In his paper Linear equations in non-commutative fields (Ann. of Math. vol. 32 (1931) pp. 463-477) Professor Oystein Ore defines regularity and irregularity of rings and an "order of irregularity" in such a way that regularity becomes irregularity of order 1. Herewith the following problem is proposed: Do irregular rings of order n>\ really exist? If so of what type are they? In this note these...

This paper proposes a nonparametric steganalysis method for quantization index modulation (QIM) based steganography. The proposed steganalysis method uses irregularity (or randomness) in the test-image to distinguish between the coverand the stego-image. We have shown that plain-quantization (quantization without message embedding) induces regularity in the resulting quantized-image; whereas me...

Let Γ(G) be a set of all simple graphs of order n and sizem, without isolated vertices, with vertex degree sequence d1 ≥ d2 ≥ ·· · ≥ dn > 0. A graph G is regular if and only if d1 = d2 = · · ·= dn. Each mapping Irr : Γ(G) 7→ [0,+∞) with the property Irr(G) = 0 if and only if G is regular, is referred to as irregularity measure of graph. In this paper we introduce some new irregularity measures ...