Let G be a group. Recall that the intersection graph of subgroups of G is an undirected graph whose vertex set is the set of all nontrivial subgroups of G and distinct vertices H,K are joined by an edge in this graph if and only if the intersection of H and K is nontrivial. The aim of this article is to investigate the interplay between the group-theoretic properties of a finite group G and the...

We generalize the matroid intersection theorem to distributive supermatroids, a structure that extends the matroid to the partially ordered ground set. Distributive supermatroids are special cases of both supermatroids and greedoids, and they generalize polymatroids. This is the first good characterization proved for the intersection problem of an independence system where the ground set is par...

We present a comparative study of GPU ray tracing implemented for two different types of ray-triangle intersection algorithms used with BVH (Bounding Volume Hierarchy) spatial data structure evaluated for performance on three static scenes. We study how number of triangles placed in a BVH leaf node affects rendering performance. We propose GPUoptimized SIMD ray-triangle intersection method eval...

We propose new intersection problems in the q-ary n-dimensional hypercube. The answers to the problems include the Katona’s t-intersection theorem and the Erdős–Ko–Rado theorem as special cases. We solve some of the basic cases of our problems, and for example we get an Erdős–Ko–Rado type result for t-intersecting k-uniform families of multisets with bounded repetitions. Another example is obta...

In this dissertation, we address a problem of safe and efficient intersection crossing traffic management of autonomous and connected ground traffic. Toward this objective, an algorithm that is called the Discrete-time occupancies trajectory based Intersection traffic Coordination Algorithm (DICA) is proposed. All vehicles in the system are Connected and Autonomous Vehicles (CAVs) and capable o...

The passive direction finding cross localization method is widely adopted in passive tracking, therefore there will exist masses of false intersection points. Eliminating these false intersection points correctly and quickly is a key technique in passive localization. A new method is proposed for passive locating and tracking multi-jammer target in this paper. It not only solves the difficulty ...

In this article we consider the intersection graph G(R) of nontrivial proper ideals of a finite commutative principal ideal ring R with unity 1. Two distinct ideals are adjacent if they have non-trivial intersection. We characterize when the intersection graph is complete, bipartite, planar, Eulerian or Hamiltonian. We also find a formula to calculate the number of ideals in each ring and the d...