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Generalized Close-To-Convex Functions and Related Topics

Thesis Info

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Author

Riaz, Sadia

Program

PhD

Institute

COMSATS University Islamabad

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2019

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/10188/1/Sadia%20Riaz_Maths_2019_Comsats_PRR.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726258997

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Aim of this thesis is to introduce and study properties of certain new subclasses of analytic functions in the open unit disc. The concepts of q-calculus are used to define the q-extensions of starlike and close-to-convex functions. “q-Bernardi Integral Operator’’ which is the advancement of well-known Bernardi integral operator is investigated. It is shown that our newly defined classes are invariant under this integral operator. Further, Ordinary fractional derivative operator and q-fractional derivative operator are used to study certain interesting properties of these classes. The idea of qbounded radius rotation and the behavior of starlike functions of negative order with negative coefficients involving q-difference operator is also examined. The relevant connections of our new classes and results to known ones are also pointed out.
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مولانا محمد الحسنی

مولانا محمد الحسنی
ایک عربی شاعر نے کہا ہے:
من لم یمت عبطۃً یمت ھرما
1للموت کاساًفالمرء ذائقاً
¹’’جولوگ جوانی میں نہیں مرتے وہ بوڑھے ہوکرمریں گے۔بہرحال موت کی شراب ہرشخص کے لیے چشیدنی ہے۔‘‘
افسوس ہے گذشتہ مہینہ ہمارے علوم دینیہ و عربیہ کے دومرکزوں میں چند روز کے فرق سے شعر میں مذکوردونوں قسم کی حسرتناک موتیں واقع ہوئیں، پہلا واقعہ دارالعلوم ندوۃ العلماء لکھنؤ میں مولوی محمدالحسنی کی اچانک وفات کاپیش آیا۔ مرحوم صحیح معنی میں متنبی کے اس شعر کے مصداق تھے:
وشیخ فی الشباب ولیس شیخاً
-یسمی کل من بلغ المشیبا
وہ کہنے کومولانا سید ابوالحسن علی میاں کے بھتیجے تھے مگردرحقیقت وہ مولانا کے لیے فرزند حقیقی سے بڑھ کرتھے۔مولانا نے اپنے فیض تعلیم وتربیت اورتوجہ خصوصی سے اس جوہر قابل کوایسا چمکایا کہ مرحوم عربی ادب وانشا میں مولانا کے مثنی بن گئے۔عرصہ سے’’البعث الاسلامی‘‘کے رئیس التحریر تھے، اس حیثیت سے انھوں نے جومقالات اوراداریے لکھے انہوں نے ہندوبیرونِ ہند کے اسلامی حلقوں میں دھوم مچادی۔ ان کی کتاب’’الاسلام الممتحن‘‘جوعالم اسلام اور خصوصاً عرب ممالک کے معاملات ومسائل سے متعلق اُن کے بیس برس کے اداریوں اورمقالات کامنتخب مجموعہ ہے، وہ عرب میں اس درجہ مقبول ہوئی کہ چندبرسوں میں اس کے متعدد ایڈیشن چھپ چکے ہیں۔ وہ اردو زبان کے بھی ادیب تھے۔مصنف اورمترجم کی حیثیت سے اس زبان میں بھی ان کی متعدد یادگاریں ہیں۔عمل وکردار اوراخلاق وعادات کے اعتبارسے وہ اپنے خانوادۂ والاتبار کی روایات کامکمل نمونہ تھے۔یعنی نہایت دیندار، صالح، متواضع، فقیر منش، طبیعت کے نہایت غیور و خوددار، خاموش اور باہمہ و بے ہمہ، دنیا اور اس کے زفارف عیش و عشرت سے قطعاً بے نیاز و روگرداں، عمر چالیس کے لگ بھگ ہوگی۔
؂ خوش درخشید و بے شعلۂ مستعجل بود ۔
رحمہ اﷲ رحمۃ واسعۃ
[ جولائی۱۹۷۹ء]

میاں بیوی میں سے ایک کا قبول اسلام

In the early days of Islam, either of the married couple entering into Islam does not affect their marriage contract and it continued to be valid even after the Emigration of the Holy Prophet (peace and mercy be upon him) to Madina. In fact, it has been observed until Hudhabiya Truce was signed. It was also included the terms if someone from Quraish without accompanying the wali approaches the Holy Prophet (Peaceand Mercy be upon him), he/she will be returned to Makkah. After this agreement, many women came to Madina and embraced Islam. But their spouses and relatives followed them their way to Madina. They claimed them back to Makkah. In this respect, Allah almighty revealed a verse of Surah Mumtahina, which is an express evidence that such believing women must not be returned to their former infidel husbands. They were commanded so to marry believing husbands after their separation from their disbelieving spouses. Through this verse, Muslim husbands were forbidden to stay and have conjugal relations with their nonbelieving wives, too. Similarly,  every believing wife was forbidden to reside with her disbelieving husband. The companions abided by the ruling in its entirety and separated from their non- believing spouses. Jurists have derived many instructions from the verse 10 of Surah Mumtahina, which are discussed in this paper.

Exploring the Perceptions of Graduate Students About Formative Feedback Strategies on Their Written Assignments at Higher Education

Expertise in academic writing provides opportunities to the graduate students to produce high quality papers and assignments for successful completion of their graduates' courses. Therefore, formative feedback strategies helped students to produce quality assignments. The study has highlighted several factors that impede the process of feedback. Understanding these factors, therefore, was integral in helping students to improve their written assignments at the graduate level. This study aimed to explore graduate students' perceptions about formative feedback strategies on their written assignments in a public sector university in Pakistan. Six students from the final cohort of the four-year B.Ed. programme were selected purposefully as primary participants and two teachers; one Assistant professor and one senior Lecturer were selected as secondary participants. Data generated from teachers' interviews helped in triangulation of the findings. In addition, data collection tools were document analysis, interviews from teachers and focus group discussion with students. The data were analyzed based on Creswell's model of analysis (2013) that dealt with organization of the raw data, general sense making, codification and identification of emerging themes. Moreover, there is a continuous back and forth approach by reading and rereading the data repeatedly. The study revealed that students perceived teachers' feedback on their writing as incredibly important for the quality of their written assignments. They were of the view that teachers were using different forms of formative feedback strategies such as debriefing conferences, corrective and directive feedback, facilitative feedback and peer feedback. Furthermore, the entire discourse also revealed few important hindering factors such as teachers' workload, teachers' lack of competency, lack of permanent teaching faculty, and institutional policy. Moreover, the students articulated concerns such as teachers were reluctant and not professionally equipped to provide effective feedback on their writing specimens. The findings have implications for teachers to think and rethink about their feedback strategies in classroom particularl producing well-written assignments for a graduate course. In other hand, students are also need to understand the improtance of peer and self assessment than that to rely on teachers feedback for all the time. Moreover, Roushan University needs to make formative feedback as an integral part of the policy framework to focus of the development of graduate students' writing skills to meet the demands of a graduate course.