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Spline Solutions for Some Fractional Order Boundary Value Problems

Thesis Info

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Author

Khalid, Nauman

Program

PhD

Institute

National College of Business Administration and Economics

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2019

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/14331/1/Nauman%20Khalid%20maths%202019%20ncbae%20lhr%20prr..pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727227067

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In this thesis, the spline solutions to some fractional order boundary value problems have been proposed using different spline collocation techniques. The Caputo’s definition for fractional order derivatives is used, as it allows imposing the boundary constraint(s) in terms of integer order derivative(s). An efficient technique based on non-polynomial quintic spline functions, comprised of a trigonometric part and polynomial part, has been developed for solving fourth order fractional boundary value problems involving product terms. The C¥ differentiability of the trigonometric part of non-polynomial spline compensates for the loss of smoothness inherent in polynomial spline. The second and fourth order convergence of the presented algorithm has been discussed in detail. Moreover, the approximate solutions of three very important time fractional models, advection-diffusion equation, Allen-Cahn equation and diffusion-wave equation, have been studied by means of redefined and modified forms of cubic B-spline functions. The Caputo time-fractional derivatives have been discretized by finite difference formulations whereas B-spline functions are used for spatial discretization. The unconditional stability and theoretical convergence of proposed numerical algorithms have been proved rigorously. Some test examples have been considered for numerical experiments. The computational results are in line with theoretical expectations and exhibit a superior agreement with the analytical exact solutions as compared to the existing techniques.
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الفصل الثاني: أشعار نازك الملائكة وبروين شاکر(المختلفة)

الفصل الثاني: أشعار نازك الملائكة وبروين شاکر(المختلفة)

 سأتحدث في ھذا الفصل عن أشعار نازک الملائکۃ وبروین شاکر المختلفۃ، ولا أقصد من ذلک بأن لیست ھُناک متشابھات أبداً في ھذہ القصائد، ولکن أقصد من ذلک أن الإختلافات أکثر من المتشابھات، وأرید أن ألفت ذھن القاریء إلی شيء أو موضوع معین، ولکن الشاعرتين مختلفتان في الرأي، وتحکمان علی شعور معین بوجھات نظرھما، والمثال علی ذلک أن نازک الملائکۃ في قصیدتھا ’’أغنیۃ للحیاۃ‘‘ تعتبر الحب مزیجا من السعادۃ والتعاسۃ، ولکن الشاعرۃ بروین شاکر في غزلھا "الموت في العشق لیس سهلاً ’’ عشق میں بھی مرنا اتنا آسان نہیں‘‘ تقول بأن الحب ھو سعادۃ وسعادۃ فقط دون التعاسۃ، والأمثلۃ کثیرۃ علی المتشابھات والإختلاف في قصائدھما، ولکن لم أتطرق إلی جمیع أشعارھما، فسأحاول أن أوضح جزءا أو بعض أشعارھما المختلفۃ في ھذا الفصل، وھي أنني سآخذ قصیدۃ لنازک الملائکۃ وقصیدۃ لبروین، وسأقوم بمقارنتھما، وأعطیت الأسماء الخیالیۃ من تلقاء نفسي لکلا القصیدتین (قصیدۃ لنازک الملائکۃ وقصیدۃ لبروین شاکر) ھکذا۔



[1] الملائکۃ، نازک، ديوان نازك الملائكة ، المجلد الأول(ص ۔365)

[2] الضوء

[3] الصفاء

[4] القلاع: الحصن ا الممتنع في الجبل۔

[5] کأس (کؤوس)۔

[6] قلت: تعرضت للھلاک۔والمقصود هنا العيون

[7] البوار: الخراب، الھلاک، خُسران۔

[8] شاکر، پروین، خوشبو، مراد پبلیکیشنز ۔۔۔۔(ص 142)۔

[9] پیراہن کا مخفف، کپڑا، پوشاک / اللباس أو القماش

 

 

The Issue of Human Cloning: A Review in Semitic Religions’ Context

Human cloning has emerged as a new and innovative technology in the reproductive and therapeutic science in the recent past. So far it has not been practiced over human beings but owing to its huge potential and possible scope, it has attracted the attention of not only the masses (particularly the infertile couples and LGBTQs etc) but the other stakeholders including the religious scholars from worlds’ prominent religions have given their views on this technology in order to guide their followers. This paper examines and reviews the religious points of view on human cloning. For this purpose, three Semitic religions in the world i-e Judaism, Christianity, and Islām have been examined. As far as Islam is concerned, this portion has been divided into two broad sections elaborating the Shī‘ah and Sunnī schools’ opinions. Being an innovative topic, the religious teachings do not address it directly hence the injunctions related to the reproduction are most relevant to it. Three Semitic religions have been examined from the perspective of admissibility or non-admissibility of human cloning, the rationale behind the verdict on human cloning and the possible solutions to the issues and problems faced by the followers in the case of acceptance or rejection of this biomedical technology. Most of the religions emphasize over adaptability of the natural mode of reproduction only, where male and female genders contribute to the reproductive cycle. The Semitic religions reject the reproductive cloning generally. The religious experts need to conduct more focused and updated research before coming to any conclusion about the permissibility or non-permissibility of this technique.

Isolation and Characterization of Genes Related to the Suppression of Host Immune Response by Bracon Hebetor Say Hymenoptera: Braconidae

Host-parasitoid interactions in insects offer a great opportunity to identify new genes and molecules responsible for the alteration of the host physiology. To circumvent the host immune response, female of the parasitic wasp injects a blend of secretions containing mainly ovarian proteins, calyx fluid, polydnaviruses and venom in their host insects. Crude venom extract containing a wide range of bioactive proteinaceous compounds inhibits the motility of larval hemocytes and prevents the formation of cell aggregates upon artificial envenomation in vitro. In the present research work, a host parasitoid relationship of ectoparasitic wasp, Bracon hebetor (Say) (Hymenoptera, Braconidae) and host insect, greater wax moth, Galleria mellonella (Lepidoptera, Pyralidae) was studied for comprehensive analysis of the venom glands Transcriptome of the wasp B. hebetor through different Bioinformatics tools for fishing out immunosuppressive genes which reveals the occurance of a number of novel genes with immune suppressive acitivities in the venom blend of the wasp suggesting their toxic/ insecticidal potential. Out of them, Venom acid phosphatase, Tryptase -2 and CTD nuclear envelope phosphatase were selected for more detailed studies on the basis of high sequence homology/identity. The selected contigs were partial sequences of the immunosuppressive genes and their 5’ ends were isolated by Rapid Amplification of cDNA Ends repair kit (RACER kit, Invitrogen) and then full-length genes were isolated by III RT module of Gene Racer kit. Isolated genes were cloned in pGEMTeasy vector in DH5-Alpha competent cells. Screening of blue white colonies of E. coli and colony PCR were also performed for the confirmation of inserts along with the plasmid extraction of the desired colony by Plasmid DNA mini prep. Cloned genes were sequenced, analysed and characterized by different bioinformatics tools i.e., Expasy translate tool, Clustal Omega and SignalP etc. Deduced amino acid sequences of immune suppressive genes were multialighned with other parasitoid species in the database which revealed significant homologies with other braconid species. Functional bioassays of the crude venom and recombinant proteins were performed through artificial microinjection techniques in which different concentrations of the crude venom and different combinations of the recombinant proteins were injected into the last instar larvae of the host and mortality data was recorded. The effects of parasitization by the wasp on cellular immune response of the host larvae were also investigated by following an approach of hemocytes count methodology. It may be concluded that B. hebetor venom and its recombinant proteins have significant impact on survival of the host larvae by inducing biochemical and physological alterations in the parasitized host insects. Analysis of the venom glands Transcriptome of the B. hebetor has shown the natural occurance of a number of novel venom genes with potential insecticidal activity involved significantly in the suppression of host immune response in the venom blend of the wasp which may be exploited further for indepth studies through integrated approaches of functional genomics and proteomics for the development of innovative plant protection strategies for sustainable control of diverse range of insect pests of Pyralidae of agriculture crops. Further, this preliminary research work has a significant contribution towards sustainable programmes for food security and food safety by controlling the insects through natural means and reducing the toxic residues of the synthetic chemicals in food chain supply system