Some Normality Criteria

In this article we prove some normality criteria for a family of meromorphic functions which involves sharing of a non-zero value by certain differential monomials generated by the members of the family. These results generalizes some of the results of Schwick.Comment: 16 Pages. Comments are welcome, Communicate

On a Theorem of Schwick

Let D be a domain, n, k be positive integers and n >= K+3. Let F be a family of functions meromorphic in D. If each f in F satisfies (f^n)^(k) not equal to 1 for z in D, then F is normal family. This result was proved by Schwick. In this paper we extend this result.Comment: Comments are welcom

A Criterion for quasi normality in Cn\mathbb{C}^n

In this article, we give a Zalcman type renormalization result for the quasinormality of a family of holomorphic functions on a domain in $\mathbb{C}^n$ that takes values in a complete complex Hermitian manifold.Comment: 11 page

Intranight Optical Variability of Radio-Quiet Weak Emission Line Quasars-III

This is continuation of our programme to search for the elusive radio-quiet BL Lacs, by carrying out a systematic search for intranight optical variability (INOV) in a subset of `weak-line quasars' which are already designated as `high-confidence BL Lac candidate' and are also known to be radio-quiet. For 6 such radio-quiet weak-line quasars (RQWLQs), we present here new INOV observations taken in 11 sessions of duration >3 hours each. Combining these data with our previously published INOV monitoring of RQWLQs in 19 sessions yields INOV observations for a set of 15 RQWLQs monitored in 30 sessions, each lasting more than 3 hours. The 30 differential light curves, thus obtained for the 15 RQWLQs, were subjected to a statistical analysis using the F-test, and the deduced INOV characteristics of the RQWLQs then compared with those published recently for several prominent AGN classes, also applying the F-test. From our existing INOV observations, there is a hint that RQWLQs in our sample show a significantly higher INOV duty cycle than radio-quiet quasars and radio lobe-dominated quasars. Two sessions when we have detected strong (blazar-like) INOV for RQWLQs are pointed out, and these two RQWLQs are therefore the best known candidates for radio-quiet BL Lacs, deserving to be pursued. For a proper comparison with the INOV properties already established for (brighter) members of several prominent classes of AGN, a factor of 2-3 improvement in the INOV detection threshold for the RQWLQs is needed and it would be very interesting to check if that would yield a significantly higher estimate for INOV duty cycle than is found here.Comment: 9 pages, 1 figure and 4 tables, accepted for publication in MNRAS main journal. arXiv admin note: text overlap with arXiv:1212.5384, arXiv:1403.744

Subconvexity bound for GL(2)GL(2) L-functions: \lowercase{t}-aspect

Let $f$ be a holomorphic Hecke eigenform or a Hecke-Maass cusp form for the full modular group $SL(2, \mathbb{Z})$. In this paper we shall use circle method to prove the Weyl exponent for $GL(2)$ $L$-functions. We shall prove that $$L \left( \frac{1}{2} + it, f \right) \ll_{f, \epsilon} \left( 2 + |t|\right)^{1/3 + \epsilon},$$ for any $\epsilon > 0.

Intranight Optical Variability of Radio-Quiet Weak Emission Line Quasars-IV

We report an extension of our program to search for radio-quiet BL Lac candidates using intra-night optical variability (INOV) as a probe. The present INOV observations cover a well-defined representative set of 10 `radio-quiet weak-emission-line quasars' (RQWLQs), selected from a newly published sample of 46 such sources, derived from the Sloan Digital Sky Survey (Data release 7). Intra-night CCD monitoring of the 10 RQWLQs was carried out in 18 sessions lasting at least 3.5 hours. For each session, differential light curves (DLCs) of the target RQWLQ were derived relative to two steady comparison stars monitored simultaneously. Combining these new data with those already published by us for 15 RQWLQs monitored in 30 sessions, we estimate an INOV duty cycle of $\sim 3\%$ for the RQWLQs, which appears inconsistent with BL Lacs. However, the observed INOV events (which occurred in just two of the sessions) are strong (with a fractional variability amplitude $\psi >$ 10\%), hence blazar-like. We briefly point out the prospects of an appreciable rise in the estimated INOV duty cycle for RQWLQs with a relatively modest increase in sensitivity for monitoring these rather faint objects.Comment: 8 pages, 2 figures, accepted in MNRA

On Heterogeneous Regenerating Codes and Capacity of Distributed Storage Systems

Heterogeneous Distributed Storage Systems (DSS) are close to real world applications for data storage. Internet caching system and peer-to-peer storage clouds are the examples of such DSS. In this work, we calculate the capacity formula for such systems where each node store different number of packets and each having a different repair bandwidth (node can be repaired by contacting a specific set of nodes). The tradeoff curve between storage and repair bandwidth is studied for such heterogeneous DSS. By analyzing the capacity formula new minimum bandwidth regenerating (MBR) and minimum storage regenerating (MBR) points are obtained on the curve. It is shown that in some cases these are better than the homogeneous DSS.Comment: submitted to conference Netcod 2014, 3 figures, 5 page

Intranight Optical Variability of Radio-Quiet Weak Emission Line Quasars-II

This is continuation of our search for the elusive radio-quiet blazars, by carrying out a systematic programme to detect intranight optical variability (INOV) in a subset of `Weak-Lines-Quasars' (WLQs) which are designated as `high confidence BL Lac candidates' and are known to be radio-quiet. For 10 such RQWLQs, we present here the INOV observations taken in 16 sessions of durations > 3.5 hours each. Combining these data with our previously published INOV monitoring of RQWLQs in 13 sessions, gives a set of INOV observations of 15 RQWLQs monitored in 29 sessions each lasting more than 3.5 hours. The 29 differential light curves (DLCs), thus obtained for the 15 RQWLQs, were subjected to an statistical analysis using the F-test and the deduced INOV characteristics of the RQWLQs are compared with those published recently for several prominent AGN classes, also using the F-test. However, since the RQWLQs are generally 1-2 magnitudes fainter, a rigorous comparison has to wait for somewhat more sensitive INOV observations than those presented here. Based on our existing INOV observations, it seems that RQWLQs in our sample show a significantly higher INOV duty cycle than radio-quiet quasars and radio lobe-dominated quasars. Two sessions when we detected rather strong (blazar-like) INOV for RQWLQs are pointed out and both these RQWLQs are therefore candidates for radio-quiet BL Lacs.Comment: 8 pages, 2 figures and 3 tables, accepted for publication in MNRAS main journa

A Mathematical Model of Foreign Capital Inflow

The paper models foreign capital inflow from the developed to the developing countries in a stochastic dynamic programming (SDP) framework. Under some regularity conditions, the existence of the solutions to the SDP problem is proved and they are then obtained by numerical technique because of the non-linearity of the related functions. A number of comparative dynamic analyses explore the impact of parameters of the model on dynamic paths of capital inflow, interest rate in the international loan market and the exchange rate.Comment: 32 pages, 4 sets of figures each set consists of capital inflow, interest rate and exchange rat

Synthesis and characterization of novel benzimidazole embedded 1,3,5-trisubstituted pyrazolines as antimicrobial agents

Efficient syntheses of some new substituted pyrazoline derivatives linked to substituted benzimidazole scaffold were performed by multistep reaction sequences. All the synthesized compounds were characterized using elemental analysis and spectral studies (IR, 1D/2D NMR techniques and mass spectrometry). The synthesized compounds were screened for their antimicrobial activity against selected Gram-positive and Gram-negative bacteria, and fungi strain. The compounds with halo substituted phenyl group at C5 of the 1-phenyl pyrazoline ring (15, 16 and 17) showed significant antibacterial activity. Among the screened compounds, 17 showed most potent inhibitory activity (MIC = 64 {\mu}g mL-1) against a bacterial strain. The tested compounds werefound to be almost inactive against the fungal strain C. albicans, apart from pyrazoline-1-carbothiomide 21, which was moderately active.Comment: 9 Pages,2 figures, 1 tabl