We describe three different methods to compute all those characters of a finite group that have certain properties of transitive permutation characters. First, a combinatorial approach can be used to enumerate vectors of multiplicities. Secondly, these characters can be found as certain integral solutions of a system of inequalities. Thirdly, they are calculated via Gaussian elimination. The me...

Abstract Lyons and Sullivan conjectured in (J. Differential Geom. 19 (2), 299–323, 1984) that if p : M → N is a normal Riemannian covering, with closed, has exponential volume growth, then there are non-constant, positive harmonic functions on . This was proved recently Polymerakis (Adv. Math. 379 , 107552–107558, 2021) exploiting the Lyons-Sullivan discretization some sophisticated estimates g...

were not fever seasons. Thus, evidencing both a very indistinct acquaintance with what I have written, and greater ignorance of the actual facts, Dr. Lyons labours to prove that I am wrong by quoting official reports from Augor, Mehidpoor, Goona, Sehore, Siderpoor, Deolee, Erinpoorah, and Kherwarrah. The first five places mentioned, which at page 228 of the Gazette he refers to as within the Ra...

Precis: This paper focuses attention o n t w o aspects o f P. M . Lyons ' w o r k o n the dis t r ibut ion o f personal weal th i n Ireland. First, using a statistical procedure devised f r o m some w e l l k n o w n results, the va l id i ty o f his assumption that i n 1966 nearly twoth i rds o f the Ir ish adult popula t ion o w n e d no weal th is examined. Serious doubt is cast on the assum...

This research supported by the U.S. Army Research Office examines a myriad of facets of lifted hydrocarbon jet flames in the presence of air co-flow. At a certain jet exit velocity, a flame will lift from the fuel nozzle and stabilize at some downstream position. The partially-premixed flame front of the lifted flame oscillates, with the oscillations becoming greater in flames stabilized furthe...