Generating random elements of a finite group

We present a "Practical" algorithm to construct random elements of a finite group. We analyse its theoretical behaviour and prove that asymptotically it produces uniformly distributed tuples of elements. We discuss tests to assess its effectiveness and use these to decide when its results are acceptable for some matrix groups.     

[1, 2]-sets in graphs

A subset S⊆V$S\subseteq V$ in a graph G=(V,E)$G=(V,E)$ is a [j,k]$[j,k]$-set if, for every vertex v∈V?S$v\in V?S$, j≤|N(v)∩S|≤k$j\le |N\left(v\right)\cap S|\le k$ for non-negative integers j$j$ and k$k$, that is, every vertex v∈V?S$v\in V?S$ is adjacent to at least j$j$ but not more than k$k$ vertices in S$S$. In this paper, we focus on small j$j$ and k$k$, and relate the concept of [j,k]$[j,k]$-sets to a host of other concepts in domination theory, including perfect domination, efficient domination, nearly perfect sets, 2-packings, and k$k$-dependent sets. We also determine bounds on the cardinality of minimum [1, 2]-sets, and investigate extremal graphs achieving these bounds. This study has implications for restrained domination as well. Using a result for [1, 3]-sets, we show that, for any grid graph G$G$, the restrained domination number is equal to the domination number of G$G$.     

Ultramicroporous metal-organic framework based on 9,10-anthracenedicarboxylate for selective gas adsorption

An ultramicroporous metal-organic framework based on 9,10-anthracenedicarboxylate (PCN-13) has been synthesized and structurally characterized. The desolvated PCN-13 demonstrates selective adsorption of oxygen and hydrogen over nitrogen and carbon monoxide.     

Concerning the Relationship between Realizations and Tight Spans of Finite Metrics

Given a metric d on a finite set X, a realization of d is a weighted graph with such that for all the length of any shortest path in G between x and y equals d(x,y). In this paper we consider two special kinds of realizations, optimal realizations and hereditarily optimal realizations, and their relationship with the so-called tight span. In particular, we present an infinite family of metrics {d_k}_k≥1, and—using a new characterization for when the so-called underlying graph of a metric is an optimal realization that we also present—we prove that d_k has (as a function of k) exponentially many optimal realizations with distinct degree sequences. We then show that this family of metrics provides counter-examples to a conjecture made by Dress in 1984 concerning the relationship between optimal realizations and the tight span, and a negative reply to a question posed by Althofer in 1988 on the relationship between optimal and hereditarily optimal realizations.     

Novel octavalent cross-linker displays efficient trapping of protein-protein interactions

A novel octavalent, resorcin[4]arene derived, cross-linker designed to overcome some of the limitations of commercially available reagents is significantly more efficient for covalent stabilisation of protein-protein interactions.     

Chemorheological analysis and model-free kinetics of acid catalysed furfuryl alcohol polymerization

The complete curing of furfuryl alcohol (FA), was studied by chemorheological analysis and model-free kinetics under isothermal and non-isothermal modes. Polymerization of FA under acidic catalysis involves complex reactions, with several steps (such as condensations and Diels-Alder cycloadditions). To account for the polymerization complexity, kinetic analysis of DSC data was performed with a model-free isoconversional method. The obtained E(alpha)-dependencies were closely-correlated with the variation of complex viscosity during curing. Linear condensations are predominant during the early curing stage and are followed by two distinct stages of branching cycloadditions. Gelation and vitrification, identified by rheometric measurements, were associated with a decrease of the overall reaction rate that becomes controlled by diffusion of small oligomers. Before vitrification, the rate of crosslinking is limited by the mobility of longer polymer chains and diffusion encounters a large energy barrier due to the cooperative nature of the motions, leading to higher E(alpha) values.