Necessary and sufficient condition for hydrostatic equilibrium in general relativity

We present explicit examples to show that the `compatibility criterion' is capable of providing a {\em necessary} and {\em sufficient} condition for any regular configuration to be compatible with the state of hydrostatic equilibrium. This conclusion is drawn on the basis of the finding that the $M-R$ relation gives the necessary and sufficient condition for dynamical stability of equilibrium configurations only when the compatibility criterion for these configurations is appropriately satisfied. In this regard, we construct an appropriate sequence composed of core-envelope models on the basis of compatibility criterion, such that each member of this sequence satisfies the extreme case of causality condition $v = c = 1$ at the centre. The maximum stable value of $u \simeq 0.3389$ (which occurs for the model corresponding to the maximum value of mass in the mass-radius relation) and the corresponding central value of the local adiabatic index, $(\Gamma_1)_0 \simeq 2.5911$, of this model are found fully consistent with those of the corresponding {\em absolute} values, $u_{\rm max} \leq 0.3406$, and $(\Gamma_1)_0 \leq 2.5946$, which impose strong constraints on these parameters of such models. In addition to this example, we also study dynamical stability of pure adiabatic polytropic configurations on the basis of variational method for the choice of the `trial function', $\xi =re^{\nu/4}$, as well as the mass-central density relation, since the compatibility criterion is appropriately satisfied for these models. The results of this example provide additional proof in favour of the statement regarding compatibility criterion mentioned above.Comment: 31 pages (double-spaced) revtex style, 1 figure in `ps' forma

Dynamical stability of strange quark stars

We show that the mass-radius $(M-R)$ relation corresponding to the MIT bag models of strange quark matter (SQM) and the models obtained by Day et al (1998) do not provide the necessary and sufficient condition for dynamical stability for the equilibrium configurations, since such configurations can not even fulfill the necessary condition of hydrostatic equilibrium provided by the exterior Schwarzschild solution. These findings will remain unaltered and can be extended to any other sequence of pure SQM. This study explicitly show that although the strange quark matter might exist in the state of zero pressure and temperature, but the models of pure strange quark `stars' can not exist in the state of hydrostatic equilibrium on the basis of General Relativity Theory. This study can affect the results which are claiming that various objects like - RX J1856.5-3754, SAX J1808.4-3658, 4U 1728-34, PSR 0943+10 etc. might be strange stars.Comment: 7 pages (including 6 tables and 1 figure) in MNRAS styl

Hydrostatic equilibrium of insular, static, spherically symmetric, perfect fluid solutions in general relativity

An analysis of insular solutions of Einstein's field equations for static, spherically symmetric, source mass, on the basis of exterior Schwarzschild solution is presented. Following the analysis, we demonstrate that the {\em regular} solutions governed by a self-bound (that is, the surface density does not vanish together with pressure) equation of state (EOS) or density variation can not exist in the state of hydrostatic equilibrium, because the source mass which belongs to them, does not represent the `actual mass' appears in the exterior Schwarzschild solution. The only configuration which could exist in this regard is governed by the homogeneous density distribution (that is, the interior Schwarzschild solution). Other structures which naturally fulfill the requirement of the source mass, set up by exterior Schwarzschild solution (and, therefore, can exist in hydrostatic equilibrium) are either governed by gravitationally-bound regular solutions (that is, the surface density also vanishes together with pressure), or self-bound singular solutions (that is, the pressure and density both become infinity at the centre).Comment: 16 pages (including 1 table); added section 5; accepted for publication in Modern Physics Letters

Change Vector Analysis using Enhanced PCA and Inverse Triangular Function-based Thresholding

Change vector analysis is a very sophisticated method to evaluate land-use/land-cover changes meaningfully. By making proper choice of input data in the form of bands (for instance, red, NIR etc) or features (for instance, greenness, brightness, wetness etc), information about both the magnitude as well as the type/nature of changes can be extracted. However, improper selection of thresholds is always a hindrance to a good change detection algorithm. The paper has proposed an improved technique to select threshold appropriately by means of principal component difference and inverse triangular function. The changes have been represented using class-based circular wheel representation. Results have been shown to further testify the performance of proposed algorithm.Defence Science Journal, 2012, 62(4), pp.236-242, DOI:http://dx.doi.org/10.14429/dsj.62.107

Functional trait plasticity diverges between sexes in African cichlids: A contribution toward ecological sexual dimorphism?

Phenotypic plasticity enables development to produce multiple phenotypes in response to environmental conditions. Plasticity driven variation has been suggested to play a key role in adaptive divergence, and plasticity itself can evolve. However, the interaction of plasticity with the multiple levels involved with adaptive divergence is less understood. For example, sexual dimorphism can contribute adaptive variation through ecological sexual dimorphism (ESD), but the contribution of plasticity to this phenomenon is unknown. Therefore, to determine the potential contribution of plasticity to ESD, we used the adaptive radiation of Malawi cichlids. Two mouthbrooding species (Labeotropheus fuelleborni and Tropheops "Red Cheek") with differences in foraging tactics underwent foraging experiments using benthic and limnetic treatments while accounting for sex. Plasticity in craniofacial shape and three functionally important traits were measured. Plasticity was shown, but without any sex-based differences in shape. However, for mechanical advantage traits of the mandible sex by diet interactions were found. This suggests that ESD, may be influenced by phenotypic plasticity that diverges between sexes. Given the involvement of the mandible in parental care in cichlids this may indicate that sexual divergence in plasticity may trade-off against maternal care tactics

Study of risk factors for preterm deliveries in a tertiary hospital

Background: Preterm labour and preterm deliveries are very challenging obstetric complications. Early identification of risk factors may help identify women at risk for preterm deliveries.Methods: A one-year observational study was conducted in the department of obstetrics and gynecology, IGMC Shimla, Himachal Pradesh from 1st August 2017 to 31st July 2018. All mothers who delivered between 24 to 37 weeks were subjected to a detailed history with respect to age, parity, previous pregnancy outcomes and to identify the presence of any risk factors. A thorough obstetric and systemic examination was done. Parametric and non-parametric test of significance were used to find the association between different quantitative and qualitative variable.Results: Incidence of preterm deliveries was 11.4%. Maximum cases were of age group 25-30 years. 71.7% belonged to lower socio-economic status. 54% cases were seen in multigravida. History of previous abortion was seen in 18.4% and 9.7% had history of preterm deliveries. 12% cases had history of 1st trimester bleeding.  Spontaneous onset of preterm labour was seen in 55.1%. The significant risk factors associated were PIH and genitourinary infections.Conclusions: The risk factors of preterm birth to a large extent can be identified in antenatal period. Adolescent health education including good nutrition, good hygiene, counselling for contraception to reduce unintended pregnancies and birth spacing can lower the preterm birth rate. Better prenatal care, early identification of risk factors and complicated cases, regular follow up and proper management can help us in reducing preterm births