In this thesis, we discuss the dynamical stability of charged compact objects with the help of some mathematical models. For this purpose, we have selected three different models of charged compact objects to discuss the possible occurrence of cracking under different conditions. In first selected model, we discuss charged anisotropic compact objects with a linear equation of state. In second model, we study anisotropic charged compact object PSR J1614-2230 in quadratic regime, while in third model, we study charged compact stars corresponding to embedded class one metric with perfect inner fluid distribution. We investigate the impact of electromagnetic field on the stability regions of charged self-gravitating compact objects by using the concept of cracking. For this, we have applied local density perturbation scheme to the hydrostatic equilibrium equation as well as on physical parameters involved in the model. In particular, we have examined the cracking of charged compact objects (a) PSR J1614-2230, PSR J1903+327, Vela X-1, SMC X-1 and Cen X-3 with linear equation of state (b) PSR J1614-2230 with quadratic equation of state (c) Her X-1, PSR 1937+21, PSR J1614-2230, PSR J0348+0432 and RX J1856-37 corresponding to embedded class one metric. We conclude that these objects exhibit cracking and stability regions decreases with the increase of charge. We also extend two conventional polytropic equations of state to generalized polytropic equations of state for spherical and cylindrical symmetries in the context of general relativity. For this purpose, we formulate the general framework to discuss the physical properties of spherical and cylindrical polytropes with charged anisotropic inner fluid distribution under conformally flat condition. We investigate the stability of generalized polytropic models through Tolman-mass and Whittaker formula for spherical and cylindrical symmetries respectively. We also discuss the possible occurrence of cracking in charged anisotropic polytropes developed under the assumption of generalized polytropic equation of state in two different ways (i) by carrying out local density perturbation under conformally flat condition (ii) by parametric perturbations. We conclud that one of the generalized polytropic equations of state results into a physically viable model and cracking appears for a specific range of density and model parameters.
Allah sent his prophets for the guidance of the Human beings. Prophet Muḥammad (SAW) was the last of them. In the short span of only twenty three years, he changed the scenario of the world through the teachings of Islam. Apart from countless Muslims, the Non Muslim scholars also wrote about his life. Lesley Hazleton is a Non Muslims scholar wrote "The First Muslim-The Story of Muhammad". This book is divided into three parts; 1 The Orphan, 2 Exile & 3 The Leader. She expressed her views about the Prophet in her book openly. Many times she praises the prophet (SAW) for his achievements but like her successors, she criticizes his life. Sometimes she criticizes the family (forefathers) of the prophet, sometimes, in soft words criticizes the family life and polygamy of the Prophet (SAW). This research paper discusses her approach to the life of the Prophet (Seerah) in the light of her book.
A study was carried out to estimate metal pollution lead and cadmium (Pb 2+ and Cd 2+ ) emitting from automobiles and selection of suitable metal indicators which reflect the pollution level in the atmosphere. Two roads i.e. Motorway (M-3) and National Highway (N- 5) were selected for the purpose of study. The dust and plant samples were collected and Pb 2+ and Cd 2+ contents were recorded at five selected sites of M-3 and N-5. The dust and plant samples 50 m away from both roads were kept as reference control while soil control were taken 15 m away due to irrigated field started and analyzed for Pb 2+ and Cd 2+ profile. The maximum Pb 2+ concentration (conc.) i.e. 0.00075 mg g -1 was observed in dust samples of Hojan Town and minimum conc. (0.00016 mg g -1 ) was recorded in Kamalpur Sargodha road. The data collected from N-5 showed maximum Pb 2+ conc. (0.000244 mg g -1 ) at ZIS-textiles and minimum Pb 2+ conc. (0.00042 mg g -1 ) for roadside side dust samples. The maximum Pb 2+ conc. (0.00044 mg g -1 ) was found in roadside soil of Hojan town than that of control (0.00018 mg g -1 ) at M-3 while the high Pb 2+ value (0.0032 mg g -1 ) for roadside soil samples of Sitara valley was followed by conc. (0.00021 mg g -1 ) recorded for Chak. No. 60 Saudagarpur to their respective controls at N-5. All the gas exchange attributes like photosynthetic and transpiration rate, stomatal conductance (g s ), internal Carbon dioxide concentration (C i ), water use efficiency (WUE) of roadside plants on both roads decreased for plants which were growing away from the roadside. A decrease was also estimated in total soluble sugars, total free amino acids and total soluble proteins in all the under study plants on both roads. The Pb 2+ conc. was high in smoke samples of bus and coach at Pindi Bhattian Interchange on M-3 and same conc. was noted at Gutwala interchange at N-5. The C. procera accumulated more Pb 2+ (0.0024 mg g -1 ) in their unwashed leaves while 0.00017 mg g -1 was found in washed leaves however low Pb 2+ conc. was noticed in P. robelenii at M- 3 while at N-5, N. oleander accumulated more Pb 2+ i.e. 0.00186 mg g -1 in their leaves while less accumulation of Pb 2+ (0.0012 mg g -1 ) was noticed in unwashed leaves of P. hysterophorus. The high Cd 2+ contents (0.000024 mg g -1 ) were found in unwashed leaves of C. ciliaris and low conc. (0.000016 mg g -1 ) was recorded in C. procera at M-3 while high deposition of Cd 2+ i.e. 0.00007 mg g -1 was noticed in P. hysterophorus and low Cd 2+ traces (0.00002 mg g -1 ) was measured in unwashed leaves of C. ciliaris at N-5.