GRB000301C with peculiar afterglow emission

The CCD magnitudes in Johnson V and Cousins R and I photometric passbands are determined for GRB 000301C afterglow starting ~ 1.5 day after the gamma-ray burst. In fact we provide the earliest optical observations for this burst. Light curves of the afterglow emissions in U, B, V, R, I, J and K' passbands are obtained by combining the present measurements with the published data. Flux decay shows a very uncommon variation relative to other well observed GRBs. Overall, there is a steepening of the optical and near-infrared flux decay caused by a geometric and sideways expanding jet. This is superimposed by a short term variability especially during early time (Delta t < 8 days). The cause of variability is not well understood, though it has occurred simultaneously with similar amplitude in all the filters. We derive the early and late time flux decay constants using jet model. The late time flux decay is the steepest amongst the GRB OTs observed so far with alpha ~ 3. Steepening in the flux decay seems to have started simultaneously around Delta t ~ 7.6 day in all passbands. The value of spectral index in the optical-near IR region is ~ -1.0. Redshift determination with z=2.0335 indicates cosmological origin of the GRB having a luminosity distance of 16.6 Gpc. Thus it becomes the second farthest amongst the GRBs with known distances. An indirect estimate of the fluence > 20 keV indicates, if isotropic,> =10^53 ergs of release of energy. The enormous amount of released energy will be reduced, if the radiation is beamed which is the case for this event. Using a jet break time of 7.6 days, we infer a jet opening angle of ~ 0.15 radian. This means the energy released is reduced by a factor of ~ 90 relative to the isotropic value.Comment: LaTeX file, 11 pages including 4 figures, uses psfig.sty, Bull. Astron. Society of India(accepted, Sept, 2000 issue

Shallow Deep Transitions of Neutral and Charged Donor States in Semiconductor Quantum Dots

We carry out a detailed investigation of neutral ($D^0$) and charged ($D^-$) impurity states of hydrogen-like donors in spherical semiconductor quantum dots. The investigation is carried out within the effective mass theory (EMT). We take recourse to local density approximation (LDA) and the Harbola-Sahni (HS) schemes for treating many-body effects. We experiment with a variety of confining potentials: square, harmonic and triangular. We observe that the donor level undergoes shallow to deep transition as the dot radius ($R$) is reduced. On further reduction of the dot radius it becomes shallow again. We term this non-monotonic behaviour \textbf{SHADES}. This suggests the possibility of carrier {\textbf{\textit{``freeze out''}}} for both $D^0$ and $D^-$. Further, our study of the optical gaps also reveals a {\textbf{SHADES}} transition.Comment: 19 pages, 8 figures, Revised Versio

BVRI CCD photometric standards in the field of GRB 990123

The CCD magnitudes in Johnson $BV$ and Cousins $RI$ photometric passbands are determined for 18 stars in the field of GRB 990123. These measurements can be used in carrying out precise CCD photometry of the optical transient of GRB 990123 using differential photometric techniques during non--photometric sky conditions. A comparison with previous photometry indicates that the present photmetry is more precise.Comment: Tex file, 5 pages with 1 figure. Bull. Astron. Society India, Vol. 27 (accepted

The effect of asymmetric disorder on the diffusion in arbitrary networks

Considering diffusion in the presence of asymmetric disorder, an exact relationship between the strength of weak disorder and the electric resistance of the corresponding resistor network is revealed, which is valid in arbitrary networks. This implies that the dynamics are stable against weak asymmetric disorder if the resistance exponent $\zeta$ of the network is negative. In the case of $\zeta>0$, numerical analyses of the mean first-passage time $\tau$ on various fractal lattices show that the logarithmic scaling of $\tau$ with the distance $l$, $\ln\tau\sim l^{\psi}$, is a general rule, characterized by a new dynamical exponent $\psi$ of the underlying lattice.Comment: 5 pages, 4 figure