Accelerated spectral approximation

A systematic development of higher order spectral analysis, introduced by Dellwo and Friedman, is undertaken in the framework of an appropriate product space. Accelerated analogues of Osborn's results about spectral approximation are presented. Numerical examples are given by considering an integral operator.

     

Modified No-hair Conjecture and the Limiting Process

It is argued that the Schwarzschild black hole solution follows as a unique limit of the Brans-Dicke Class I solutions, provided the correct iterated limit is taken. Such a uniqueness is essential for the validity of a recent version of the no-hair conjecture. A non-trivial modification to this version is proposed in order to exclude Brans-Dicke Class IV solutions which appear to represent scalar hair black holes in general.     

Modified solutions of some oscillators by iteration procedure

The modified solutions of some nonlinear oscillators have been obtained based on the classical iteration procedure. In this article we have used the Fourier series and utilized all of its terms (sometimes approximately) in each iterative step. The third and fourth approximate frequencies of different nonlinear problems show good agreement with the exact values.     

Discontinuous change in the helical pitch of cholesteric liquid crystals by photoisomerization of a chiral azobenzene molecule

This paper describes the discontinuous change in the helical pitch of a cholesteric liquid crystal (ChLC) by means of the photoisomerization of chiral azobenzene molecules under homogenous alignment conditions. A mixture of E44, R811 and Azo was prepared in the ratio 68/28/4, respectively. R811 and Azo have opposite twisting abilities such that they induce right- and left-handed helices, respectively when added to E44. The mixture was injected into a glass cell having a 2 or 5?µm cell gap, and treated for homogeneous molecular orientation. The wavelength of selective reflection from the ChLC was shifted to shorter wavelengths by the trans-cis photoisomerization of Azo. The change in the helical pitch was not only discontinuous, but also dependent on the cell thickness. The discontinuous change in the helical pitch was estimated to be almost the same as the half turn of the helical pitch in each cell gap, and was dependent on the number of helical half pitches in the glass cell. The homogeneous alignment condition affects the photochemical change in the helical structure of the ChLC system.