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Existence of fixed points for generalized contractions

Thesis Info

Author

Fahim ud Din

Supervisor

Muhammad Arshad Zia

Department

Department of Mathematics and Statistics

Program

MS

Institute

International Islamic University

Institute Type

Public

City

Islamabad

Province

Islamabad

Country

Pakistan

Thesis Completing Year

2014

Thesis Completion Status

Completed

Page

46

Subject

Media and Communication Studies

Language

English

Other

MS 511.8 FAE

Added

2021-02-17 19:49:13

Modified

2023-01-06 19:20:37

ARI ID

1676721952136

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سیرِ افلاک کو جائیں گے خلا ڈھونڈیں گے


سیرِِ افلاک کو جائیں گے خلا ڈھونڈیں گے
اپنی پرواز سے کچھ لوگ خدا ڈھونڈیں گے

کچھ نہیں پائیں گے یہ شہرِ صبا کے باسی
رب کو سورج کی شعائوں میں بڑا ڈھونڈیں گے

پتھروں کو کبھی پوجیں گے تو آتش کو کبھی
بے وفائوں سے وفائوں کا صلہ ڈھونڈیں گے

روشنی پھیل چکی نورِ حرا کی ؛ پھر بھی
آتشِ وادیِ سینا میں ضیاء ڈھونڈیں گے

گردشِ وقت سے اوراق ہیں بکھرے بکھرے
ایسے تحریف شدہ نسخوں میں کیا ڈھونڈیں گے

شہرِ خاموش میں جا کر یہ صدائیں دیں گے
ماہیِ آب کو صحرائوں میں جا ڈھونڈیں گے

نکہتِ بادِ بہاری سے چھڑا کر دامن
بادِ صر صر میں یہ خوشبو کی فضا ڈھونڈیں گے

قافلہ راہ میں اخلاص کا لُٹ جائے گا
راہزن لوٹ ہی لیں گے جو بھلا ڈھونڈیں گے

راہبر راہ میں رہ جائیں گے ہر راہی کے
راہ جب آپؐ کی راہوں سے جدا ڈھونڈیں گے

نورِ عرفانؔ خدا اُن کا مقدّر ہے جو لوگ
’’آپؐ کی سیرتِ اطہر سے ضیاء ڈھونڈیں گے‘‘

Challenges of Translating the Arabic Qur’an into English A Comparative Study of Eight Leading Translations

Any translation of the Arabic Qur’an in English or any European language is likely to be imperfect. This is primarily due to the differences in the language, semantics, idiom, style and culture. Almost fifty such translations have appeared in the last fifty years, both by Muslim and other scholars, but none can claim any perfection in imaging the Arabic Qur’an. Nevertheless, there are some that are faithful to word-by-word (literal) or sense-for-sense (free) translation, but most lack the flavor of the Qur’anic essence and image either due to the translating approach, or inadequate understanding of the meaning of Sacred Arabic Text, or constraints of eloquence of the English language. This paper examines eight of the leading translations and draws conclusions relating to the use of translation techniques and literary devices and concepts that add beauty to the eloquence of Arabic Qur’an and makes it a living and literary masterpiece. It is found that the meaning of the lexical expressions have been maintained to a high degree in the process of translation and the use of literary devices has been adequately captured by the selected translations.

Some Analytic Methods for Solving Higher Order Nonlinear Boundary and Initial Value Problems

Nonlinear phenomenon plays vital role in engineering and applied sciences. Higher order nonlinear boundary value and initial value problems are known to describe a large variety of phenomena. We are mainly concerned with finding the analytic solution of boundary value and initial value problems of the type T ( u ) = 0, subject to some boundary and initial conditions, where T is any differential or integral operator. We study and develop some analytic methods for solving higher order nonlinear boundary value and initial value problems. We propose several modifications in variation of parameters method for finding the approximate solution of several higher order nonlinear boundary value, initial value, parametric boundary value, higher dimensional and system of nonlinear Volterra integro differential problems. We apply the exp-function method to construct generalized soliton, travelling wave and periodic solution of several higher order nonlinear partial differential equations. We apply the exp-function method for finding the exact solution of some higher order nonlinear boundary value problems. All the suggested techniques are compared with well known classical techniques and are found quite efficient, well suited and reliable for the solution of higher order nonlinear boundary and initial value problems of diversified nature.