A power digraph, denoted by $G(n,k)$, is a directed graph with $Z_{n}={0,1,..., n-1}$ as the set of vertices and $L={(x,y):x^{k}equiv y~(bmod , n)}$ as the edge set, where $n$ and $k$ are any positive integers. In this paper, the structure of $G(2q+1,k)$, where $q$ is a Sophie Germain prime is investigated. The primality tests for the integers of the form $n=2q+1$ are established in terms of th...

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We consider two-player games over graphs and give tight bounds on the memory size of strategies ensuring safety conditions. More specifically, we show that the minimal number of memory states of a strategy ensuring a safety condition is given by the size of the maximal antichain of left quotients with respect to language inclusion. This result holds for all safety conditions without any regular...

I n the coming decade, distributed computing will establish itself as the default mode of operation for a wide variety of applications. With the proliferation of mobile devices and ubiquitous computing environments today, applications are beginning to place specialized requirements on the computing and communication infrastructure. Interactive applications, including personal multimedia service...

This book is not a discussion of vital statistics, as the name might imply but rather the observations of a life-time study of obstetrics in many countries, some in the far corners of the globe. The author is convinced that if the process of childbirth is to be made more safe certain essentials are requisite. Chief of these are: 1. The round pelvic brim. 2. Flexible pelvic joints. 3. Natural po...