Continuous Functional Calculus for Quaternionic Bounded Normal Operators

In this article we give an approach to define continuous functional calculus for bounded quaternionic normal operators defined on a right quaternionic Hilbert space.Comment: Submitted to a journal. There was a gap in the previous version. We have corrected it and stated all the results for bounded cas

On the polar decomposition of right linear operators in quaternionic Hilbert spaces

In this article we prove the existence of the polar decomposition for densely defined closed right linear operators in quaternionic Hilbert spaces: If $T$ is a densely defined closed right linear operator in a quaternionic Hilbert space $H$, then there exists a partial isometry $U_{0}$ such that $T = U_{0}|T|$. In fact $U_{0}$ is unique if $N(U_{0}) = N(T)$. In particular, if $H$ is separable and $U$ is a partial isometry with $T = U|T|$, then we prove that $U = U_{0}$ if and only if either $N(T) = \{0\}$ or $R(T)^{\bot} = \{0\}$.Comment: 17 page

Observation of Mixed Alkali Like Behaviour by Fluorine Ion in Mixed Alkali Oxyfluro Vanadate Glasses: Analysis from Conductivity Measurements

In this communication we report the fluorine ion dynamics in mixed alkali oxyfluro vanadate glasses. We have measured the electrical conductivity using impedance spectroscopy technique Room temperature conductivity falls to 5 orders of magnitude from its single alkali values at 33 mol% of rubidium concentration. We have also estimated the distance between similar mobile ions using the density values. Assuming this distance as the hopping distance between the similar ions we have estimated the anionic (Fluorine ion in our case) conductivity. It is observed that the fluorine ion dynamics mimics the mixed alkali effect and scales as the onset frequency f0.Comment: submitted to DAE-SSDP 2018 Indi

Linear and Nonlinear Optical Properties of Mn doped Benzimidazole Thin Films

In the present work, the Mn doped benzimidazole (BMZ) thin films were prepared by simple chemical bath deposition technique. The material was directly deposited as thin film on glass substrates and the metal concentration in the solution was varied in weight percentage in order to investigate the dopant effect on the properties of thin films. Similarly, the Mn doped BMZ films were deposited in different solution temperature to study the effect of deposition temperature on the properties of thin films. The PXRD and FT-IR spectroscopy are used to study the structural and the presence of functional groups in the BMZ medium. Depending upon the solution temperature, thickness of the films varying from 0.6 to 1.2 {\mu}m and the optical transparency of the samples increases with the increasing temperature up to 50 {\deg}C. Second Harmonic Generation (SHG) efficiency of the films is measured for all the films. Third order nonlinear optical properties of the films were analyzed using Z-scan technique. The experimental results show that Mn doped BMZ films exhibits saturation absorption and negative nonlinearity.Comment: This has been presented in DAE 58th Solid State Symposium held at Thapar University, Patiala, Punjab, India. Will be published in AIP conference proceedings soo