By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fai...

We study the constraints imposed by the requirement of Asymptotic Safety on a class of inflationary models with an inflaton field non-minimally coupled to the Ricci scalar. The critical surface in the space of theories is determined by the improved renormalization group flow which takes into account quantum corrections beyond the one loop approximation. The combination of constraints deriving f...

We examine the open problem of finding the shortest string that contains each of the n! permutations of n symbols as contiguous substrings (i.e., the shortest superpermutation on n symbols). It has been conjectured that the shortest superpermutation has length ∑n k=1 k! and that this string is unique up to relabelling of the symbols. We provide a construction of short superpermutations that sho...

A finite group G is called a B-group if every proper subgroup of G is either normal or abnormal in G. In this paper the authors classify the non-B-groups whose proper subgroups are all B-groups.

Inflationary scenarios based on simple non-minimal coupling aφ2R and its generalizations are studied. First, generalizing the form of non-minimal coupling to K(φ)R with an arbitrary function K, we show that the flat potential still is obtainable when V (φ)/K2(φ) is asymptotically constant. Very interestingly, if the ratio of the dimensionless quartic coupling(λ) of the inflaton field and the no...