It is shown that matrices over algebraically closed fields that are farthest apart in the commuting graph must be non-derogatory. Rank-one matrices and diagonalizable matrices are also characterized in terms of the commuting graph.

It is shown that matrices over algebraically closed fields that are farthest apart in the commuting graph must be non-derogatory. Rank-one matrices and diagonalizable matrices are also characterized in terms of the commuting graph.

A minimax two-facility location problem in multidimensional space with Chebyshev metric is examined subject to box constraints on the feasible area. In problem, there are two groups of points known coordinates, and one needs find coordinates for optimal new under given constraints. The considered if it minimizes maximum following values: distance between first point farthest group, second point...

Semantic segmentation in LiDAR point clouds has become an important research topic for autonomous driving systems. This paper proposes a dynamic graph convolution neural network cloud semantic using polar bird’s-eye view, referred to as DGPolarNet. are converted coordinates, which rasterized into regular grids. The points mapped onto each grid distribute evenly solve the problem of sparse distr...

the wiener index w(g) of a connected graph g is defined as the sum of the distances betweenall unordered pairs of vertices of g. the eccentricity of a vertex v in g is the distance to avertex farthest from v. in this paper we obtain the wiener index of a graph in terms ofeccentricities. further we extend these results to the self-centered graphs.

Clustering is the process of grouping of data, where the grouping is established by finding similarities between data based on their characteristics. Such groups are termed as Clusters. A comparative study of clustering algorithms across two different data items is performed here. The performance of the various clustering algorithms is compared based on the time taken to form the estimated clus...

This video presents an application of geodesic computation on 3D meshes to surface remeshing. The farthest point paradigm [1] is a powerful greedy algorithm that allows fast and accurate sampling of the underlying surface. The use of a varying speed function for front propagation enables an adaptive placement of the seed points. The connectivity of the resulting mesh is computed using a geodesi...

We study inequalities for the infima of Green potentials on a compact subset of an arbitrary domain in the complex plane. The results are based on a new representation of the pseudohyperbolic farthest-point distance function via a Green potential. We also give applications to sharp inequalities for the supremum norms of Blaschke products. 1. Green potentials Let G ⊂ C be a domain possessing the...

Wireless Sensor Networks (WSN) consist of a large number of sensors which have limited battery power. One of the major issues in WSN is the need to improve the overall network lifetime. Hence, WSN necessitate energyefficient routing protocols. In this paper, a cross-layer routing protocol (PLOSA) is designed to offer a high delivery rate, a low end-to-end delay, and a low energy consumption. To...

Two properties concerning the space of differences of sublinear functions D(X) for a real Banach space X are proved. First, we show that for a real separable Banach space (X, ‖ · ‖) there exists a countable family of seminorms such that D(X) becomes a Fréchet space. For X = R this construction yields a norm such that D(R) becomes a Banach space. Furthermore, we show that for a real Banach space...