Countable Fuzzy Topological Space and Countable Fuzzy Topological Vector Space

This paper deals with countable fuzzy topological spaces, a generalization of the notion of fuzzy topological spaces. A collection of fuzzy sets F on a universe X forms a countable fuzzy topology if in the definition of a fuzzy topology, the condition of arbitrary supremum is relaxed to countable supremum. In this generalized fuzzy structure, the continuity of fuzzy functions and some other related properties are studied. Also the class of countable fuzzy topological vector spaces as a generalization of the class of fuzzy topological vector spaces has been introduced and investigated

A Note on Strongly Lower Semi-Continuous Functions and the Induced Fuzzy Topological Space Generated by Them

A new class of functions called strongly lower semi-continuous (SLSC) functions is defined and its properties are studied. It is shown that the arbitrary supremum and finite infimum of SLSC functions are again SLSC. Using these functions, an induced fuzzy topological space, called s-induced fuzzy topological space on a topological space (X, T), is introduced. Moreover, some incorrect results on fuzzy topological spaces obtained previously by some authors are identified and modified accordingly. Examples of the newly defined induced space are given and their various properties are investigated. Interrelationships between a fuzzy topological space (X, F) and the s-induced fuzzy topological space generated by the crisp members of F are examined. In this process, different lower semi-continuities and induced fuzzy spaces generated by them have been defined in a general set up and their few properties have been studied

Probing deviation of tribimaximal mixing and reach of θ13\theta_{13} using neutrino factory at CERN and ICAL detector at INO

We investigate the deviation from tribimaximal mixing value and the reach of $\theta_{13}$ using neutrino factory at CERN and ICAL detector at INO.Comment: 5 pages LaTeX, 3 eps figures. Talk given by Debasish Majumdar at NUFACT07 at Okayam

DC electrical properties and non–adiabatic small polaron hopping in V2O5–CdO–ZnO glass nanocomposites

Semiconducting transition metal oxide (TMO) doped glass nanocomposites xV2O5–(1–x) (0.05CdO–0.95ZnO), x=0.3, 0.5, 0.7 and 0.9 have been prepared by melt quenching method. DC electrical conductivity of as prepared glass nanocomposites is are investigated over a wide temperature range. Formation of small polarons has been confirmed from dc electrical conductivity experimental data, whereas conductivity is due to mainly polaron hopping from V+4 to V+5 valence state in these glassy systems. Temperature dependent conductivity data have been analyzed using the small polaron hopping (SPH) model. Low, high temperature activation energy, optical phonon frequency and Debye’s temperature have been determined. Conductivity data have been analyzed in view of Mott’s variable range hopping (VRH) models and Greaves VRH models; the density of states at the Fermi level has been evaluated. Various polaron hopping parameters such as polaron radius, polaron binding energy, polaron band width and polaron coupling constant (γP) have been estimated. It has been ascertained by these estimated quantities and different approaches that the nature of hopping conduction is non–adiabatic variable range hopping of small polarons. The evaluated values of hopping carrier mobility (μ) and hopping carrier concentration (NC) are found to depend on composition and temperature

A GEANT-based study of atmospheric neutrino oscillation parameters at INO

We have studied the dependence of the allowed space of the atmospheric neutrino oscillation parameters on the time of exposure for a magnetized Iron CALorimeter (ICAL) detector at the India-based Neutrino Observatory (INO). We have performed a Monte Carlo simulation for a 50 kTon ICAL detector generating events by the neutrino generator NUANCE and simulating the detector response by GEANT. A chi-square analysis for the ratio of the up-going and down-going neutrinos as a function of $L/E$ is performed and the allowed regions at 90% and 99% CL are displayed. These results are found to be better than the current experimental results of MINOS and Super-K. The possibilities of further improvement have also been discussed.Comment: 8 pages, 13 figures, a new figure added, version accepted in IJMP