Galactic black hole candidates GRS 1915+105 and IGR J17091-3624 have many similarities in their light curves and spectral properties. However, very little is known about the orbital elements of their companions. In case the orbits are eccentric, tida
l forces by the black hole on the companion can cause modulations of accretion rates in orbital time scale. We look for these modulations in the light curves of these two objects and find that their periodicities are around 28.3 d (29.0 d) and 32.2 d respectively. Eccentricities are at the most 0.071 and 0.46 respectively. We conclude that both these objects have long orbital periods and are eccentric. This could be a reason why light curves have several similar variability class transitions as reported in the literature.
Stellar companion of a black hole orbiting in an eccentric orbit will experience modulating tidal force with a periodicity same as that of the orbital period. This, in turn, would modulate accretion rates, and the seed photon flux which are inverse C
omptonized to produce harder X-rays. By analyzing complete all sky monitor (ASM) data (1.5-12 keV) of RXTE and all sky survey data (15-50 keV) of Swift/BAT we discover this periodicity in several objects. We also estimate eccentricities from the RMS power of the peak around quasi-orbital periods (QOP). Our method provides an independent way to obtain time periods and eccentricities of such compact binaries.
The central theme of this thesis is noncommutativity in string theory. We explore in detail how noncommutative structures can emerge in case of the interacting bosonic string and even in the fermionic sector of superstring theory. We have shown in va
rious approaches that string coordinates must be noncommutative in order to be compatible with boundary conditions. These noncommutative structures lead to new involutive algebra of constraints but generate same Virasoro algebra, indicating the internal consistency of our analysis
