A series scheme is discussed for the determination of the normalization constants of the even and odd Mathieu-Gauss (MG) optical beams. We apply a suitable expansion in terms of Bessel-Gauss (BG) beams and also answer the question of how many BG beams should be used to synthesize a MG beam within a tolerance. The structure of the normalization factors ensures that MG beams will always be normal...

First Person is a series of interviews with the first authors of a selection of papers published in Journal of Cell Science, helping early-career researchers promote themselves alongside their papers. Brandy Hyndman and Mathieu Crupi are co-first authors on 'Differential recruitment of E3 ubiquitin ligase complexes regulates RET isoform internalization', published in Journal of Cell Science. Br...

Introduction Although the Mathieu groups are probably best known today as the first instances of the sporadic simple groups, Mathieu's discovery of them arose rather from his search for highly transitive permutation groups; only later were the Mathieu groups shown to be simple. In modern mathematics, the Mathieu groups are studied chiefly in conjunction with sphere packing and error-correcting ...

The sporadic Mathieu group M12 can be viewed as an errorcorrecting code, where the codewords are the group’s elements written as permutations in list form, and with the usual Hamming distance. We investigate the properties of this group as a code, in particular determining completely the probabilities of successful and ambiguous decoding of words with more than 3 errors (which is the number tha...

let $g$ be a finite group‎. ‎we say that $g$ has emph{spread} r if for any set of distinct non-trivial elements of $g$ $x:={x_1,ldots‎, ‎x_r}subset g^{#}$ there exists an element $yin g$ with the property that $langle x_i,yrangle=g$ for every $1leq ileq r$‎. ‎we say $g$ has emph{exact spread} $r$ if $g$ has spread $r$ but not $r+1$‎. ‎the spreads of finite simple groups and their decorations ha...

In the space of the system parameters, the stability charts are determined for the delayed and damped Mathieu equation defined as ẍ~t!1k ẋ~t!1~d1« cos t!x~t!5bx~t22p! . This stability chart makes the connection between the Strutt-Ince chart of the damped Mathieu equation and the Hsu-Bhatt-Vyshnegradskii chart of the autonomous second order delay-differential equation. The combined charts descri...