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Some Classes of Multi Valued Dynamical Systems

Thesis Info

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Author

Rizwan. Ahmed

Program

PhD

Institute

Government College University Lahore

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2018

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/9476/1/Rizwan_Ahmed_Maths_HSR_2018_GCU_Lahore_31.07.2018.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727195317

Similar


In this thesis we study three di erent problems. First, we study a class of a multivalued perturbations of m-dissipative evolution inclusions with nonlocal initial condition in arbitrary Banach spaces. We prove the existence of solutions when the multivalued right hand side is Lipschitz and admits nonempty closed bounded but, in general case, neither convex nor compact values. Illustrative example is provided. Second, we prove two variants of the well known lemma of Filippov{Pliss in case of dynamical inclusions on time scale. Therst variant is when the right-hand side is Lipschitz continuous on the state variable. Afterward we introduce one sided Perron conditions for multifunctions on time scale and prove the second variant of that lemma. Some discussions on relaxed systems is provided. Third, we investigate fuzzy fractional integral inclusions under compactness type conditions. We prove the existence of solutions when the right-hand side is almost upper semicontinuous. We also show that the solution set is connected. Finally, an application to fuzzy fractional di erential inclusions is given.
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کتابیات

کتابیات
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٭ اقبال،اقبال نامہ تصحیح و ترمیم شدہ یک جلدی،مرتبہ،شیخ عطاء اللہ(لاہور: اقبال اکادمی پاکستان)2005ء
٭اقبال،علامہ اقبال کا خطبہ الہ آباد 1930ء ایک مطالعہ،تفسیر و توضیح،ندیم شفیق ملک(لاہور:فیروز سنز)باراول1998ء
٭اقبال،کلیاتِ اقبال۔اردو(لاہور:اقبال اکادمی پاکستان)اشاعت ششم2004ء
٭ اقبال،کلیاتِ مکاتیبِ اقبال،جلد اول، مرتبہ،سید مظفر حسین برنی(نئی دہلی: اصیلا آفسیٹ پریس،دریا گنج)اشاعت پنجم 1999ء
٭ اقبال،کلیاتِ مکاتیبِ اقبال،جلد دوم، مرتبہ،سید مظفر حسین برنی(نئی دہلی: ثمر آفسیٹ،دریا گنج)اشاعت دوم،1993ء
٭ اقبال،کلیاتِ مکاتیبِ اقبال،جلد سوم، مرتبہ،سید مظفر حسین برنی(نئی دہلی6: سیما آفسٹ پریس،چوڑی دالان)1993ء
٭ اقبال، کلیاتِ مکاتیبِ اقبال،جلد چہارم،مرتبہ،سید مظفر حسین برنی(دہلی: اردو اکادمی)طبع دوم 1998ء
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٭ توقیر احمد خاں، تبصرے(نئی دہلی: جامع نگر،ایف 14/13)دسمبر 2009ء
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مکتوبات
٭ پروفیسر عبدالحق،مکتوب بنام محمد عامر اقبال،یکم فروری...

اسلام اور مغرب: ڈاکٹر محمود احمد غازی کے افکار کا خصوصی مطالعہ

The comparative study of civilizations, their conflicts, clashes and their harmony are the significant issues of this era. It's a reality that in the present clash of civilizations, Islam is being pushed to a tight corner. The Islamic world today is facing severe challenges and odd circumstances in maintaining their vital values and re-establishing their identity and gaining their due place in the modern world because some of the western thinkers believe that after demolishing the Soviet Union, their next encounter would be with the ideology of Islam. In this situation, the comparison of civilizations and their comprehension has acquired a significant place and it is necessary to highlight the essential elements of various civilizations in such a way that they can sustain their individuality and the misunderstandings among them may be removed to create a peaceful atmosphere which is based on love, mutual tolerance, co-existence and  the supremacy of basic human rights so that the world may return to the merger of various civilizations and harmony among different religions. Allama Iqbal is the thinker who has shown extraordinary depth in his approach towards the study of Islam and the western world, highlighting their differences and the traditions, points and levels of their merger and harmony with a balanced and impartial approach. It's necessary to comprehend Iqbal's ideas keeping in view the history of Islam and the western world, the current demands of the present age and considering organized, solid, argumentative analysis in an objective way  revealing the soul of Islam and the spirit of the west in context of Iqbal's philosophy so that the modern world can move towards a peaceful and creative situation. Dr. Mehmood Ahmad Ghazi was the realization of Iqbal's dream. He is simultaneously an educationist, a great researcher and an illustrator and interpreter of the Holy Quran and narrator of Hadiths. His personality was equally well versed in Islamic art and learning and all their offshoot disciplines. It's the trait of his personality that in spite of travelling far and wide and having done a vast study, he is not impressed at all except by the ideology of Islam. He has very successfully passed on the ancient heritage to its modern heirs with honesty, skill and sagacity. Here an effort has been made to present a review of his views where he has propounded a critical, analytical and scholarly analysis of the western world.

Synthesis and Biological Evaluation of Thiazole, Oxadiazole and Indole Derivatives

This dissertation has been divided into four chapters and each chapter has its own numbering of compounds and references. General introduction related to the importance of natural products and natural product based drugs, drug designing and value of lead molecules in drug designing. This research work describes synthesis and bioactivities of different class of heterocycles such as thiazole, oxadiazole and indole analogs in search of important therapeutic agents. During this research study, a variety of thiazole, oxadiazole and indole analogs were synthesized and screened for enzyme inhibition studies (thymidine phosphorylase, α-glucosidase, urease and β-glucuronidase activities). The results obtained from this study are encouraging which are discussed separately in the forthcoming chapters 1, 2 and 3. In the first chapter, thiazole analogs are described. In the thiazole series, sixteen analogs (1-16) were synthesized and evaluated for thymidine phosphorylase inhibitory potential. Out of sixteen analogs, nine analogs such as analogs 1, 2, 3, 5, 6, 8, 10, 13 and 15 showed good phosphorylase inhibitory potentials when compared with the standard 7-Deazaxanthine. The remaining seven analogs showed moderate to good activity. In 2nd chapter, oxadiazole analogs are described. Sixteen analogs (1-16) of oxadiazole were synthesized and evaluated for thymidine phosphorylase activity. Out of sixteen analogs, fourteen analogs such as analogs 1-7 and 9-15 showed excellent thymidine phosphorylase inhibitory potentials which is many folds better than the standard 7-Deazaxanthine. Analog 16 showed good inhibitory potential while analog 8 remain inactive among the series. In chapter third, three series of indole are described. In first series, We have synthesized thirty-two (32) bis-indolylmethane analogs (1-32) with varying degree of β-glucuronidase inhibition potential ranging in between 0.10 ± 0.01 to 48.50 ± 1.10 μM when compared with the standard drug D-saccharic acid 1,4-lactone (IC50 value 48.30 ± 1.20 μM). All of thirty-two analogs 1-32, showed outstanding β-glucuronidase inhibitory potentials. In second series, eighteen derivatives (1-18) of bis-indolylmethane thiosemicarbazide were synthesized and evaluated for their urease inhibitory potential. These derivatives displayed varying degree of inhibition in the range of 0.14 ± 0.01 to 18.50 ± 0.90 μM when compared with the standard inhibitor thiourea having an IC50 value 21.25 ± 0.90 μM. All derivatives showed outstanding urease inhibitory potentials which are many folds better than the standard thiourea. In third series, twenty one analogs of tris-indole hybrid scaffold with oxadiazole ring (1-21) were synthesized and evaluated for α-glucosidase inhibitory potential. All compounds displayed superior α-glucosidase inhibitory activities having IC50 value in the range of 2.00 ± 0.01-292.40 ± 3.16 μM as compared to standard acarbose (IC50 = 895.09 ± 2.04 μM). In chapter four, procedures for different biological assay are described.