Graphs of relations and Hilbert series

We are discussing certain combinatorial and counting problems related to quadratic algebras. First we give examples which confirm the Anick conjecture on the minimal Hilbert series for algebras given by $n$ generators and $\frac {n(n-1)}{2}$ relations for $n \leq 7$. Then we investigate combinatorial structure of colored graph associated to relations of RIT algebra. Precise descriptions of graphs (maps) corresponding to algebras with maximal Hilbert series are given in certain cases. As a consequence it turns out, for example, that RIT algebra may have a maximal Hilbert series only if components of the graph associated to each color are pairwise 2-isomorphic.

Hydroisomerisation of n-alkanes over partially reduced MoO3: Promotion by CoAlPO-11 and relations to reaction mechanism and rate-determining step

The reaction mechanism and the rate-determining step (RDS) of the isomerisation of n-alkanes (C-4-C-6) over partially reduced MoO3 catalysts were studied through the effects of the addition of an alkene isomerisation catalyst (i.e. CoAlPO- 11). When an acidic CoAlPO- 11 sample was mechanically mixed with the MoO3, a decrease of the induction period and an increase of the steady-state conversion of n-butane to isobutane were observed. These data support previous assumptions that a bifunctional mechanism occurred over the partially reduced MoO3 (a complex nanoscale mixture of oxide-based phases) during n-butane isomerisation and that the RDS was the skeletal isomerisation of the linear butene intermediates. The only promotional effect of CoAlPO-11 on the activity of partially reduced MoO3 for C-5-C-6 alkane hydroisomerisation was a reduction of the induction period, as the RDS at steady-state conditions appeared to be dehydrogenation of the alkane in this case. However, lower yields of branched isomers were observed in this case, the reason of which is yet unclear. (c) 2005 Elsevier B.V. All rights reserved.

New peace, new teachers: student teachers’ perspectives on diversity and community relations in Northern Ireland

This paper reflects upon student teachers’ conceptions of inter-community relations and the preparation they receive to address issues of diversity and mutual understanding. The study in Northern Ireland is set against a backdrop of political, social and educational change, where a shared, peaceful future appears possible. Student teachers at a Catholic institution and a predominantly Protestant institution indicated a willingness to engage with issues concerning diversity and inter-community relations, despite having a limited knowledge of the concepts. However they also demonstrated clear views about the relevance and value of the preparation they received. The findings are evaluated using multicultural theory.

Relations between premise similarity and inductive strength

According to the diversity principle, diverse evidence is strong evidence. There has been considerable evidence that people respect this principle in inductive reasoning. However, exceptions may be particularly informative. Medin, Coley, Storms, and Hayes (2003) introduced a relevance theory of inductive reasoning and used this theory to predict exceptions, including the nondiversity-by-property-reinforcement effect. A new experiment in which this phenomenon was investigated is reported here. Subjects made inductive strength judgments and similarity judgments for stimuli from Medin et al. (2003). The inductive strength judgments showed the same pattern as that in Medin et al. (2003); however, the similarity judgments suggested that the pattern should be interpreted as a diversity effect, rather than as a nondiversity effect. It is concluded that the evidence regarding the predicted nondiversity-by-property-reinforcement effect does not give distinctive support for relevance theory, although this theory does address other results.

Towards variance-matrix characterization of complementarity relations in a continuous variable system

We discuss complementarity relations in a bipartite continuous variable system. Building up from the work done on discrete d-dimensional systems, we prove that for symmetric two-mode states, quantum complementarity relations can be put in a simple relation with the elements of the variance matrix. When this condition is not satisfied, such a connection becomes non-trivial. Our investigation is the first step towards an operative characterization of the complementarity in a scenario that has not been investigated so far.