We study the complexity of the following problem: Given two weighted voting games G′ and G′′ that each contain a player p, in which of these games is p’s power index value higher? We study this problem with respect to both the Shapley-Shubik power index [SS54] and the Banzhaf power index [Ban65, DS79]. Our main result is that for both of these power indices the problem is complete for probabili...

In this study, the stirring mechanism of shear-thinning fluids benefiting from four blades in turbulent flow is considered. The fluid is studied inside a stirred cylindrical tank with a flat bottom. The height of fluid is equal to the cylinder’s diameter and the impeller is positioned centrally. A CFD simulation has been carried out and three-dimensional turbulent flow is numerically analyzed u...

In this paper, we analyze the decisional power index, the so called Hoede-Bakker index. This index takes the preferences of the players into account, as well as the social structure in which players may influence each other. We investigate the properties of the Hoede-Bakker index. We adapt some postulates for power indices and voting power paradoxes for the Hoede-Bakker set up. We investigate w...

Research on graphs combined with groups is an interesting topic in the field of combinatoric algebra where are used to represent a group. One type graph representation group power graph. A G defined as whose vertex set all elements and two distinct vertices b adjacent if only or for positive integer . In addition mathematics, theory can be applied various fields science, one which chemistry, re...

Abstract: Voltage instability is a major threat for security of power systems. Preserving voltage security margin at a certain limit is a vital requirement for today’s power systems. Assessment of voltage security margin is a challenging task demanding sophisticated indices. In this paper, for the purpose of on line voltage security assessment a new index based on the correlation characteristic...

This paper presents an analysis of the introduction of power quality assessment through power quality indexes within the framework of an agent-based power system control. The objective is to account for power quality in the power management of systems where the total power of the loads significantly exceeds the power available from generation. This is typically the case of next generation all-e...