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.     

Frequency shifts in the hydrogen spectrum due to interaction with the electromagnetic field

Frequency shifts of hydrogen atom spectral lines are analyzed, both from the “exact” numerical solutions of the coupled equations and the perturbation theory. A numerical method for solving the set of the time-dependent equations is described that includes both the bound and the continuumstates of the hydrogen atom which is stable on a long time scale.     

Two-dimensional model of molecule—surface scattering

Rotational excitation in molecule—surface scattering is analyzed in a simple quantum two-dimensional model. The true molecule—surface potential is replaced by a hard-core ellipsoid. The model accurately describes the dominant features of the transition probability distribution. This is demonstrated by comparing rotational transition probabilities calculated from our model with the results of IOS calculations of Voges and Schinke using realistic potential. The model predicts a new scaling property concerning the anisotropy parameter of the potential surface.     

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.     

Connected graphs of fixed order and size with maximal index: Some spectral bounds

The index (or spectral radius) of a simple graph is the largest eigenvalue of its adjacency matrix. For connected graphs of fixed order and size the graphs with maximal index are not yet identified (in the general case). It is known (for a long time) that these graphs are nested split graphs (or threshold graphs). In this paper we use the eigenvector techniques for getting some new (lower and upper) bounds on the index of nested split graphs. Besides we give some computational results in order to compare these bounds.     

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.