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Left Diitoplogical Group Structure on Texture Spaces

Thesis Info

Author

Beenish Bashir

Supervisor

Moiz Ud Din Khan

Department

Department of Mathematics

Program

RMT

Institute

COMSATS University Islamabad

Institute Type

Public

City

Islamabad

Province

Islamabad

Country

Pakistan

Thesis Completing Year

2018

Thesis Completion Status

Completed

Subject

Mathematics

Language

English

Added

2021-02-17 19:49:13

Modified

2023-01-06 19:20:37

ARI ID

1676720707701

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عشق کا گائوں

یہ دل جب جوان ہوا تھا
اس کا ابرو کمان ہوا تھا
ہر نقش اس کا قاتل تھا
نشانے پہ میرا دل تھا
دُور دُور رہا کرتا تھا وہ
کچھ نہ کہا کرتا تھا وہ

ہر روز اسے دیکھتا تھا میں
کہ اس کا فریفتہ تھا میں

دیکھا تھا اسے جب سے
مانگا ہر شب رب سے

اسے پیار ہونا مشکل تھا
میرا اعتبار ہونا مشکل تھا
پر جذبے میں سچائی تھی
وہ آخر پگھل آئی تھی
اُسے اعتبار آ گیا آخر
مجھ پہ پیار آ گیا آخر

یوں شروع پھر فسانہ ہوا
کہ وہ بھی میرا دیوانہ ہوا
پر ایک دن بھید کھل گیا اپنا
سب کو سراغ مل گیا اپنا
آخر عشق و زمانہ لڑ گئے
اور یوں ہوا کہ ہم بچھڑ گئے

اس سانحے پہ بہت روئے ہم
جانے کتنی ہی راتیں نہ سوئے ہم
دل پہ خوشیوں کا ڈیرہ نہیں رہا
یہ سچ ہے کہ وہ میرا نہیں رہا
عمریں بیت گئی پر سوال وہی رہا
کہ اُ س کے جانے کا ملال وہی رہا

یہ سچ ہے بہت ہم اداس رہتے ہیں
یہ بھی سچ ہے نہ اک دوسرے کے پاس رہتے ہیں
یہ بھی مانا کہ ہیں مجبور بہت
پر اس ظالم سماج سے دور بہت
اک عشق کا گاؤں آتا ہے
جہاں نہ کوئی اداس رہتا ہے
وہاں وہ میرے پاس رہتا ہے

ولادت النبیﷺ سے متعلق سیرۃ کی چند روایات کا تحقیقی جائزہ

Allah sent Hadrat Muhammad (SAW) as last Prophet and preserved his all aspect of life for the complete guidance of mankind. Love with the Holy Prophet (SAW) is a part of the Faith. But it has become the standard of his love that all the things which are attributed to him either authentic or unauthentic are accepted without research. Regarding the S╚rah (life) of Holy Prophet (SAW) numerous authentic narrations are exist, but on the other hand some fabricated narrations also mentioned by the story-teller historians, so be careful while propagating these narrations. Some narrations are very famous regarding the birth of the Holy prophet (SAW) which are far away from the reality. In this article some narrations regarding the birth of the Holy prophet (SAW) are scholarly reviewed in the light of the views of the scholars of Jarh-o- Ta‘d┘l in order to find their legal status.

Exact Solutions of Different Motions of Non-Newtonian Fluids With/Without Fractional Derivatives

In the present thesis, we will present the analytical studies of some fluid flow models. We wish to analyze two main scenarios, one of which deals with non-fractional (or- dinary) models and the other with fractional models for the flow of non-Newtonian fluids. We use classical computational techniques capable of accurately operating in order to obtain exact analytical solutions. Our studies include Couette flows of a Maxwell fluid under slip conditions between the fluid and walls. The motion of the bottom plate is assumed to be a rectilinear translation in its plane while, the upper plate is at rest. Two particular cases, namely translation with constant velocity and sinusoidal oscillations of the bottom plate are considered. Next, unsteady motions of Oldroyd–B fluids over an infinite plate between two side walls will be investigated. The motion of the fluid is due to the bottom plate that applies two types of shears to fluid. Extending our studies, we look at the unsteady magnetohydrodynamic (MHD) flow of fractional Oldroyd–B fluid between two side walls perpendicular to a plate. Expressions of the obtained solutions are presented in a series form in terms of the generalized G functions. Finally, the unsteady flow of an Oldroyd–B fluid with frac- tional derivative model between two infinite coaxial circular cylinders is studied. The motion of the fluid is produced by the inner cylinder that, at time t = 0+ , applies a time dependent longitudinal shear stress to the fluid. Expressions of the obtained results are presented in a series form in terms of the generalized G and R functions. In all the flow models, we obtained the exact analytical solutions for motions with technical relevance, both for the velocity field and the shear stress(es). These solu- tions corresponding to some flows in which either velocity or the shear stress is given on the boundary are established for different kinds of non-Newtonian fluids as well as for fractional models. The exact analytical solutions that have been presented in all the fluid flow models satisfy all imposed initial and boundary conditions. Further on, the flow properties of models and the comparison to other models are highlighted with graphical illustrations.