On Artin's braid group and polyconvexity in the calculus of variations

Let Ω ⊂ 2 be a bounded Lipschitz domain and let F : Ω × 2×2 + −→ be a Carathèodory integrand such that F (x, ·) is polyconvex for L2-a.e. x ∈ Ω. Moreover assume that F is bounded from below and satisfies the condition F (x, ξ) ∞ as det ξ 0 for L2-a.e. x ∈ Ω. The paper describes the effect of domain topology on the existence and multiplicity of strong local minimizers of the functional [u] := Ω F (x,∇u (x)) dx, where the map u lies in the Sobolev space W1,p id (Ω,2) with p 2 and satisfies the pointwise condition det ∇u (x) > 0 for L2-a.e. x ∈ Ω. The question is settled by establishing that [·] admits a set of strong local minimizers on W1,p id (Ω,2) that can be indexed by the group n ⊕ n, the direct sum of Artin’s pure braid group on n strings and n copies of the infinite cyclic group. The dependence on the domain topology is through the number of holes n in Ω and the different mechanisms that give rise to such local minimizers are fully exploited by this particular representation

Native and non-native speakers of English in summarising expository texts

This study examines how native and non-native English speakers summarise expository texts. It investigates if there is any difference in quality between the summaries produced by two groups of students; namely native speakers of English, who acquire the language in early childhood and have their education (from kindergarten / grade 1 to high school) in English, and non-native speakers, who acquire the language in an ESL/EFL context. The sample consisted of seventy undergraduates from a private Malaysian university, comprising thirty-five native and thirty-five non-native speakers of English. Data for the study include summaries by students, response to teacher and student questionnaires as well as interviews with both teachers and students. The results of the study revealed that there was a significant difference in the quality of summaries of native and non-native English speakers in expository text

On the existence and multiplicity of topologically twisting incompressible HH-harmonic maps and a structural H-condition

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Nostalgia, reflexivity, and the narratives of self : reflections on Devine's 'removing the rough edges?'

This paper offers some theoretical insights on Devine’s account of the Riverside Museum in Glasgow. It elaborates on three interrelated themes authors have derived from Devine’s report: 1) how historical representations arouse nostalgic sensations and sensibilities in museum visitors 2) the role of narratives in visitors’ development of their nostalgic experiences 3) the importance of engagement to the creation of such nostalgic experiences. The paper contributes to the existing literature on nostalgia, experiential consumption, and the museum experience literature by establishing a relationship between nostalgia, reflexivity, and individuals’ narratives of self

Marketing applications: from Angry Birds to happy marketers

This marketing teaching case is focussed on the rapidly emergent industry associated with Apps for mobile devices. After setting the context in respect of the awe-inspiring numbers associated with these markets the case is made that innovative marketing is happening across all parts of the basic marketing framework – the 4Ps. The case presents many specific examples of marketing related decision making and outcomes, focussing on games-Apps such as Rovio’s best-selling Angry Birds game

Zero divisors and units with small supports in group algebras of torsion-free groups

We associate a graph to a possible non-zero zero-divisor in the group algebra of a torsion-free group.Comment: to appear in Communications in Algebra. arXiv admin note: substantial text overlap with arXiv:1612.0093

Zero divisors of support size 33 in group algebras and trinomials divided by irreducible polynomials over GF(2)GF(2)

A famous conjecture about group algebras of torsion-free groups states that there is no zero divisor in such group algebras. A recent approach to settle the conjecture is to show the non-existence of zero divisors with respect to the length of possible ones, where by the length we mean the size of the support of an element of the group algebra. The case length $2$ cannot be happen. The first unsettled case is the existence of zero divisors of length $3$. Here we study possible length $3$ zero divisors in rational group algebras and in the group algebras over the field with $p$ elements for some prime $p$