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Dynamical Evolution of Collapsing Stellar Systems in F R Gravity

Thesis Info

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Author

Yousaf, Zeeshan

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/123456789/9585/1/Zeeshan_Yousaf_Math_2015_Univ_of_the_Punjab_11.04.2016.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676725929751

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This thesis is devoted to study the dynamical instability of some relativistic collapsing self-gravitating structures with both Newtonian and post-Newtonian approximations in metric f(R) gravity. In this setting, we consider evolution of spherical, cylin- drical and restricted axial stellar systems ¯lled with expansion and expansion-free adiabatic/non-adiabatic matter con¯gurations. We analyze the role of adiabatic index (sti®ness parameter) in the instability constraints of these self-gravitating structures. We construct dynamical equation using contracted Bianchi identities of the e®ective dark sources as well as usual matter distribution. The perturbation approach is ap- plied on physical variables and then formulate modi¯ed versions of collapse equation which leads to instability constraints at both N and pN regimes. We ¯rst consider spherically and cylindrically symmetric spacetimes ¯lled with charged and uncharged expansion-free anisotropic matter distributions. It is found that the adiabatic index does not have any role in the expansion-free evolution within N and pN approximations. Rather, this range is governed by pressure anisotropy, ra- dial pro¯le of system energy density, f(R) model and electric charge (for charged distribution). We also explore the role of heat radiations in non-viscous charged spherical and cylindrical systems as well as shearing viscous uncharged axial relativis- tic interior. It is found that heat radiations try to decrease stability of the evolving systems, while viscosity tends to increase system stability. The electromagnetic ¯eld decreases instability regions for charged spherical systems while its opposite e®ects have been observed for cylindrical collapsing self-gravitating systems. We conclude that f(R) dark energy sources coming up from the well-known f(R) models a®ect xi xii the whole dynamical behavior of collapsing systems due to its repulsive nature. Finally, we study the factors involved in the energy density irregularities of rela- tivistic planar °uid distribution in the presence of Palatini f(R) corrections. For this purpose, we develop a link between the Weyl scalar and structural properties of the system by a couple of di®erential equations. We also investigate the e®ects of Palatini f(R) terms in the formulation of structure scalars obtained by orthogonal splitting of the Riemann tensor in general relativity. We then identify the parameters which produce energy density irregularities in expansion and expansion-free dissipative as well as non-dissipative matter distributions. It is found that particular combinations of the matter variables lead to irregularities in an initially homogeneous °uid dis- tribution. We conclude that Palatini f(R) extra corrections tend to decrease the inhomogeneity, thereby imparting stability to the self-gravitating system.
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84. Al-Inshiqaq/The Splitting Apart

84. Al-Inshiqaq/The Splitting Apart

I/We begin by the Blessed Name of Allah

The Immensely Merciful to all, The Infinitely Compassionate to everyone.

84:01
a. When the celestial realm will be split apart,

84:02
a. and obey the Command of its Rabb - The Lord,
b. as it would be obliged to do!

84:03
a. And when the earth will be leveled,

84:04
a. after it would have thrown out whatever was within it and emptied itself.

84:05
a. And it will also obey the Command of its Rabb - The Lord,
b. as it would be obliged to do!

84:06
a. O The People!
b. You would have to strive and strive hard towards your Rabb - The Lord, only then will you meet HIM.

84:07
a. So whoever will be given his record from his right hand side,

84:08
a. he will then have an easier process of accountability,

84:09
a. and return to his family, rejoicing.

84:10
a. But whoever will be given his record from behind his back,

84:11
a. he will call out for his own destruction/death.

724 Surah 84 * Al-Inshiqaq

84:12
a. and he will enter the Blazing Fire - that is kindled and ignited time and again.

84:13
a. Indeed, during his worldly life he used to live among his family, rejoicing,

84:14
a. thinking that he would never be brought back to his Rabb - The Lord, and held accountable.

84:15
a. Yes indeed!
b. Indeed, his...

PENERAPAN MANAJEMEN STRATEGIK DALAM MENINGKATKAN MUTU PENDIDIKAN MADRASAH

In its development, madrasas have undergone various changes, namely from the pesantren learning system to the madrasa system; from traditional to classical methods; from halaqah system to benches, desks and blackboards; from traditional to modern curricula; from classical education to modern educational reform. The change indicates the existence of process or efforts of development of madrasah education in the direction of more advanced, qualified and competitive from time to time. Conceptually, one way to improve the quality of education and competitiveness of madrasah in the era of globalization competition is to implement strategic management which includes 4 stages such as environmental analysis, formulating, implementing and evaluating strategic decisions between functions that enable an organization to achieve its goals in the future. Strategic Management is based on the entire scope of the work. Thus it can be utilized well for makronya environment for example in government management and also can be utilized also for in mikronya environment for example in company management or organization or pengeloalan Madrasah. However, it should be understood only here that in the use of macro and micro scope there are a number of fundamental differences such as the following exposures.

Bio-Economic Assessment of Barley and Legume Crops Grown under Different Planting and Water Use Techniques

In Pakistan, population is increasing at rapid rate while cultivated area is shrinking day by day and resources are becoming short. Resources are limited and becoming short for human beings. So, there is a dire need to increase the yield of different cereals and pulses particularly food grains per unit area to maintain a balance between demand and supply gap. The increase in area under winter pulses is difficult due to competition with staple cereals grown. Therefore, present study is planned with the objectives to develop new techniques in order to grow pulses and cereals at the same time for increasing yield per unit area and time. Field experiments were conducted to test the effects of barley, berseem and lentil intercropping during 2014-2015 and 2015-16 at the student farm, University of Agriculture, Faisalabad. Both experiments were laid out in randomized complete block design (RCBD). The area of each experimental unit was of 3.6 × 7.0 m. In first experiment barley was sown on beds with five planting geometries i.e. flat sowing with row to row distance of 30 cm (Farmer practice), 45 cm spaced three row strips, 60 cm spaced four row strips, 90 cm spaced six row strips and 120 cm spaced eight row strips and berseem was intercropped in between the space of barley strips. Row to row distance in case of crop sown in strips was 15 cm. Similarly, in 2nd experiment lentil was sown on raised beds with similar geometric arrangements as in experiment I and barley was intercropped in between the space of lentil strips as berseem in first experiment. The irrigation was applied in furrows keeping in view the water requirement of the crop sown on lower beds in both experiments, while flood irrigation was applied to conventionally sown treatments. Observations on different agro-physiological parameters of the component crops were recorded by following standard procedures. Data collected were statistically analysed by applying Fisher’s analysis of variance techniques using a computer programme MSTAT-C and least significance difference (LSD) test at 5% probability level was used to compare the differences among treatment means. The results revealed that sole barley accumulated more dry matter than the intercropped barley. The number of grains per spike, 1000-grain weight, biological yield and grain yield were influenced significantly by legume intercrop during both year studies. All the associated cultures reduced barley yield to a significant extent. However, in barley production, the extra harvest obtained from associated cultures rewarded more than losses. Barley-berseem intercropping gave 56 to 68 percent yield advantage on mono-cropped barley with the highest income of Rs. 174258/ha. Similarly, intercropping of barley-lentil gave 69 to 86 percent yield advantage on mono-cropped barley with the highest income of Rs. 143224/ha. Raised bed water use technology caused substantial saving of irrigation water over flat irrigation system. There was a progressive decrease in the amount of water used with increase in the size of strip from 3 to 8 rows with 45 to 120 cm irrigation furrows. The maximum water use efficiency of 4.84 and 3.55 kg/cf3 was recorded for both experiments for 8-row strip system with 120 cm irrigation furrows as compared to 1.49 and 1.18 kg/cf3 for conventional system of flood irrigation application.