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Effects of Modified Theories on Stellar Structures and Cosmic Evolution

Thesis Info

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Author

Siddiqa, Aisha

Program

PhD

Institute

University of the Punjab

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2019

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/9968/1/Aisha%20Siddiqa_Maths_2019_UoP_Punjab_PRR.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726023249

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This thesis is devoted to explore stellar structures as well as evolution, gravitational waves and viscous cosmology in the framework of modi¯ed theories of gravity. Firstly, we study physical characteristics of stellar structures in the absence as well as presence of electromagnetic ¯eld in the framework of f(R; T) theory. We consider the compact stars whose pressure and density are related through polytropic equation of state and MIT bag model. The energy conditions are satis¯ed and stellar con¯gurations are found stable for the assumed values of free parameters. Secondly, we discuss anisotropic non-static charged spherical as well as cylindrical sources describing the phenomena of collapse and expansion in f(R; T) theory. We analyze the behavior of density, pressures, anisotropic parameter as well as mass and examine the in°uence of charge as well as model parameter on these quantities. Thirdly, we ¯nd the polarization modes of gravitational waves for some f(R) dark energy models with the help of Newman-Penrose formalism and ¯nd two extra modes than general relativity. We also investigate the propagation of axial gravita- tional waves in the background of °at FRW universe in f(R; T) theory through axial perturbations. It is found that axial waves can induce velocity memory e®ect. Finally, we consider viscous modi¯ed Chaplygin gas interacting with f(R; T) grav- ity in °at FRW universe. We investigate the behavior of total energy density, pressure and equation of state parameter for emergent, intermediate as well as logamediate scenarios of the universe with two interacting models. It is found that bulk viscos- ity enhances the expansion for the intermediate and logamediate scenarios. We also study the evolution using LRS Bianchi type-I model and discuss the behavior of scale factors as well as deceleration parameter in dark energy dominated era for di®erent bulk viscosity models. We conclude that expansion is faster when bulk viscosity is proportional to the Hubble parameter.
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مولانا سعید احمد اکبر آبادی

مولانا سعید احمد اکبر آبادی کی رحلت
(ڈاکٹر محمد اسلم)
علم و حکمت کا وہ آفتاب جو گذشتہ نصف صدی سے برصغیر پاک و ہند کو منور کررہا تھا، مورخہ ۲۴؍ مئی مطابق ۳؍ رمضان المبارک بروز جمعہ افطار سے تھوڑی دیر پہلے غروب ہوگیا، یعنی حضرت مولانا سعید احمد اکبرؔ آبادی عالم فانی سے عالم جادوانی کی طرف کوچ فرماگئے۔ اناﷲ وانا الیہ راجعون۔
مولانا کی علالت کا سلسلہ طویل رہا، گذشتہ سال مئی کے وسط میں حضرت مفتی عتیق الرحمن عثمانی کا انتقال ہوا تو ان پر اس سانحہ کا بڑا اثر ہوا، اس کے دو ماہ بعد ان کے بڑے بیٹے عمر سعید آناً فاناً وفات پاگئے، ان کی طبیعت پر اس کا بھی بڑا اثر ہوا، بیٹے کی وفات کے روز انھوں نے ان کو کسی وجہ سے خوب ڈانٹا تھا، وہ گولیاں کھا کر سونے کے عادی تھے، مولانا کا خیال ہے کہ اس روز آزردہ ہوکر انھوں نے مقررہ مقدار سے زائد گولیاں کھالیں، اور اس لحاظ سے وہ اپنے آپ کو قصور وار سمجھنے لگے تھے، گذشتہ اگست میں میرے قیام علی گڑھ کے دوران میں انھیں کتے نے کاٹ لیا، ڈاکٹر نے ان کے شکم میں متعدد انجکشن لگائے، لیکن چند روز بعد وہ جگہ متورم ہوگئی، اور انھیں بخار آنے لگا، ڈاکٹروں نے ملیریا بخار کی تشخیص کی اور انھیں کونین کھلانا شروع کردیا، ضرورت سے زیادہ کونین کے استعمال سے ان کا جگر خراب ہوگیا، اور خون پیدا ہونا بند ہوگیا، خرابی جگر سے یرقان ہوگیا، علی گڑھ یونیورسٹی کے ہسپتال میں بغرض علاج داخل ہوگئے، لیکن افاقہ نہ ہوا، حکیم افہام اﷲ خان صاحب اور حکیم عبدالحمید صاحب کے ہی زیر علاج رہے، لیکن کمزوری دن بہ دن بڑھتی چلی گئی، ان کی علالت بڑھتی گئی ان کی بیٹی مسعودہ سعید کراچی سے علی گڑھ پہنچیں...

اسلام اور جین مت میں طہارت کا تقابلی جائزہ

      Allah created all the required things fo the world since the world was given existence. Human was made its tenant and was equipped with art of living and eversince human life exists in all the corners of the world whatsoever religion they follow, but  they do follow a set of social principles in life. And literal meaning of those principles is called religion, because religion literally mean"way of living or manner of living". And contextually religion may be defined as the principles followed to live life.       In the light of this definition of religion some people have been confronted having no concept  of  religion, they are called Communists. But anyone who does not believe in Allah and the Prophet PBUH are termed Communists. In the following dissertation a comparison has been drawn between Islam and jeen Mat to show that no religion can compete Islam in terms of Clarity or cleanliness.

Misconceptions of Students Learning in Mathematics at Primary Level

This study intended to investigate misconceptions and errors commonly made by the students at primary level, finding out the reasons for these misconceptions and designing a remedial intervention for removing these misconceptions. The following research questions were developed to accomplish the task: • What are the misconceptions of students in learning mathematics at primary level? • What are the possible causes of these misconceptions of students in learning mathematics at primary level? • How can these misconceptions be rectified / removed? • How can teachers help the students to learn mathematics in a better way and remove the targeted misconceptions? The study was conducted in 12 sample schools and concepts included in the investigation were not limited to grade IV rather, all contents of mathematics were included from grade I to IV, excluding grade V. The grade V was excluded for the reason that the pre-test was administered in the beginning of the grade V study. The content tested through the pre-test was classified into eight concept areas namely, numbers, operations on numbers, fractions, operations on fractions, decimals, measurement, information handling and geometry. It was expected that the study would focus on misconceptions in few of these eight areas, but the findings of the pre-test and interviews with the teachers compelled the researcher to include all the eight areas as a significant number of misconceptions was found in all of the concept areas. The study was a mixed design approach (quantitative and qualitative). The pre-test and the post-test provided quantitative data while the interviews with the teachers and sample students helped to collect the qualitative data.On the basis of identification of the misconceptions and errors through the pre-tests, four students from each of the 12 schools were interviewed along with their teachers. The analysis of the qualitative and quantitative data provided insight about the causes of them is conceptions of students, and to remove these misconceptions a teachers training program was developed and conducted.At this stage, the study was converted into Pre test-intervention-post-test design keeping only one school out of the 12 schools as control group and the remaining 11 as the experimental group. Key misconceptions include numbers and operations on numbers; these were considered difficult by the students due to misconceptions regarding numbers’ names (language problem) and their place value. Fractions were thought as two numbers instead of part of a whole. Decimals were considered mostly on the basis of digits without having proper understanding of the place value of the digits written in a decimal number. Understanding of units for measuring different quantities was not entrenched due to not using measuring tools practically by the students. Mostly estimation of length, mass and area were made full of mistakes. Scale for drawing a graph,both line and bar graphs was not understood; it was seemed that students were having the wrong conception as they were not trained to draw a graph. Geometry was full of misconceptions starting from measuring a line segment or drawing a line segment of given measurement.The use of simple geometrical tools like protractor, straight edge, compass or set squares was felt difficult by most of the students and their teachers. The training of the teachers of the experimental group was focused on providing an opportunity to them to have an experience of doing mathematics as well as consolidating content including knowledge they were lacking.Misconceptions of the students in different concept areas were discussed with the teachers.The difference in gain scores of the experimental group students provided evidence that the students’ achievement improved in most of the concepts after being re taught by the experimental group teachers.