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Fixed Point Theorems for Various Spaces and Their Applications

Thesis Info

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Author

Shah, Rahim

Program

PhD

Institute

University of Peshawar

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/123456789/12788/1/Rahim%20Shah_Math_2018_UoPsw_PRR.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726213558

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In this thesis, we prove some fixed point theorems in various spaces with applications. We discuss the uniqueness and existence of a fixed point in a dislocated metric and dislocated quasi metric spaces. Several results of fixed point under different kind of contractive assumptions are introduced that generalize and unify a number of related results in the existing literature. Some important examples are presented to support our main results. We also establish some fixed point theorems in ordered cone b–metric spaces. These new results generalize and unify numerous popular theorems in literature to ordered cone b–metric spaces. Several auxiliary examples are also provided. Some new theorems of fixed point are established in G–metric spaces by using integral type contraction with supporting examples and applications. We also analyze the Ulam type stability to some families of function equations via fixed point theory. In particular, of certain delay Volterra integro–differential equations are established by using a fixed point method in a generalized complete metric spaces. We provide some examples of our established results. After applying the idea of fixed point technique, we examine the Hyers–Ulam stability and the Hyers–Ulam–Rassias stability of impulsive Volterra integral equations in complete generalized metric spaces.
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ہم کہ زندانی ہیں جس کے پیار کے

ہم کہ زندانی ہیں جس کے پیار کے
چھیڑیے قصے نگاہِ یار کے

موت کی وادی ہے جلوہ حسن کا
عشق کے سب دائرے ہیں دار کے

آنکھ کے تیور، مَیں اُن کے کیا کہوں
دل جگر چھلنی ہیں اس تلوار کے

اُن سے دوری جان لیوا ہو گئی
قرب کے وعدے تھے مجھ سے یار کے

تم فضاؔ مجھ زیست کا سامان ہو
اولیں ہو آخریں بھی پیار کے

الرؤية الإصلاحية للإمام النورسي: أثرها وامتدادها في العالم

الإصلاح عملية تقتضي مقاربة شمولية من حيث مدلولها، يلتقي فيها الجانب النظري بالتطبيقي، مع وضوح في الرؤية والمنهج، ذلك أنه يأخذ بعين الإعتبار الوضع القائم والإنطلاق منه بتثيت الصالح فيه، وتقويم ما اندرس للإنتقال به إلى وضع جديد أفضل. ومن هنا تأتي هذه الورقة العلمية لتسليط الضوء على فكر وعطاء العلامة بديع الزمان النورسي، قصد الإلمام بحيثيات مشروعه الإصلاحي، ودراسة أثره الممتد إن على المستوى الفكري أو السياسي أو الحضاري، فقد عَبَرَ النورسي بأفكاره ومُعطياته حدود الزمان والمكان، وشكّل منعطفاً حضارياً هاماً في معالجاته الشمولية لمفاهيم هذا الدين العظيم، وفي تقديمه لمشاريع إصلاحية رائدة يحتاج إليها المصلحون، وعليه لا تزال الحاجة إلى دارسات معمقة ومتتابعة ومن جوانب متعددة، لمشروعه الإصلاحي ، للإرشاد في محاولة الرقي والإستئناف الحضاري. الكلمات المفتاحية: الإمام النورسي، التجديد، الإصلاح، المنهج الإصلاحي.

Catalytic Hydrocracking of Waste Plastics to Liquid Fuels

The worldwide production of plastic products has been increasing rapidly over the last few decades. This increase in plastic production has resulted in gigantic amount of plastic waste. Conventional methods for waste plastic management such as landfilling and incineration are susceptible to many environmental hazards that necessitate the need of recycling of plastic wastes. Chemical recycling methods are encouraged all over the world and hydrocracking is the most advantageous process among them. Hydrocracking occurs at low temperatures and converts waste plastics into high quality liquid fuel. In the present work, hydrocracking of a municipal waste model plastic mixture is studied using inhouse synthesized mesoporous and composite catalysts. Commercial zeolite USY (CBV720), ZSM-5 (CBV2314), and beta (CP811C-300) catalysts are used to prepare their respective micro-mesoporous composite catalysts. Al-SBA-15 and various Al-SBA-16 catalysts are synthesized with increased acidic character. Some mesoporous composite catalysts with zeolite nano-seeds are also prepared. The catalysts are characterized by using SEM, TEM, XRD, EDX, N2-BET, FTIR, and py-FTIR techniques. The results of characterizations showed the desired form of the catalysts. In order to screen out some of the catalysts, hydrocracking experiments with the model plastic mixture are conducted in a high pressure autoclave reactor. Initial experiments are performed at initial cold hydrogen pressure of 20 bar, 60 min residence time, feed to catalyst ratio of 20:1 (by wt.), and at various levels of temperature (350‒425°C). The products of the reactions are analyzed for conversion and yields of gas, oil (n-heptane soluble portion of liquid), and liquid. The oil produced is further analyzed with GC-FID and FTIR analysis. On the basis of conversion and selectivity towards liquid enriched with gasoline, five best performing catalysts are chosen for additional experimentation. These catalysts are then tested with HDPE and actual waste plastic mixture. Stability of these five supports is evaluated by using spent catalysts and regenerated spent catalysts from a previous run. Two catalysts performed remarkably well in all these experiments. The two catalysts are the composite of zeolite ZSM-5 (ZC-FP) and the composite of zeolite beta (BC27). The five best catalysts are then impregnated with 0.5wt% of platinum to prepare their respective bifunctional catalysts. The performance of these five platinum impregnated catalysts is then evaluated by hydrocracking the model plastic mixture at three reaction temperatures (325°C, 350°C, and 375°C). It is found that after platinum impregnation all the catalysts produced higher conversion and higher gaseous yield than that of their corresponding catalysts without impregnation. The quality of oil obtained over these platinum catalysts is much better with higher amounts of alkanes, lower amounts of aromatics, and lower quantities of unsaturated compounds. Among these impregnated catalysts PtBC27 produced the highest liquid yield with increased gasoline content. This catalyst is then tested with actual waste plastic mixture at 60 min residence time, 20 bar initial cold hydrogen pressure, feed to catalyst ratio of 20:1 (by wt.), and reaction temperature of 375°C. It is observed that this catalyst delivered 90.1wt% conversion and 68.6wt% liquid yield with gasoline content of 65.8wt%. In parallel reactions, ZC-FP catalysts is impregnated with different combinations of metals and tested with model plastic mixture at 325°C, 350°C, and 375°C. It is found that CoRuZC-FP catalyst produced the highest liquid yield at 375°C. However, its oil contained lower quantity of gasoline than that obtained over PtZC-FP and PtPdZCFP catalysts. The ZC-FP catalyst is also used to investigate the effect of change in initial cold hydrogen pressure, catalyst amount, and residence time at different reaction temperatures. This data is then used to study the kinetics of the hydrocracking reaction. The regression of the experimental data is carried out and a simple kinetic model is developed where the activation energy for the hydrocracking reaction is found to be 236.8 kJ/mol. Finally, a commercial hydrocracking unit is conceptualized and a process flow diagram of the process is developed.