complete graph , complete bipartite graph  and complete 3-partite graph  for every .

Human skin detection, which usually performed before image processing, is the method of discovering skin-colored pixels and regions that may be of human faces or limbs in videos or photos. Many computer vision approaches have been developed for skin detection. A skin detector usually transforms a given pixel into a suitable color space and then uses a skin classifier to mark the pixel as a skin or a non-skin pixel. A skin classifier explains the decision boundary of the class of a skin color in the color space based on skin-colored pixels. The purpose of this research is to build a skin detection system that will distinguish between skin and non-skin pixels in colored still pictures. This performed by introducing a metric that measures the distances of pixel colors to skin tones. Results showed that the YCbCr color space performed better skin pixel detection than regular Red Green Blue images due to its isolation of the overall energy of an image in the luminance band. The RGB color space poorly classified images with wooden backgrounds or objects. Then, a histogram-based image segmentation scheme utilized to distinguish between the skin and non-skin pixels. The need for a compact skin model representation should stimulate the development of parametric models of skin detection, which is a future research direction.