Visual vehicle Tracking is an important topic in intelligent transportation systems. Intersections are challenging locations for visual systems to track vehicles which are simultaneously moving in different directions. In addition, normal traffic flow may change at Intersections due to accidents. Congestion, occlusion and undetermined motion flows are the nominated challenging issues of vehicle Tracking at Intersections. In this paper, a method for Tracking multiple vehicles is proposed considering the vehicle motion directions to overcome undetermined motion flows. For this purpose, a multilayer model is presented, which assigns each motion flows to distinct layers. Moreover, we introduce different neighborhoods for various layers considering the regular motion flows in a layer. Hence, vehicles entering from the same side of Intersection with the same motion direction are assigned to the same layer. Then the Tracking is performed on different layers separately. In special cases such as vehicles crossing each other, misdetections or occlusion, the proposed Tracking method can predict the vehicles tracks by using the stored Tracking history and considering neighborhoods in that layer. Experimental results show consistency between proposed Tracking method results and ground truth, also outperformance of other Tracking methods in Tracking vehicles crossing the Intersection.

The comaximal Intersection graph $CI(R)$ of ideals of a ring $R$ is an undirected graph whose vertex set is the collection of all non-trivial (left) ideals of $R$ and any two vertices $I$ and  $J$ are adjacent if and only if $I+J=R$ and $I\cap J\neq0$. We study the connectedness of $CI(R)$. We also discuss  independence number, clique number, domination number, chromatic number of $CI(R)$.

Information retrieval can be achieved through computerized processes by generating a list of relevant responses to a query. The document processor, matching function and query analyzer are the main components of an information retrieval system. Document retrieval system is fundamentally based on: Boolean, vector-space, probabilistic, and language models. In this paper, a new methodology for matching function of Boolean retrieval systems is proposed and tried to extend postings list data structures and increase the efficiency of using postings lists and skips. The final effect of these considerations is in decreasing the search time.

For any non-empty set and k-subset  , the k-Intersection graph denoted by 􀀀 m(;  ) is undirected simple graph whose vertices are all m-subsets of and two distinct vertices A and B are adjacent if and only if A \ B *  . In this paper, we determine diameter, girth, some numerical invariants and planarity, hamiltonian and perfect matching of these graphs. Moreover adjacency matrix is considered at the end.