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Stability Analysis of Self-Gravitating Collapsing Systems

Thesis Info

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Author

Zaeem Ul Haq Bhatti, Muhammad

Program

PhD

Institute

University of the Punjab

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2015

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/9204/1/M%20Zaeem%20ul%20Haq%20Bhatti_UoP_Lahore.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727229020

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This thesis deals with the dynamical instability as well as inhomogeneities in self- gravitating collapsing objects. For this purpose, the matter distribution is considered imperfect due to anisotropic pressure, shear and bulk viscosity, dissipation in di®usion and streaming out limits and electromagnetic e®ects. For instability regimes, the interior region is taken as spherical, cylindrical and axially symmetric spacetimes which are matched with suitable exterior to explore Darmois conditions. The ¯eld equations and conservation laws are formulated and then perturbed up to ¯rst order in perturbation parameter to construct the collapse equation. The instability regimes are investigated under both N and pN approximations. A crucial role of adiabatic index has been analyzed in the presence of expansion scalar. For spherical con¯guration, the matter distribution is considered to be charged anisotropic dissipative with shear viscosity. The charged cylindrical geometry is dis- cussed with three types of °uid con¯gurations. In the ¯rst case, we take anisotropic pressure, bulk viscosity and dissipation only in di®usion approximation. The second case studies the instability epochs with anisotropic pressure under zero expansion con- dition while in the third case we take isotropic °uid with dissipation in streaming out limit. The dynamical instability for axially symmetric geometry includes two kinds of matter con¯gurations. Initially, this analysis is done only with anisotropic matter, but later we discuss the role of heat °ux and shear viscosity as well. We conclude that the radial pro¯le of material variables like energy density, principal stresses, dissipation, viscosity and electric charge control the stability of self-gravitating objects. The inhomogeneity factors have been identi¯ed for charged plane symmetric space- time with some particular cases of non-dissipative and dissipative °uids. In the non- dissipative case, we analyze inhomogeneity factor for dust, isotropic and anisotropic matter distributions while dissipative matter distribution includes only geodesic dust °uid. We ¯nd that electric charge increases inhomogeneity in the energy density, which is due to shear scalar, anisotropy and dissipation. Also, we explore some dynamical variables, structure scalars as well as an explicit expression for the super- Poynting vector associated with tilted and non-tilted Szekeres spacetime.
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منگ نہ میتھوں پیار او بیلی

منگ نہ میتھوں پیار او بیلی
اِسراں ہی ہن سار او بیلی

اوکھے ویلے نس جاندے نیں
ویکھو اج دے یار او بیلی

ساڈا بھارا کسے نہ چایا
بیلی اُنج ہزار او بیلی

اس بندے دے منہ نہ لگیں
جسدے یار ہزار او بیلی

اک پاسے تے موت کھڑی اے
اک پاسے نے یار او بیلی

کسے گھڑی وی چل سکدے نے
ایٹم دے ہتھیار او بیلی

EFFECT OF STATIC STRETCHING OF HAMSTRING ON NON-SPECIFIC LOW BACK PAIN

Objective: To determine the effect of static stretching of hamstring muscle on the non-specific low back pain. Methodology: A Quasi-Experimental study was conducted in Rabia Moon Institute of Neurology which total 30 participants were included through non-probability purposive sampling. Thirty participants were selected who fulfilled our inclusion criteria, they were divided into two groups; group A or treatment group received conventional physiotherapy treatment as well a static stretching exercise protocol for 5 days. Group B or control group received conventional physiotherapy treatment only. VAS (Visual analog scale) and Oswestry Disability questionnaire, SFGD (Standing Finger to ground Distance,) PSLR (passive straight leg raise) for both legs were measured pre- and post-treatment. Result: A total of 30 patients aged 20-55 were included in the study. Mean age of the participants was found to be 37.88 years.  The difference in means of all the assessment parameters pre and post-treatment for both groups were analyzed through paired t-test. There was a significant improvement in VAS, SFGD, Passive Straight leg Raise PSLR (right leg), PSLR (left leg) and level of disability pre- and post-treatment in the treatment group. Conclusion: This present study concluded that static stretching of hamstrings is effective in decreasing non-specific low back pain.

Synthesis and Characterization of Potentially Biologically Active Derivatives of Polyhydroquinoline and Quinoline Ring Systems

Multi-component reactions (MCRs) have emerged as an efficient and powerful tool in modern synthetic organic chemistry allowing the facile creation of several new bonds in a one-pot reaction. Clearly, for multi-step synthetic procedures, the number of reactions and purification steps is among the most important criteria for the efficiency and practicability of a process The classical four-component Hantzsch condensation provides access to pharmaceutically active polyhydroquinolines. We had carried out the reactions of cyclohexanone or cyclohexane dione or dimedone with malononitrile or ethylacetoacetate and different aliphatic and substituted aromatic aldehydes in the presence of ammonium acetate in ethanol. These multicomponent reactions were carried out both by solvent free grinding and by classical heating for comparison purposes. The catalytic activity of p-TSA (10 mol %) and guainidine HCl (5 mol%) in these reactions was tested over a set of aldehydes. Through catalytic screening, guainidine HCl (5mol%) at ambient temperature is proven to act as a very active catalyst for multicomponent reactions (MCRs) of 2-amino-4-phenyl-3-cyano-5-oxo-1,4,5,6,7,8-hexahydroquinoline derivatives and 2-methyl-4-phenyl-5-oxo-1,4,5,6, 7, 8- hexahydroquinoline-3-carboxylate in excellent yield up to 96% from aldehydes, 1,3-cyclohexadione, malanonitrile/ ethylacetoacetate and ammonium acetate. we develop an expedient multi-component synthesis of 2-amino-5-oxo-4-substituted phenyl-1,4,5,6,7,8-hexahydroquinoline-3-carbonitrile 4-4f and 2-amino-5-oxo-4-substituted phenyl-1,4,5,6,7,8-hexahydroquinoline-3-carboxylate 5-5l by using P-TSA under ultraviolet irradiation. Chemical reactions were carried out by the absorption of long-wavelength ultraviolet light by reactants to form product in a short period of time. We carried out the synthesis of polyhydroquinoline via irradiating the cyclohexanone/ cyclohexane dione/ dimedone with malononitrile/ethylacetoacetate and different aliphatic and substituted aromatic aldehydes in the prescence of ammonium acetate and P-TSA catalyst in ethanol assisted with ultraviolet light. The absorption of ultraviolet radiation by substrate allows a reaction to proceed by bringing the molecule to the activation energy, by changing the symmetry of the molecule and by changing the configuration of molecules. The reaction time is reduced from 1.5h to 4-5 min whereas % yield increased significantly by the ultraviolet assisted reactions. Thus, the superiority of the ultraviolet assisted protocol for the synthesis of polyhydroquinoline over thermal method had proved. Extensive biological studies on these v polyhydroquinolines with a variety of substitution patterns exhibit that these compounds have a mild potential of antimicrobial and antioxidant activities. Chalcones are secondary metabolites of terrestrial plants, precursors for the biosynthesis of flavonoids and exhibit various biological activities. A simple and regioselective synthesis of substituted 2-chloro-3-formyl quinolines through Vilsmeier-Haack cyclization of N-arylacetamide bearing an electron donating group at the meta position was carried out. Yields with electron donating groups were good in all cases. First, the chalcones were synthesized by direct Claisen-Schmidt condensation reactions between an equimolar quantity of quinoline-3-formaldehyde and different heterocyclic/aromatic ketones (a-i) by a base catalysed (40% NaOH solution) condensation. The 1H-NMR spectra of the synthesized compounds were in good agreement with the structures of the synthesized compounds. Extensive pharmaceutical studies in literature on various other quinolinyl chalcones indicate that these compounds have a significant potential of biological activity.