The behavior of the Mathieu functions is illustrated by using a variety of plots with representative examples taken from mechanics. We show how Mathieu functions can be applied to describe standing, traveling, and rotating waves in physical systems. Some background is provided on notation and analogies with other mathematical functions. Our goal is to increase the familiarity with Mathieu functions in the scientific and academic community using visualization. For this purpose we adopt a strategy based on visual recognition rather than only looking at equations and formulas.

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Location management of mobile users is of primary importance in personal communication networks (PCNs), and it is mainly aimed to facilitate the delivery of incoming calls to destination users and to make a more efficient use of network resources. In practical PCNs, the location management algorithms need to keep track of mobile users in a dynamic manner, and it is a design concern to minimize the generated signaling traffic. In this paper, we present the cost analysis for the dynamic movementbased location update scheme. Our model is based on renewal theory arguments, and it is general enough to include a variety of probability distributions for modeling cell residence times (CRTs) in hyperexponentially distributed location area residence times and exponentially distributed intercall times. We compare the location update cost for the dynamic and static schemes. We present numerical results regarding the exponential and circular CRT distributions and discuss the optimal threshold distance for location update that minimizes the cost of the dynamic movementbased scheme.

Abstract. The aim of this work is to prove some basic properties of coquaternions and to find the zeros of polynomials involving coquaternionic elements. We also provide some expansions of hyperholomorphic function on coquaternion algebra by using Fueter polynomials.