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Approximation of Oscillatory Integrals and Integral Equations Via Localized Kernel Based Method

Thesis Info

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Author

Ullah, Zeyad Min

Program

PhD

Institute

University of Engineering and Technology

City

Peshawar

Province

KPK

Country

Pakistan

Thesis Completing Year

2018

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/13271/1/Zeyad_Min_Ullah_Numerical_Analysis_HSR_2018_UET_Peshawar_31.07.2018.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676725528564

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One of the most important area of mathematical sciences is the numerical evaluation of oscillatory integrals and integral equations. Variety of applications constitute these integrals including acoustic scattering problems. In the present research we construct numerical schemes which are based on localized kernel based method for approximation of oscillatory integrals and integral equations. This localized setting results in small size interpolation matrices. The advantages of these small size interpolation matrices would enable us to cope with the huge amount of data points and solve the integral problems for thousand of scattered points in complex shaped domains. In the first part of this thesis the problem of integration is transformed into ODE’s and PDE’s and apply a localized collocation scheme to solve the resultant ODE’s and PDE’s numerically. For large amount of data points in the integration domain, the present numerical scheme has the ability to compute the oscillatory integrals. In the second part of this thesis we extend our work for computing more generalized fast oscillatory integrals. The method is efficient for computing more generalized oscillatory integrals involving Bessel functions with large oscillation parameter. In the third part we consider finite highly oscillatory Hankel transform arises in electromagnetic and acoustic scattering problems, a numerical scheme is developed which is based on the local kernel based method. In the last part of this thesis we used radial kernels for computing more generalized fast oscillatory integral equations. The present method is efficient for computing oscillatory integral equations with large oscillation parameters.
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روش صدیقی

روش صدیقی
افسوس ہے گزشتہ ماہ جناب روش صدیقی بھی رہ گزائے عالم جادوانی ہوگئے۔ مرحوم بلند پایہ اورصاحب فن شاعرتھے۔ان کی شہرت کا آغاز رومانی نظموں سے ہوا جو اس زمانہ کے مشہور ادبی رسالوں میں بڑے اہتمام سے چھپتی تھیں اورجنہیں وہ اپنی خاص پرجوش آواز میں لہرالہراکر پڑھتے تھے۔بعد میں ان کی شاعری حکمت وفلسفہ اورانسانی ووطنی مسائل وآلام کی ترجمان بن گئی لیکن ان کا کلام غامض اور دقیق ہوتاتھااورالفاظ اورتراکیب پرشکوہ وباوقار،طبیعت میں روانی اورجدت پسندی بلا کی تھی۔اخلاقی اعتبار سے بڑے باوضع،ملنسار اورمذہبی حیثیت سے صوم وصلوٰۃ کے اورارادو وظائف تک کے پابند تھے۔انتقال سے چھ سات روزپہلے(۱۴/جنوری)کوشام کے وقت نئی دہلی کے ریلوے اسٹیشن پر اچانک ملاقات ہوگئی توحسب معمول بڑے تپاک سے ملے اورمعانقہ کیا۔کافی ہشاش بشاش اورمگن تھے۔اس وقت اس کاوہم وگمان بھی نہیں ہو سکتا تھا کہ اس عالم آب وگل میں وہ بس اب چندروز کے اورمہمان ہیں اوران سے یہ آخری دید و شنید ہے۔شاہ جہاں پور کے ایک مشاعرے میں گئے تھے وہیں دل کادورہ ہوا اور جاں بحق ہوگئے۔اﷲ تعالیٰ ان کی قبر کو ٹھنڈی رکھے اوران کے پسماندگان کا حامی وناصرہو۔آمین [فروری۱۹۷۱ء]

 

حروف مقطعات کے حوالے سے مستشرق نولڈ یکے اور آٹو لوتھ کی آراء کا تجزیاتی مطالعہ

Mystical letters are among the miracles of Quran. These mystical letters are present at the start of Quranic Surah’s (Chapters). These are among the mutashabihat (Analogies) of Quran. Muslim scholars tried to define their meanings. Like other aspects of Quran and Hadith orientalists talk about mystical letters of the Quran. This article analyses the theories of Noldeke and Otto Loth regarding mysterious letters of Quran. What are their views about mystical letters of the Quran? Are their views according to the Islamic point of view of mystical letters? What are the deviations and differences as compared to traditional Islamic point of view of mystical letters? This research has been analytical by nature, both qualitative and analytical methods have been implemented.  Analyses of the views of both of the scholars in the light of traditional Islamic concept of mystical letters, shows that Orientalists including Noldeke and Otto Loth thought that mystical letters are not the part of revelation. According to them these are the names of the sources from which different chapters of the Quran had been taken during its compilation. These are on the same pattern as mystical letters are present in the Jewish books. Holy Prophet had copied them. The present study argues that Quran being the book of Lord is unchanged and mystical letters are a part of it. It is further highlighted that even some orientalists argue that the opinion of Noldeke and Otto Loth is not correct.

A Study of a Schools Professional Development Activities With Particular Reference to the Role of the Principal in Ensuring Effective Professional Development

This dissertation is based on the exploration of the professional development practices of a school and of the role of the principal in ensuring the effective professional development of teachers. The study was carried in a higher secondary school in Karachi, Pakistan. The school might be considered as effective in terms of students' achievements at the Board Examinations. However, it would seem simplistic to attribute the school's success solely to the professional development of teachers. There is a combination of other factors, which were identified as contributing to school effectiveness. The study showed that there are many and varied professional development activities carried out in the school. But professional development is not only carried our through professional development courses or workshops. There are other areas, which can contribute to professional development such as appraisal (identification of teachers' professional development needs), reflective practice and Follow-up. The findings suggest that appraisal is used for two purposes in the school--for identification of teachers' professional development needs, and for evaluation of the teachers' performance. Reflective practice and Follow-up have not received essential attention in the school, and they are practiced on the irregular basis. The principal does a great deal to attempt to ensure effective professional development for his teachers. He encourages and supports professional development of teachers in a variety ways, but the absence of a planned and structured approach to professional development means that, professional development is not so effective as it might be. The study offers some recommendations to school and its principal, which may be useful for ensuring effective professional development. Among these are suggestions to prepare a structured plan of professional development of teachers in the school and to separate two kinds of appraisal. This report also includes the lessons I learned from the study. The findings of the study will be useful for me as a future teacher educator in my native context of Kyrgyzstan, as I found many similarities in organization of the professional development in both systems. I also learned some skills necessary for conducting qualitative research.