On the direct product of two weak uniquely completable partial latin squares

In this note we show by counter-example that the direct product of two weak uniquely completable partial latin squares is not necessarily a uniquely completable partial latin square. This counter-example rejects a conjecture by Gower (see [3]) on the direct product of two uniquely completable partial latin squares.

Diversity and commonality in national identities: an exploratory analysis of cross-national patterns

Issues of boundary maintenance are implicit in all studies of national identity. By definition, national communities consist of those who are included but surrounded (literally or metaphorically) by those who are excluded. Most extant research on national identity explores criteria for national membership largely in terms of official or public definitions described, for example, in citizenship and immigration laws or in texts of popular culture. We know much less about how ordinary people in various nations reason about these issues. An analysis of cross-national (N = 23) survey data from the 1995 International Social Science Program reveals a core pattern in most of the countries studied. Respondents were asked how important various criteria were in being 'truly' a member of a particular nation. Exploratory factor analysis shows that these items cluster in terms of two underlying dimensions. Ascriptive/objectivist criteria relating to birth, religion and residence can be distinguished from civic/voluntarist criteria relating to subjective feelings of membership and belief in core institutions. In most nations the ascriptive/objectivist dimension of national identity was more prominent than the subjective civic/voluntarist dimension. Taken overall, these findings suggest an unanticipated homogeneity in the ways that citizens around the world think about national identity. To the extent that these dimensions also mirror the well-known distinction between ethnic and civic national identification, they suggest that the former remains robust despite globalization, mass migration and cultural pluralism. Throughout the world official definitions of national identification have tended to shift towards a civic model. Yet citizens remain remarkably traditional in outlook. A task for future research is to investigate the macrosociological forces that produce both commonality and difference in the core patterns we have identified.

The play of identities in Cypriot-Australian family storytelling

This article adopts a microanalytic approach to examine storytelling as a co-construction by family members in a Cypriot-Australian family. Previous studies on family storytelling have focused on the various roles of family members in storytelling with a means of studying family socialization (Miller et al., 1990; Ochs & Taylor, 1992; Blum-Kulka, 1997). These studies used critical discourse analysis, socioculturel theories, performance and pragmatic approaches to storytelling. This article offers a distinctive approach to family storytelling by examining the discourse and social identities that family members display during the storytelling. The data originate in a study that involves interviews with three generations of Greek-Australian and Cypriot-Australian women regarding their relationships with each other. In this paper we investigate the contributions of the father and the daughters in the course of the mother's turn at storytelling. The first part of the analysis focuses on the husband's discourse identities as a contributor, initiator and elicitor of his wife's storytelling. During the storytelling we also observe the production and exchange of different social identities between the husband and the mother, such as the 'unwilling suitor', the 'embarrassed schoolgirl' or the 'forceful but teasing husband'. The second part describes how the daughters take part in their mother's storytelling, producing a variety of identities such as the 'impatient mother', the 'complaining', 'happy', or 'good' mothers and daughters. These investigations succinctly illustrate how narratives become a resource for members' 'display' and 'play' of identities. Copyright ©2002, John Benjamins B.V.

Human GC-AG alternative intron isoforms with weak donor sites show enhanced consensus at acceptor exon positions

It has been previously observed that the intrinsically weak variant GC donor sites, in order to be recognized by the U2-type spliceosome, possess strong consensus sequences maximized for base pair formation with U1 and U5/U6 snRNAs. However, variability in signal strength is a fundamental mechanism for splice site selection in alternative splicing. Here we report human alternative GC-AG introns (for the first time from any species), and show that while constitutive GC-AG introns do possess strong signals at their donor sites, a large subset of alternative GC-AG introns possess weak consensus sequences at their donor sites. Surprisingly, this subset of alternative isoforms shows strong consensus at acceptor exon positions 1 and 2. The improved consensus at the acceptor exon can facilitate a strong interaction with U5 snRNA, which tethers the two exons for ligation during the second step of splicing. Further, these isoforms nearly always possess alternative acceptor sites and always possess alternative acceptor sites and exhibit particularly weak polypyrimidine tracts characteristic of AG-dependent introns. The acceptor exon nucleotides are part of the consensus required for the U2AF(35)-mediated recognition of AG in such introns. Such improved consensus at acceptor exons is not found in either normal or alternative GT-AG introns having weak donor sites or weak polypyrimidine,tracts. The changes probably reflect mechanisms that allow GC-AG alternative intron isoforms to cope with two conflicting requirements, namely an apparent need for differential splice strength to direct the choice of alternative sites and a need for improved donor signals to compensate for the central mismatch base pair (C-A) in the RNA duplex of U1 snRNA and the pre-mRNA. The other important findings include (i) one in every twenty alternative introns is a GC-AG intron, and (ii) three of every five observed GC-AG introns are alternative isoforms.

Myth, moment and the challenge of identities: Stories from Australians of Indigenous and Chinese ancestry

There has been a long history of contact between Indigenous and Chinese people in north-eastern Australia. This is evidenced in contemporary communities by the significant presence of mixed-heritage individuals of Indigenous and Chinese ancestry. This paper employs the stories of 10 such individuals to examine their incorporation of 'otherculture' ancestries into identity constructs. In doing so, the paper sheds light on how identities are narrated at the intersection of 'myth' and 'moment', and how challenge evokes transformation and discontinuity. Three broad identity responses emerge from the data: affirmation of singular constructs; questioning and contemplation; and pluralist embracing of both cultures. Historical and contemporary discourses feature prominently, covertly and overtly restricting potential identifications. Mutuality and hegemonic rivalry are found to underpin the narration of relations between the two marginalised and racialised groups.

Quantum doubles from a class of noncocommutative weak Hopf algebras

The concept of biperfect (noncocommutative) weak Hopf algebras is introduced and their properties are discussed. A new type of quasi-bicrossed products is constructed by means of weak Hopf skew-pairs of the weak Hopf algebras which are generalizations of the Hopf pairs introduced by Takeuchi. As a special case, the quantum double of a finite dimensional biperfect (noncocommutative) weak Hopf algebra is built. Examples of quantum doubles from a Clifford monoid as well as a noncommutative and noncocommutative weak Hopf algebra are given, generalizing quantum doubles from a group and a noncommutative and noncocommutative Hopf algebra, respectively. Moreover, some characterizations of quantum doubles of finite dimensional biperfect weak Hopf algebras are obtained. (C) 2004 American Institute of Physics.

Partial regularity of weak solutions of the liquid crystal equilibrium system

For a parameter, we consider the modified relaxed energy of the liquid crystal system. Each minimizer of the modified relaxed energy is a weak solution to the liquid crystal equilibrium system. We prove the partial regularity of minimizers of the modified relaxed energy. We also prove the existence of infinitely many weak solutions for the special boundary value x.