Stable 2-pairs and (X,Y)-intersection graphs

Given two fixed graphs X and Y, the (X,Y)-intersection graph of a graph G is a graph where

1. each vertex corresponds to a distinct induced subgraph in G isomorphic to Y, and

2. two vertices are adjacent iff the intersection of their corresponding subgraphs contains an induced subgraph isomorphic to X.

This notion generalizes the classical concept of line graphs since the (K₁,K₂)-intersection graph of a graph G is precisely the line graph of G.

Let ( , respectively) denote the family of line graphs of bipartite graphs (bipartite multigraphs, respectively), and refer to a pair (X,Y) as a 2-pair if Y contains exactly two induced subgraphs isomorphic to X. Then and , respectively, are the smallest families amongst the families of (X,Y)-intersection graphs defined by so called hereditary 2-pairs and hereditary non-compact 2-pairs. Furthermore, they can be characterized through forbidden induced subgraphs. With this motivation, we investigate the properties of a 2-pair (X,Y) for which the family of (X,Y)-intersection graphs coincides with (or ). For this purpose, we introduce a notion of stability of a 2-pair and obtain the desired characterization for such stable 2-pairs. An interesting aspect of the characterization is that it is based on a graph determined by the structure of (X,Y).     

Crystal Shape Characterisation of Dry Samples using Microscopic and Dynamic Image Analysis

A standard method to determine particle shape and size is by image analysis. This paper addresses microscopic image analysis (semi‐automated) investigations of two different organic crystalline chemicals generated by batch cooling crystallisation. The results generated from microscopic image analysis were compared with data obtained by dynamic image analysis (automated) because very few contributions are available in the open literature. The chemical systems were polymorphic L‐glutamic acid which crystallises into α (prismatic) or β (needle) form and the non‐polymorphic mono sodium glutamate which crystallises into needles. The images from these techniques were processed to generate information on crystal shape and size. It has been observed that shape effects can distort the size obtained in size characterization studies. In this study, comparisons were made of processing time, number of crystals and accuracy between microscopic and dynamic image analysis. For representative microscopic image analysis, 5000 crystals were analysed in an average of eight hours while several hundred thousand crystals were processed using dynamic image analysis within 15 minutes. Using the parameters D₁₀, D₅₀, D₉₀, span and aspect ratio for statistical comparison, it was found that the results obtained for D₅₀ by the two techniques were comparable and in accordance with other measurements (laser diffraction spectroscopy and ultrasonic attenuation spectroscopy) even though these non‐spherical particles had different orientations during measurement by the two methods. However, substantial differences in span of the distribution and aspect ratio were returned by the two techniques.     

Spatial and geometrical control of silicification using a patterned poly-l-lysine template

A simple process to achieve patterned silica films is described. The patterning of the catalyst poly-l-lysine via photolithography and liftoff enables the spatial and geometrical control of silicification. Microscopy and chemical characterization demonstrate that this process enables consistent patterning of silica with 10 μm resolution in a variety of geometries. In addition, the spatial and geometrical control of the silica is demonstrated under different reaction conditions and yields various silica morphologies. The ability to simultaneously pattern bio-inspired silica and control its morphology may allow the tailoring of silica and other silicon-based materials for future applications.     

An alternative separation procedure for 90Sr age dating using DGA Resin

Journal of Radioanalytical and Nuclear Chemistry - The likelihood of an attack by a terrorist organization using a radiological dispersal device (RDD) is much higher than that of an attack with an...