For a simple, undirected graph G with, at most one isolated vertex and no edges, labeling f:E(G)→{1,2,…,k1} of positive integers to the edges is called irregular if weights each has different value. The integer k1 then irregularity strength G. If number vertices in or order |G|, μ:E(G)→{1,2,…,k2} modular remainder divided by |G| k2 disjoint union two more graphs, denoted ‘+’, an operation where...

Cortical abnormalities at the distal postero-medial femoral metaphysis may be relatively common. We reviewed the plain radiographs of 197 knees in 130 children aged between 5 and 12 years to investigate the incidence of distal femoral cortical irregularities (DFCI) and their association with symptoms. An adductor magnus lesion was found in 15% of cases, with an even number of irregular and cyst...

The paper presents an approach to extract irregularities in document corpora, where the documents originate from different sources and the analyst’s interest is to find documents which are atypical for the given source. The main contribution of the paper is a voting-based approach to irregularity detection and its evaluation on a collection of newspaper articles from two sources: Western (UK an...

I construct normal del Pezzo surfaces, and regular weak del Pezzo surfaces as well, with positive irregularity q > 0. Such things can happen only over nonperfect fields. The surfaces in question are twisted forms of nonnormal del Pezzo surfaces, which were classified by Reid. The twisting is with respect to the flat topology and infinitesimal group scheme actions. The twisted surfaces appear as...