Abstract:
Motivated by the need for rapid localisation of newly discovered faint millisecond pulsars (MSPs) we have developed a coherently dedispersed gating correlator. This gating correlator accounts for the orbital motions of MSPs in binaries while folding the visibilities with best-fit topocentric rotational model derived from periodicity search in simultaneously generated beamformer output. Unique applications of the gating correlator for sensitive interferometric studies of MSPs are illustrated using the Giant Metrewave Radio Telescope (GMRT) interferometric array. We could unambiguously localise five newly discovered Fermi MSPs in the on-off gated image plane with an accuracy of +-1". Immediate knowledge of such precise position allows the use of sensitive coherent beams of array telescopes for follow-up timing observations, which substantially reduces the use of telescope time (~ 20X for the GMRT). In addition, precise a-priori astrometric position reduces the effect of large covariances in timing fit (with discovery position, pulsar period derivative and unknown binary model), which in-turn accelerates the convergence to initial timing model. For example, while fitting with precise a-priori position (+-1"), timing model converges in about 100 days, accounting the effect of covariance between position and pulsar period derivative. Moreover, such accurate positions allows for rapid identification of pulsar counterpart at other wave-bands. We also report a new methodology of in-beam phase calibration using the on-off gated image of the target pulsar, which provides the optimal sensitivity of the coherent array removing the possible temporal and spacial decoherences.

Abstract:
We introduce the concept of a weak nil clean ring, a generalization of nil clean ring, which is nothing but a ring with unity in which every element can be expressed as sum or difference of a nilpotent and an idempotent. Further if the idempotent and nilpotent commute the ring is called weak* nil clean. We characterize all $n\in \mathbb{N}$, for which $\mathbb{Z}_n$ is weak nil clean but not nil clean. We show that if $R$ is a weak* nil clean and $e$ is an idempotent in $R$, then the corner ring $eRe$ is also weak* nil clean. Also we discuss $S$-weak nil clean rings and their properties, where $S$ is a set of idempotents and show that if $S=\{0, 1\}$, then a $S$-weak nil clean ring contains a unique maximal ideal. Finally we show that weak* nil clean rings are exchange rings and strongly nil clean rings provided $2\in R$ is nilpotent in the later case. We have ended the paper with introduction of weak J-clean rings.

Abstract:
We show that the delta function potential can be exploited along with perturbation theory to yield the result of certain infinite series. The idea is that any exactly soluble potential if coupled with a delta function potential remains exactly soluble. We use the strength of the delta function as an expansion parameter and express the second-order energy shift as an infinite sum in perturbation theory. The analytical solution is used to determine the second-order energy shift and hence the sum of an infinite series. By an appropriate choice of the unperturbed system, we can show the importance of the continuum in the energy shift of bound states.

Abstract:
We have developed a multi-pixel beamformer technique, which can be used for enhancing the capabilities for studying pulsars using an interferometric array. Using the Giant Metrewave Radio Telescope (GMRT), we illustrate the application of this efficient technique, which combines the enhanced sensitivity of a coherent array beamformer with the wide field-of-view seen by an incoherent array beamformer. Multi-pixel beamformer algorithm is implemented using the recorded base-band data. With the optimisations in multi-pixelisation described in this paper, it is now possible to form 16 directed beams in real-time. We discuss a special application of this technique, where we use continuum imaging followed by the multi-pixel beamformer to obtain the precise locations of newly discovered millisecond pulsars with the GMRT. Accurate positions measured with single observations enable highly sensitive follow-up studies using coherent array beamformer and rapid follow up at higher radio frequencies and other wavelengths. Normally, such accurate positions can only be obtained from a long-term pulsar timing program. The multi-pixel beamformer technique can also be used for highly sensitive targeted pulsar searches in extended supernova remnants. In addition this method can provide optimal performance for the large scale pulsar surveys using multi-element arrays.

Abstract:
We present the results of the multi-frequency scatter time measurements for ten radio pulsars that were relatively less studied in this regard. The observations were performed using the Giant Meterwave Radio Telescope at the observing frequencies of 150, 235, 325, 610 and 1060~MHz. The data we collected, in conjunction with the results from other frequencies published earlier, allowed us to estimate the scatter time frequency scaling indices for eight of these sources. For PSR J1852$-$0635 it occurred that its profile undergoes a strong evolution with frequency, which makes the scatter time measurements difficult to perform, and for PSR J1835$-$1020 we were able to obtain reliable pulse broadening estimates at only two frequencies. We used the eight frequency scaling indices to estimate both: the electron density fluctuation strengths along the respective lines-of-sight, and the standardized amount of scattering at the frequency of 1 GHz. Combining the new data with the results published earlier by Lewandowski et al., we revisited the scaling index versus the dispersion measure (DM) relation, and similarly to some of the earlier studies we show that the average value of the scaling index deviates from the theoretical predictions for large DM pulsars, however it reaches the magnitude claimed by L\"ohmer et al. only for pulsars with very large DMs ($>$650 pc cm$^{-3}$). We also investigated the dependence of the scattering strength indicators on the pulsar distance, DM, and the position of the source in the Milky Way Galaxy.

Abstract:
Bound and resonance states of helium atom have been investigated inside a quantum dot by using explicitly correlated Hylleraas type basis set within the framework of stabilization method. To be specific, precise energy eigenvalues of bound 1sns (1Se) [n = 1-6] states and the resonance parameters i.e. positions and widths of 1Se states due to 2sns [n = 2-5] and 2pnp [n = 2-5] configuration of confined helium below N = 2 ionization threshold of He+ have been estimated. The two-parameter (Depth and Width) finite oscillator potential is used to represent the confining potential representing the quantum dot. It has been explicitly demonstrated that electronic structure properties become a sensitive function of the dot size. It is observed from the calculations of ionization potential that the stability of an impurity ion within quantum dot may be manipulated by varying the confinement parameters. A possibility of controlling the autoionization lifetime of doubly excited states of two-electron ions by tuning the width of the quantum cavity is also discussed here.

Abstract:
Domestic violence is a wide spread problem, its actual extent is difficult to measure. According to available statistics throughout the world, about 33 percent women have experienced violence at some point of their life (WHO, 1997). In India, women form about half of the population and enjoy various freedom and rights but simultaneously, like other developing countries, violence against women is overwhelming and is a matter of concern. Domestic violence leads to violence of human rights and prevents them from enjoying their fundamental rights. Though the types of violence differs from society to society, nations to nations, religion to religion, but it prevails in underdeveloped, developing and developed countries, too. Domestic violence refers to “assaultive and coercive behaviours that adults use against their intimate partners” (Holden, 2003). In India, there are a set of well equipped legislations which protect women against violence. And Protection of Women against Domestic Violence Act, 2005 is the milestone in the history of legal control and judicial response in domestic violence affairs. But the rate of violence against women increased 44 percent during 1993 to 2011. The findings of the paper are expected to enlighten individuals and the community on the causes and consequences of violence against women. The paper comes out with policy prescription for government and non-government organizations towards addressing the problem.

Abstract:
In this qualitative study we investigated
the role of bantering in creating a learning community for science education.
The curriculum was centered on a technology-integrated Project Based Approach
(PBA). We examined the pattern of in-service teachers’ interaction with such a
learning environment and perceptions of their future instructional practices
that result from collaborative reflection on the use of Banter throughout the
semester. The findings suggest that exposure to bantering interaction not only
helped the in-service teachers to make decisions about the scientific issues
they will face in the future but also helped to construct a more inquiry based
understanding of the issues in science teaching. Methodological limits and
possibilities were explored through the use of data analysis software such as
Inspiration and NVivo.

Abstract:
We are conducting a survey for pulsars and transients using the Giant Metrewave Radio Telescope (GMRT). The GMRT High Resolution Southern Sky (GHRSS) survey is an off-Galactic-plane (|b|>5) survey in the declination range -40 deg to -54 deg at 322 MHz. With the high time (up to 30.72 micro-sec) and frequency (up to 0.016275 MHz) resolution observing modes, the 5-sigma detection limit is 0.5 mJy for a 2 ms pulsar with 10% duty cycle at 322 MHz. Total GHRSS sky coverage of 2866 square-deg, will result from 1953 pointing, each covering 1.8 square-deg. The 10-sigma detection limit for a 5 milli-sec transient burst is 1.6 Jy for the GHRSS survey. In addition, the GHRSS survey can reveal transient events like rotating radio transients or fast radio bursts. With 35% of the survey completed (i.e. 1000 square-deg), we report the discovery of 10 pulsars, one of which is a millisecond pulsar (MSP), one of the highest pulsar per square degree discovery rates for any off-Galactic plane survey. We re-detected 23 known in-beam pulsars. Utilising the imaging capability of the GMRT we also localised 4 of the GHRSS pulsars (including the MSP) in the gated image plane within +/- 10 arc-second. We demonstrated rapid convergence in pulsar timing with a more precise position than is possible with single dish discoveries. We also exhibited that we can localise the brightest transient sources with simultaneously obtained lower time resolution imaging data, demonstrating a technique that may have application in the SKA.

Abstract:
The historical daily rainfall data for the period of 40 years (1972-2011) of Dinhata in Koch Behar district of W.B. were analyzed to know weekly, monthly, seasonal, annual and decadal rainfall variability and probabilities at different level for suitable crop planning. The overall mean annual rainfall was 2909.88 mm, with standard deviation 658.39 mm and coefficient of variation 22.62 %. The annual rainfall of 2800.5 mm with 105 rainy days and 2487.2 mm rainfall and 91 rainy days may be expected with 51.24% and 75.64 % probability level, respectively. The seasonal rainfall was distributed as 2158.6 mm, 535.86 mm and 215.39 mm in kharif (June to September), summer (March to May) and rabi (October to February) seasons, respectively.