Is toric duality a Seiberg-like duality in (2+1)-d ?

We show that not all $(2+1)$ dimensional toric phases are Seiberg-like duals. Particularly, we work out superconformal indices for the toric phases of Fanos ${\cal{C}}_3$, ${\cal{C}}_5$ and ${\cal{B}}_2$. We find that the indices for the two toric phases of Fano ${\cal{B}}_2$ do not match, which implies that they are not Seiberg-like duals. We also take the route of acting Seiberg-like duality transformation on toric quiver Chern-Simons theories to obtain dual quivers. We study two examples and show that Seiberg-like dual quivers are not always toric quivers.Comment: 21 pages, 7 figures, to be published in JHE

Partial resolution of complex cones over Fano B{\cal{B}}

In our recent paper arXiv:1108.2387, we systematized inverse algorithm to obtain quiver gauge theory living on the M2-branes probing the singularities of special kind of Calabi-Yau four-folds which were complex cones over toric Fano $\mathbb{P}^3$, ${\cal{B}}_1$, ${\cal{B}}_2$, ${\cal{B}}_3$. These quiver gauge theories cannot be given a dimer tiling presentation. We use the method of partial resolution to show that the toric data of $\mathbb{C}^4$ and Fano $\mathbb{P}^3$ can be embedded inside the toric data of Fano ${\cal{B}}$ theories. This method indirectly justfies that the two node quiver Chern-Simons theories corresponding to $\mathbb{C}^4$, Fano $\mathbb{P}^3$ and their orbifolds can be obtained by higgsing matter fields of the three node parent quiver corresponding to Fano ${\cal{B}}_1$, ${\cal{B}}_2$, ${\cal{B}}_3$, ${\cal{B}}_4$ three-folds.Comment: 22 pages, 8 figure

Photon redshift and the appearance of a naked singularity

In this paper we analyze the redshift as observed by an external observer receiving photons which terminate in the past at the naked singularity formed in a Tolman-Bondi dust collapse. Within the context of models considered here it is shown that photons emitted from a weak curvature naked singularity are always finitely redshifted to an external observer. Certain cases of strong curvature naked singularities, including the self-similar one, where the photons are infinitely redshifted are also pointed out.Comment: Latex file, 14 pages, no figures, one change in the reference. Accepted for publication in Phys. Rev.

Null Geodesic Expansion in Spherical Gravitational Collapse

We derive an expression for the expansion of outgoing null geodesics in spherical dust collapse and compute the limiting value of the expansion in the approach to singularity formation. An analogous expression is derived for the spherical collapse of a general form of matter. We argue on the basis of these results that the covered as well as the naked singularity solutions arising in spherical dust collapse are stable under small changes in the equation of state.Comment: 10 pages, Latex File, No figure

Spectroscopic Observations and Modelling of Impulsive Alfv\'en Waves Along a Polar Coronal Jet

Using the Hinode/EIS 2$"$ spectroscopic observations, we study the intensity, velocity, and FWHM variations of the strongest Fe XII 195.12 \AA\ line along the jet to find the signature of Alfv\'en waves. We simulate numerically the impulsively generated Alfv\'en waves within the vertical Harris current-sheet, forming the jet plasma flows, and mimicking their observational signatures. Using the FLASH code and the atmospheric model with embedded weakly expanding magnetic field configuration within a vertical Harris current-sheet, we solve the two and half-dimensional (2.5-D) ideal magnetohydrodynamic (MHD) equations to study the evolution of Alfv\'en waves and vertical flows forming the plasma jet. At a height of $\sim 5~\mathrm{Mm}$ from the base of the jet, the red-shifted velocity component of Fe XII 195.12 \AA\ line attains its maximum ($5~\mathrm{km\,s}^{-1}$) which converts into a blue-shifted one between the altitude of $5-10~\mathrm{Mm}$. The spectral intensity continously increases up to $10~\mathrm{Mm}$, while FWHM still exhibits the low values with almost constant trend. This indicates that the reconnection point within the jet's magnetic field topology lies in the corona $5-10~\mathrm{Mm}$ from its footpoint anchored in the Sun's surface. Beyond this height, FWHM shows a growing trend. This may be the signature of Alfv\'en waves that impulsively evolve due to reconnection and propagate along the jet. From our numerical data, we evaluate space- and time- averaged Alfv\'en waves velocity amplitudes at different heights in the jet's current-sheet, which contribute to the non-thermal motions and spectral line broadening. The synthetic width of Fe XII $195.12~\mathrm{\AA}$ line exhibits similar trend of increment as in the observational data, possibly proving the existence of impulsively generated (by reconnection) Alfv\'en waves which propagate along the jet

Coarse wavelength division multiplexer on silicon-on-insulator for 100 GbE

A four-channel cascaded MZl based de-multiplexer at O-band with coarse channel spacing of 20 nm and band flatness of 13 nm is demonstrated on silicon-on-insulator. The device shows a mean crosstalk and insertion loss below -16 dB and 2.5 dB

Residual Impact of Triazophos on the germination of wheat (Triticum aestivum L.) Var. Lok-1

Increased demand for food and fiber has lead to the chemicalization of agriculture with an increased input of chemical fertilizers and synthetic pesticides for amplified returns. It is estimated that India approximately looses 18 % of crop yield valued at Rs.900 billion due to pest attacks, against which specific pest management chemicals are applied frequently. Present study evaluates the effect of Triazophos (Organophosphorous broad spectrum insecticide and acricide) on the germination of Wheat (Triticum aestivum L.) Var. Lok-1. The pesticide is mostly used on Soyabean for pest suppression; its residual nature can influence the subsequent germination of the cereal crop and diminish the returns there from. The effect of two concentrations of Triazophos, 0.5% and 1%, were assessed for a period of 14 days on the germination of Wheat seeds. Compared with the control, the results showed a significant decrease in the rate of germination with the increasing concentration of the pesticide. Also germination time increased drastically when compared with control. Key words: Triazophos, agriculture, Pest suppression, Residual natur