Stability of Naked Singularity arising in gravitational collapse of Type I matter fields

Considering gravitational collapse of Type I matter fields, we prove that, given an arbitrary $C^{2}$- mass function $\textit{M}(r,v)$ and a $C^{1}$- function $h(r,v)$ (through the corresponding $C^{1}$- metric function $\nu(t,r)$), there exist infinitely many choices of energy distribution function $b(r)$ such that the `true' initial data ($\textit{M},h(r,v)$) leads the collapse to the formation of naked singularity. We further prove that the occurrence of such a naked singularity is stable with respect to small changes in the initial data. We remark that though the initial data leading to both black hole and naked singularity form a "big" subset of the true initial data set, their occurrence is not generic. The terms `stability' and `genericity' are appropriately defined following the theory of dynamical systems. The particular case of radial pressure $p_{r}(r)$ has been illustrated in details to get clear picture of how naked singularity is formed and how, it is stable with respect to initial data.Comment: 16 pages, no figure, Latex, submitted to Praman

Opinion dynamics with varying susceptibility to persuasion

A long line of work in social psychology has studied variations in people's susceptibility to persuasion -- the extent to which they are willing to modify their opinions on a topic. This body of literature suggests an interesting perspective on theoretical models of opinion formation by interacting parties in a network: in addition to considering interventions that directly modify people's intrinsic opinions, it is also natural to consider interventions that modify people's susceptibility to persuasion. In this work, we adopt a popular model for social opinion dynamics, and we formalize the opinion maximization and minimization problems where interventions happen at the level of susceptibility. We show that modeling interventions at the level of susceptibility lead to an interesting family of new questions in network opinion dynamics. We find that the questions are quite different depending on whether there is an overall budget constraining the number of agents we can target or not. We give a polynomial-time algorithm for finding the optimal target-set to optimize the sum of opinions when there are no budget constraints on the size of the target-set. We show that this problem is NP-hard when there is a budget, and that the objective function is neither submodular nor supermodular. Finally, we propose a heuristic for the budgeted opinion optimization and show its efficacy at finding target-sets that optimize the sum of opinions compared on real world networks, including a Twitter network with real opinion estimates

North-South Distribution of Solar Flares during Cycle 23

In this paper, we investigate the spatial distribution of solar flares in the northern and southern hemisphere of the Sun that occurred during the period 1996 to 2003. This period of investigation includes the ascending phase, the maximum and part of descending phase of solar cycle 23. It is revealed that the flare activity during this cycle is low compared to previous solar cycle, indicating the violation of Gnevyshev-Ohl rule. The distribution of flares with respect to heliographic latitudes shows a significant asymmetry between northern and southern hemisphere which is maximum during the minimum phase of the solar cycle. The present study indicates that the activity dominates the northern hemisphere in general during the rising phase of the cycle (1997-2000). The dominance of northern hemisphere is shifted towards the southern hemisphere after the solar maximum in 2000 and remained there in the successive years. Although the annual variations in the asymmetry time series during cycle 23 are quite different from cycle 22, they are comparable to cycle 21.Comment: 6 pages, 2 figures, 1 table; Accepted for the publication in the proceedings of international solar workshop held at ARIES, Nainital, India on "Transient Phenomena on the Sun and Interplanetary Medium" in a special issue of "Journal of Astrophysics and Astronomy (JAA)

Study of Distribution and Asymmetry of Solar Active Prominences During Solar Cycle 23

In this paper we present the results of a study of the spatial distribution and asymmetry of solar active prominences (SAP) for the period 1996-2007 (solar cycle 23). For more meaningful statistical analysis we have analysed the distribution and asymmetry of SAP in two subdivisions viz. Group1 (ADF, APR, DSF, CRN, CAP) and Group2 (AFS, ASR, BSD, BSL, DSD, SPY, LPS). The north-south (N-S) latitudinal distribution shows that the SAP events are most prolific in the 21-30degree slice in the northern and southern hemispheres and east-west (E-W) longitudinal distribution study shows that the SAP events are most prolific (best visible) in the 81-90degree slice in the eastern and western hemispheres. It has been found that the SAP activity during this cycle is low compared to previous solar cycles. The present study indicates that during the rising phase of the cycle the number of SAP events were roughly equal on the north and south hemispheres. However, activity on the southern hemisphere has been dominant since 1999. Our statistical study shows that the N-S asymmetry is more significant then the E-W asymmetry.Comment: 21 pages 5 figures; Published online; 02 October, 2009; Solar Physics Journa

Characterization of finger millet [Eleusine coracana (L.) Gaertn.] germplasm for morphological parameters under field conditions

The trial was conducted at the research block of Crop Improvement, GBPUAT, Hill Campus, Ranichauri using randomized block design (RBD) to characterize finger millet germplasm for morphological characters viz., plant height, flag leaf length, number of tiller plant-1, number of finger ear-1, ear length, no. of grain finger-1, no. of grain ear-1 and grain yield plant-1. Among all germplasms, number of finger ear-1, number of grain finger-1 and grain yield plant-1(g) had recorded highest in VL 149 which were 9.96, 150.66, 2.63 g respectively. The germplasm GEC 1406 attained lowest plant height (75.89 cm), GEC 961 had recorded higher flag leaf length (40.96 cm), GEC 268 had recorded maximum number of tiller plant-1 (3.30), GEC 199 had recorded higher ear length (9.20 cm), GEC 1044 had recorded maximum number of grain ear-1 (663) among all germplasm of finger millet. This study is helpful to identify superior germplasm so they can be used for further finger millet crop improvement programs