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Uniformly Convex and Bazilevic Functions

Thesis Info

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Author

Khalil Ahmad

Program

PhD

Institute

COMSATS University Islamabad

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2014

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/2183/1/2748S.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727638393

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Uniformly Convex and Bazilevic Functions This work is in the field of Geometric Function Theory in which we study geometric properties of analytic functions. It was originated around the turn of 20th century and has many applications in the field of applied sciences such as engineering, physics, electronics, medicines. In this dissertation, we define and discuss some new subclasses of normalized analytic functions by using some integral operators such as the operator Q a given by Q a f(z) z a ( )za 1 ta 0 2 log z t 1 f (t)dt, where G denotes gamma function, f(z) is analytic in open unit disc, a>0 and 0. We also study generalized Bazilevič functions. The functions in these classes generalize the idea of Bazilevič functions, k-uniformly convexity and bounded boundary and bounded radius rotations. The subordination and convolution tools are used to investigate the geometric properties of the functions in these classes and several inclusion results with some interesting consequences have been proved. We have investigated the univalency condition and coefficient bounds, arc length problem, integral preserving properties and rate of growth of Hankel determinant for these functions. The most of our results are sharp and they have been connected with previously known results.
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مولانا عبدالعزیز میمن

مولانا عبدالعزیز میمنی راجکوٹی
عربی زبان و ادب سے دلچسپی رکھنے والوں کے لئے مولانا عبدالعزیز میمنی کی وفات بڑی افسوس ناک ہے، انھوں نے خاصی طویل عمر پائی، انتقال کے وقت ۹۶ برس کے تھے، لیکن عربی علم و ادب اور تاریخ و تحقیق کے میدان میں ان کا جو مرتبہ تھا، اس کی بناء پر درازی عمر کے باوجود ان کا انتقال بہت محسوس ہوگا، اور عرصہ دراز تک انھیں یاد کیا جاتا رہے گا۔
وہ ۱۸۸۹؁ء میں راجکوٹ (کاٹھیاواڑ) میں پیدا ہوئے، عنفوان شباب میں تحصیل علم کے لئے دہلی کا سفر کیا، اور وہاں ایک عرصہ تک تحصیل علم میں مشغول رہے، انھوں نے باقاعدہ کسی درس گاہ سے سند فراغ نہ لی تھی، لیکن اہل کمال کی خدمت میں رہ کر عربی ادب میں کمال پیدا کیا، شیخ طیب عرب سے مدتوں اکتساب فیض کیا، ڈپٹی نذیر احمد سے بھی کافی استفادہ کیا، مطالعہ کتب کا خاص اہتمام تھا، اس طرح کامل دستگاہ حاصل کرلی اور اقران و اماثل میں ممتاز سمجھے جانے لگے، تلاش معاش کے لئے پہلے اسلامیہ کالج پشاور پہنچے، وہاں عربی کے استاد کی حیثیت سے کچھ عرصہ تک درس و تدریس کی ملازمت انجام دی، اپریل ۱۹۲۱؁ء میں اورینٹل کالج لاہور میں ایڈیشنل مولوی کی حیثیت سے ایک سو روپیہ ماہوار تنخواہ پر تقرر ہوا، یہاں کی علمی و ادبی فضا نے ان کی خوابیدہ صلاحیتوں کو بیدار کیا، چنانچہ درس و تدریس کے ساتھ تصنیف و تحقیق کا ذوق پروان چڑھا، چار سال بعد آخر ۱۹۲۵؁ء میں یہاں سے علی گڑھ چلے آئے، پہلے شعبۂ عربی میں استاد ہوئے، پھر صدر شعبہ ہوگئے، ۱۹۴۹؁ء میں یہاں سے ریٹائر ہوکر کراچی چلے گئے، وہاں کراچی یونیورسٹی کے قیام پر شعبۂ عربی کے صدر منتخب ہوئے، یہاں سے سبکدوشی کے بعد اکتوبر ۱۹۵۴؁ء میں مرکزی ادارۂ تحقیقات اسلامی کے پہلے اعزازی...

وجوه الإعجاز عند المتكلمين: الرماني والخطابي نموذجا

There are several points which illustrate Qur’ānic I‘jāz and probably rely on Islamic Theologians -Mutakallimin’s- efforts as well as exertions regarding Qur’ānic I‘jāz. Mutakallimin for having good command over Arabic rhetorical structures have demonstrated Qur’ānic I‘jāz in two contexts: theoretically and empirically. They actually validated, that Qur’ān is the book of Allah Almighty, through comparing both standard Arabic texts: prose and poetry into face of Qur’ānic text. All these cherished efforts of Mutakallimin are rooted in Arabic rhetoric which stands for that Arabic Rhetoric and ‘ilm al-Kalām; both have very primary relation resulting in that cannot be ignored while analyzing I‘jāz phenomenon.

Development and Analysis of Risedronate Sodium Loaded Multi-Particulate Drug Delivery System Using Superabsorbent Polymer

In this study biocompatible and sustained released multiparticulate systems comprising superabsorbent polymer particles were prepared to reduce the local irritant effect of risedronate sodium. SAP based on 2-hydroxyethyl methacrylate, itaconic acid and polyvinyl pyrrolidone /chitosan were prepared by solution polymerization and fractioned to form SAP particles. Ethylene glycol dimethacrylate, potassium persulfate and N,N,N,N tetramethylethylene diamine were used as crosslinker, initiator and activator, respectively. Various concentrations of polymer and monomers were used in the formulations. Crosslinking was confirmed by Fourier transform infrared spectroscopy. The dynamic swelling studies were carried at pH 1.2, 5.5 6.5 and 7.5, which indicated a direct relationship of concentration of IA and media pH to swelling. By increasing the IA content or decreasing HEMA content porosity increased and a direct relationship was found in the case of gel fraction with HEMA and PVP contents. Furthermore, the values of volume fraction of polymer, molecular weight between crosslinks and solvent interaction parameters were determined. Risedronate sodium loading efficiency was determined which was dependent on IA and PVP contents. Drug release study was performed at buffers of pH 1.2 and 7.4 and result showed pH dependent drug release. The release mechanism was best described by zero order kinetics at pH 1.2 and Higuchi kinetics at pH 7.4. n value of almost all formulations was between 0.5 and 1.0, hence drug release followed non-Fickian release mechanism. A balanced, single dose, parallel study design was utilized to perform in vivo studies on rabbits. Cmax, Tmax and AUCo-∞ of formulations S1 and F1 were shifted to new values that proved the sustained release behavior. The bioavailability of drug was improved when administered in the form of multi-particulate formulation