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Language switching in a digital library; does it make a difference if the default language is set to Maori?
In this paper we investigate the effect of default interface language on usage patterns of the Niupepa digital library (a collection of historic Māori language newspapers), by switching the default interface language between Māori and English in alternate weeks.
Transaction analysis of the Niupepa collection logs indicates that changing default language affects the length of user
sessions and the number of actions within sessions, and that the English language interface was used most frequently
Semi-regular Relative Difference Sets with Large Forbidden Subgroups
Motivated by a connection between semi-regular relative difference sets and
mutually unbiased bases, we study relative difference sets with parameters
in groups of non-prime-power orders. Let be an odd prime. We
prove that there does not exist a relative difference set in any
group of order , and an abelian relative difference set can
only exist in the group . On the other hand, we
construct a family of non-abelian relative difference sets with parameters
, where is an odd prime power greater than 9 and
(mod 4). When is a prime, , and 1 (mod 4), the
non-abelian relative difference sets constructed here are
genuinely non-abelian in the sense that there does not exist an abelian
relative difference set with the same parameters
Theory of linear G-difference equations
We introduce the notion of difference equation defined on a structured set.
The symmetry group of the structure determines the set of difference operators.
All main notions in the theory of difference equations are introduced as
invariants of the symmetry group. Linear equations are modules over the skew
group algebra, solutions are morphisms relating a given equation to other
equations,symmetries of an equation are module endomorphisms and conserved
structures are invariants in the tensor algebra of the given equation. We show
that the equations and their solutions can be described through representations
of the isotropy group of the symmetry group of the underluing set. We relate
our notion of difference equations and solutions to systems of classical
difference equations and their solutions and show that our notions include
these as a special case.Comment: 34 page
Subsets of finite groups exhibiting additive regularity
In this article we aim to develop from first principles a theory of sum sets
and partial sum sets, which are defined analogously to difference sets and
partial difference sets. We obtain non-existence results and characterisations.
In particular, we show that any sum set must exhibit higher-order regularity
and that an abelian sum set is necessarily a reversible difference set. We next
develop several general construction techniques under the hypothesis that the
over-riding group contains a normal subgroup of order 2. Finally, by exploiting
properties of dihedral groups and Frobenius groups, several infinite classes of
sum sets and partial sum sets are introduced
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