Some notes on the threshold graphs

In this paper we consider threshold graphs (also called nested split graphs) and investigate some invariants of these graphs which can be of interest in bounding the largest eigenvalue of some graph spectra.     

A one parameter method for the matrix inverse square root

This paper is motivated by the paper [3], where an iterative method for the computation of a matrix inverse square root was considered. We suggest a generalization of the method in [3]. We give some sufficient conditions for the convergence of this method, and its numerical stabillity property is investigated. Numerical examples showing that sometimes our generalization converges faster than the methods in [3] are presented.     

A novel pimara-8(9) ,15-diene from lycopus europaeus

Identification of a novel trioxygenated Δ^8(9),15_ pimaric acid methyl ester from plant species Lycopus europaeus by means of two-dimensional ¹H NMR spectroscopy (COSY and NOESY) is reported.     

Generalized line graphs

Generalized line graphs extend the ideas of both line graphs and cocktail party graphs. They were originally motivated by spectral considerations. in this paper several (nonspectral) classical theorems about line graphs are extended to generalized line graphs, including the derivation and construction of the 31 minimal nongeneralized line graphs, a Krausz-type covering characterization, and Whitney-type theorems on isomorphisms and automorphisms.     

Novel trioxygenated caryophyllenes from Inula Spiraefolia

The identification of two novel isomeric trioxygenated caryophyllenes from the plant species $\text{Inula Spiraefolia}$ is reported.     

Branching of colloidal chains in capillary-confined nematics

We report on the observation of colloidal chain assembly and branching inside capillaries filled with a nematic liquid crystal. Because of the homeotropic anchoring of liquid crystalline molecules on the capillary and colloidal droplet surfaces, the assembly of droplets along the capillary axis is expected, producing a transformation of the nematic director field from an escape-radial to quasiradial configuration. However, the subsequent over time branching of the straight colloidal chains is counterintuitive. By numerical simulations, we demonstrate that chain branching can occur by overcoming an energy barrier and can at least dwell as a metastable configuration. Moreover, manipulation of colloidal chains by electric fields and their gradients demonstrates various regimes of chain behavior in electric fields.