Characteristic Variability Time Scales of Long Gamma-Ray Bursts

We determined the characteristic variability time scales (\Delta t_p) of 410 bright and long GRBs, by locating the peaks of their Power Density Spectra, defined and calculated in the time domain. We found that the averaged variability time scale decreases with the peak flux. This is consistent with the time-dilation effect expected for the cosmological origin of GRBs. We also found that the occurrence distribution of the characteristic variability time scale shows bimodality, which might be interpreted as that the long GRB sample is composed of two sub-classes with different variability time scales. However, we found no difference for some other characteristics of these two sub-classes.Comment: 10 pages, 5 figures, corrected some typos and syntaxes, enlarged the label fonts in fig.3 and fig.

Fish diseases in India, their causes and control measures - Winter school on recent advances in diagnosis and management of diseases in mariculture, 7th to 27th November 2002, Course Manual

In recent years intensive fish culture is being practiced in the brackishwater, coastal water and freshwater impoundments of India. Recent techniques of intensive and super intensive fish culture involve high rates of stocking and supplementary feeding which has substantially enhanced the incidence of diseases in fishes in our countr

Asymptotically Optimal Load Balancing Topologies

We consider a system of $N$ servers inter-connected by some underlying graph topology $G_N$. Tasks arrive at the various servers as independent Poisson processes of rate $\lambda$. Each incoming task is irrevocably assigned to whichever server has the smallest number of tasks among the one where it appears and its neighbors in $G_N$. Tasks have unit-mean exponential service times and leave the system upon service completion. The above model has been extensively investigated in the case $G_N$ is a clique. Since the servers are exchangeable in that case, the queue length process is quite tractable, and it has been proved that for any $\lambda < 1$, the fraction of servers with two or more tasks vanishes in the limit as $N \to \infty$. For an arbitrary graph $G_N$, the lack of exchangeability severely complicates the analysis, and the queue length process tends to be worse than for a clique. Accordingly, a graph $G_N$ is said to be $N$-optimal or $\sqrt{N}$-optimal when the occupancy process on $G_N$ is equivalent to that on a clique on an $N$-scale or $\sqrt{N}$-scale, respectively. We prove that if $G_N$ is an Erd\H{o}s-R\'enyi random graph with average degree $d(N)$, then it is with high probability $N$-optimal and $\sqrt{N}$-optimal if $d(N) \to \infty$ and $d(N) / (\sqrt{N} \log(N)) \to \infty$ as $N \to \infty$, respectively. This demonstrates that optimality can be maintained at $N$-scale and $\sqrt{N}$-scale while reducing the number of connections by nearly a factor $N$ and $\sqrt{N} / \log(N)$ compared to a clique, provided the topology is suitably random. It is further shown that if $G_N$ contains $\Theta(N)$ bounded-degree nodes, then it cannot be $N$-optimal. In addition, we establish that an arbitrary graph $G_N$ is $N$-optimal when its minimum degree is $N - o(N)$, and may not be $N$-optimal even when its minimum degree is $c N + o(N)$ for any $0 < c < 1/2$.Comment: A few relevant results from arXiv:1612.00723 are included for convenienc

Scattering of Electron by Thomas-Fermi Potential

In this paper the elastic scatterriag cross-section of electrons by the Thomas-Fermi potential as represented by the analytical forms due to Gombas and Tiets has been calculated by the Born approximation method. Our results are in fair agreement with those calculated with the exact numerical form of Thomas-Fermi potential. Further comparison shows that the Gombas-Tietz form is a good as those of Rozental and Buchdahl

Ultrapure glass optical waveguide: Development in microgravity by the sol gel process

The sol-gel process for the preparation of homogeneous gels in three binary oxide systems was investigated. The glass forming ability of certain compositions in the selected oxide systems (SiO-GeO2, GeO2-PbO, and SiO2-TiO2) were studied based on their potential importance in the design of optical waveguide at longer wavelengths

Universality of Load Balancing Schemes on Diffusion Scale

We consider a system of $N$ parallel queues with identical exponential service rates and a single dispatcher where tasks arrive as a Poisson process. When a task arrives, the dispatcher always assigns it to an idle server, if there is any, and to a server with the shortest queue among $d$ randomly selected servers otherwise $(1 \leq d \leq N)$. This load balancing scheme subsumes the so-called Join-the-Idle Queue (JIQ) policy $(d = 1)$ and the celebrated Join-the-Shortest Queue (JSQ) policy $(d = N)$ as two crucial special cases. We develop a stochastic coupling construction to obtain the diffusion limit of the queue process in the Halfin-Whitt heavy-traffic regime, and establish that it does not depend on the value of $d$, implying that assigning tasks to idle servers is sufficient for diffusion level optimality