In compositional data, an observation is a vector with non-negative components which sum to constant, typically 1. Data of this type arise in many areas, such as geology, archaeology, biology, economics and political science among others. The goal paper extend the taxicab metric newly suggested for com-positional data by employing power transformation. Both metrics are be used k-nearest neighbo...

Purpose: Because of the apparent rapid advancement in field information and communication technology its constant connection to internet, customer organizational data have become vulnerable cyber-attacks, necessitating explanation solutions ensure security protection throughout industry. Today, it is critical for governments major corporations implement cybersecurity systems confidentiality fac...

Quadratic assignment problems (QAPs) with a Hamming distance matrix of a hypercube or a Manhattan distance matrix of rectangular grids arise frequently from communications and facility locations and are known to be among the hardest discrete optimization problems. In this paper we consider the issue of how to obtain lower bounds for those two classes of QAPs based on semidefinite programming (S...

1. Introduction. Many of the most perplexing problems in number theory arise from the interplay of addition and multiplication. One important class of such problems is those in which we ask which numbers can be expressed as sums of some numbers which are defined multiplicatively. Such classes of numbers include nth powers (in this paper, for any fixed n; in a more general treatment, n could als...

The present work is devoted to the investigation of branching extremals, i.e., extremal networks, of the Manhattan length functional. Recall that the Manhattan length of a straight segment in Rn is defined as the sum of the lengths of the segment projections to the Cartesian coordinate axis. The Manhattan length of a curve can be defined as the limit of the Manhattan lengths of polygonal lines ...