In networking communication systems like vehicular ad hoc networks, the high vehicular mobility leads to rapid shifts in vehicle densities, incoherence in inter-vehicle communications, and challenges for routing algorithms. It is necessary that the routing algorithm avoids transmitting the pockets via segments where the network density is low and the scale of network disconnections is high as this could lead to packet loss, interruptions and increased communication overhead in route recovery. Hence, attention needs to be paid to both segment status and traffic. The aim of this paper is to present an intersection-based segment aware algorithm for geographic routing in vehicular ad hoc networks. This algorithm makes available the best route f

High vehicular mobility causes frequent changes in the density of vehicles, discontinuity in inter-vehicle communication, and constraints for routing protocols in vehicular ad hoc networks (VANETs). The routing must avoid forwarding packets through segments with low network density and high scale of network disconnections that may result in packet loss, delays, and increased communication overhead in route recovery. Therefore, both traffic and segment status must be considered. This paper presents real-time intersection-based segment aware routing (RTISAR), an intersection-based segment aware algorithm for geographic routing in VANETs. This routing algorithm provides an optimal route for forwarding the data packets toward their destination

The following question was raised by L.Fuchs: "what are the subgroups of an abelian group G that can be represented as intersections of pure subgroups of G ? . Fuchs also added that “One of my main aims is to give the answers to the above question". In this paper, we shall define new subgroups which are a family of the pure subgroups. Then we shall answer problem 2 of L.Fuchs by these semi-pure subgroups which can be represented as the intersections of pure subgroups.

Let be a ring. Given two positive integers and , an module is said to be -presented, if there is an exact sequence of -modules with is -generated. A submodule of a right -module is said to be -pure in , if for every -Presented left -module the canonical map is a monomorphism. An -module has the -pure intersection property if the intersection of any two -pure submodules is again -pure. In this paper we give some characterizations, theorems and properties of modules with the -pure intersection property.

Let be a ring. Given two positive integers and , an module is said to be -presented, if there is an exact sequence of -modules with is -generated. A submodule of a right -module is said to be -pure in , if for every -Presented left -module the canonical map is a monomorphism. An -module has the -pure intersection property if the intersection of any two -pure submodules is again -pure. In this paper we give some characterizations, theorems and properties of modules with the -pure intersection property.

A submoduleA of amodule M is said to be strongly pure , if for each finite subset {ai} in A , (equivalently, for each a ?A) there exists ahomomorphism f : M ?A such that f(ai) = ai, ?i(f(a)=a).A module M is said to be strongly F–regular if each submodule of M is strongly pure .The main purpose of this paper is to develop the properties of strongly F–regular modules and study modules with the property that the intersection of any two strongly pure submodules is strongly pure .