To perform surveillance tasks effectively, unobstructed views of objects are required e.g. unobstructed video of objects are often needed for gait recognition. As a result, we need to determine intervals for video collection during which a desired object is visible w.r.t. a given sensor. In addition, these intervals are in the future so that the system can effectively plan and schedule sensors ...

Let R be a ring with unity and I(R) be the set of all non-trivial left ideals of R. The intersection graph of ideals of R, denoted by G(R), is a graph with the vertex set I(R) and two distinct vertices I and J are adjacent if and only if I ∩ J 6= 0. In this paper, we study some connections between the graph-theoretic properties of this graph and some algebraic properties of rings. We characteri...

ABSTRACT Let ‎G=(V,E) ‎be a‎ ‎simple ‎connected ‎graph ‎with ‎vertex ‎set ‎V‎‎‎ ‎and ‎edge ‎set ‎‎‎E. ‎The Szeged index ‎of ‎‎G is defined by ‎ where ‎ respectively ‎ ‎ is the number of vertices of ‎G ‎closer to ‎u‎ (‎‎respectively v)‎ ‎‎than ‎‎‎v (‎‎respectively u‎).‎ ‎‎If ‎‎‎‎S ‎is a‎ ‎set ‎of ‎size‎ ‎ ‎ ‎let ‎‎V ‎be ‎the ‎set ‎of ‎all ‎subsets ‎of ‎‎S ‎of ‎size ‎3. ‎Then ‎we ‎define ‎t...

We examine the traffic lights regime to enable the fastest overall approach to a city for a specific case. The case involves a traffic light where one continues on the main road, into which additional cars are entering at the light. At this intersection an alternative route begins, which is longer but into which no additional cars are entering. To keep the total number of vehicles constant, we ...

Nielsen theory, originally developed as a homotopy-theoretic approach to fixed point theory, has been translated and extended to various other problems, such as the study of periodic points, coincidence points and roots. In this paper, the techniques of Nielsen theory are applied to the study of intersections of maps. A Nielsen-type number, the Nielsen intersection number NI(f, g), is introduce...

The intersection lines between discontinuity surfaces and their intersection points on the visible surfaces of any engineering structure may be the instability indicators. This paper describes a new approach to modelling the intersecting lines and points that would provide the first evaluation of any instability in an engineering structure characterized by the failure modes. In this work, the i...

We study the Clique problem in classes of intersection graphs of convex sets in the plane. The problem is known to be NP-complete in convex-set intersection graphs and straight-line-segment intersection graphs, but solvable in polynomial time in intersection graphs of homothetic triangles. We extend the latter result by showing that for every convex polygon P with sides parallel to k directions...

Mg,n ψ1 1 · · ·ψ dn n . Witten-Kontsevich theorem [9, 4] provides a recursive way to compute all these intersection numbers. However explicit and effective recursion formulae for computing intersection indices are still very rare and very welcome. Our n-point function formula [5] computes intersection indices recursively by decreasing the number of marked points. So it is natural to ask whether...

In recent years, determining the common information privately and efficiently between two mutually mistrusting parties have become an important issue in social networks. Many Private set intersection (PSI) protocols have been introduced to address this issue. By applying these protocols, two parties can compute the intersection between their sets without disclosing any information about compone...