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Variational Inclusions Involving Difference of Operators

Thesis Info

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Author

Kamal, Rabia

Program

PhD

Institute

COMSATS University Islamabad

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2017

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/13622/1/Rabia_kamal_Maths_2017_CIIT_HSR_14.04.2017.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727657740

Similar


A new class of general variational inclusions involving difference of operators has been investigated. Using resolvent operator and resolvent equations technique, it is shown that general variational inclusions and fixed point problems are equivalent. Using this equivalent formulations, we prove the existence of a solution of general variational inclusion. Iterative schemes and its convergence is also discussed. We study some dynamical systems associated with variational inclusion. The dynamical system is used to discuss the existence of the variational inclusion using Lipschitz continuity only. Some Merit functions are constructed for the variational inclusions. Using these merit functions, some error estimates are obtained under suitable assumptions. Sensitivity analysis is analyzed using the resolvent equations. Several classes of variational inclusion and optimization problem are discussed which can be obtained as special cases from our results.
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عثمانی دور میں حدودو قصاص کی تنفیذ

عثمانی دور میں حدودو قصاص کی تنفیذ
حضرت عمر  کی شہادت کے بعد شورٰی کی جماعت کے متفقہ فیصلے سے حضرت عثمان  یکم محرم چوبیس ہجری کو تیسرےخلیفہ نامزد ہوئےاور 18ذوالحجہ سن 35 ہجری شہادت تک خلیفہ رہے ۔ حضرت عثمان بن عفان  بڑے ہی نرم دل حکمرا ن تھے ۔ شورش پسند لوگوں نے آپ  کی اس طبعی نرم دلی کا ناجائز فائدہ اٹھانا شروع کیا ۔آخر انہی شورش پسند لوگوں نے آپ  کو 35 ہجری 18 ذی الحجہ کو شہید کر ڈالا ۔ حضرت عمر  نے جو عدالتی نظام قائم کر دیا تھا ، بدستور اسی پر عمل ہوتا رہا تاہم انہوں نے اس سلسلے میں ایک تبدیلی کی کہ عدالتی نظام کو مسجد سے علیحدہ کر دیا اور عدلیہ کے لیے ایک علیحدہ عمارت بنوا دی جو دار القضاء کے نام سے مشہور ہوئی ۔ آپ  نے اگرچہ کچھ صوبوں کے گورنروں کو تبدیل کیا لیکن حضرت عمر  کے کسی قاضی کو نہیں بدلا۔ آپ  کے دور کے چند مشہورحدود وقصاص کے واقعات مندرجہ ذیل ہیں:
حدزنا کا نفاذ
امام مالک سے مروی ہے کہ حضرت عثمان  کے پاس ایک عورت آئی
" قَدْ وَلَدَتْ فِي سِتَّةِ أَشْهُرٍ فَأَمَرَ بِهَا أَنْ تُرْجَمَ فَقَالَ لَهُ عَلِيُّ بْنُ أَبِي طَالِبٍ لَيْسَ ذَلِكَ عَلَيْهَا إِنَّ اللَّهَ تَبَارَكَ وَتَعَالَى يَقُولُ فِي كِتَابِهِ "وَحَمْلُهُ وَفِصَالُهُ ثَلَاثُونَ شَهْرًا " وَقَالَ "وَالْوَالِدَاتُ يُرْضِعْنَ أَوْلَادَهُنَّ حَوْلَيْنِ كَامِلَيْنِ لِمَنْ أَرَادَ أَنْ يُتِمَّ الرَّضَاعَةَ " فَالْحَمْلُ يَكُونُ سِتَّةَ أَشْهُرٍ فَلَا رَجْمَ عَلَيْهَا فَبَعَثَ عُثْمَانُ بْنُ عَفَّانَ فِي أَثَرِهَا فَوَجَدَهَا قَدْ رُجِمَتْ"301
" جس کا بچہ چھ ماہ میں پیدا ہوا تھا ۔آپ نے اس کے رجم کا حکم دیا۔ حضرت علی ؓنے فرمایا کہ اس پر رجم نہیں ہو سکتا ۔اللہ تعالیٰ اپنی کتاب میں فرماتے ہیں کہ آدمی کا حمل اور دودھ چھڑانا...

Role of Male Teachers in Islamic-Ethics Based Sociability Skills Promotion Among Learners in Government Primary Schools of Khyber Pakhtunkhwa

For the citizen of Islamic Republic of Pakistan, Islam is the Ideology of Pakistan. Allah Almighty’s orders are supreme for us, who has created human being as the best creature, our ideal is the Holy Prophet Muhammad Peace Be Upon Him whose ethico-moral standards are the best. The research’s main objective is to analyze “role of Teachers in Islamic Ethics Based Sociability Skills Promotion among Learners in the study region”. Now a days the Social workers, Social Scientists and Religious Scholars have a special focus over the individuals’ ethical and sociability skills promotion because these values are having core importance in the societal functioning of the individuals in the Islamic communities globally. The data was collected through interview method. In this study a sample size of 114 respondents was selected comprising of the male & female learners in the District Karak. The research results show that majority of teachers were guiding the learners about ethical values, social relations, sociability skills, effective communication and to have good behavior etc. Based on Islamic ethics.

Determination of Physic-Chemical Alterations in Tomato Due to Cmv and Role of Elicitors Against the Infection

A research was conducted at Nuclear Institute for Agriculture and Biology (NIAB), Faisalabad, Pakistan for the control of Cucumber mosaic virus in tomato. Aim of the study was to investigate the role of safe chemicals on disease control and molecular host-pathogen interaction. Safe chemicals included BTH (50mg/Litre) and Salicylic acid (SA) (1.4mg/liter) applied alone and in combination. During the first year of study, tomato plants were sown within glass house in the insect free environment and artificially inoculated with CMV. Next year, the experiment was conducted in the tunnel and plants were naturally inoculated by aphids with CMV which were found abundant during the cropping season. One month old healthy tomato nursery plants were transplanted after 1 hour root dip into the solutions of the SA and BTH. Later, BTH and SA were exogenously applied either weekly (w) or once (1) during the whole cropping season. Second objective of the study was to determine the role of BTH and SA for the induction of physical and biochemical changes in tomato under CMV stress condition. Experiments were conducted under completely Randomized design (CRD) with 5 replicates in glass house and RCBD in tunnel with three replicates. Means were compared with Tukey’s HSD test at 5% level of significance. Results from glass house experiment indicated that CMV severity index (out of 4.0) was least with the application of B-w (0.86), followed by BSA-1 (0.86), B1 (0.93) and BSA-w (1.26). Overall disease control was achieved up to 58-61%. Fruit quality parameters such as No. of fruits (30 No.) and fruit weight (558 g) were improved in the combined application of BTH and SA (BSA1). However, application of BTH alone enhanced the stress on tomato plants and resulted in minimum no. of fruits and plant height. Plant height was increased significantly in SA-w (36.66cm). Among biochemical parameters from leaf samples the Pigments (Lycopene, total carotenoids and chlorophyll) did not altered significantly. While defence related antioxidants/bioactive compounds were significantly elicited with both BTH and SA. Peroxidase (POD) activity was enhanced in weekly spray of BTH+SA. But it was more in ripened tomato fruit from SA and BTH treatments applied once in the season. Ascorbate peroxidase (APX) activity was higher after single dose of BTH. But tomato fruit showed more APX in weekly applied BTH. While Superoxide dismutase (SOD) was elevated in the SA treatments both in leaf and fruit samples. Malondialdehydes (MDA) concentration was more in weekly dose of BTH and BTH+SA combined. Tomato fruit also exhibited higher MDA contents in BTH+SA weekly treatment. Catalase (CAT) activity was accelerated after weekly dose of BTH+SA, however fruit indicated more CAT after single dose of BTH. Total Phenolic compounds (TPC) were higher in BTH treated samples and total soluble proteins also rose in weekly treatment of BTH and BTH+SA. Tunnel experiment demonstrated that CMV infection was least where BTH and SA were applied in combination. These doses were also helpful to retain the optimum yield. Additionally combined use of BTH & SA reduced aphid population during the experiment. Phytochemicals like Total proteins and Phenolics increased after single dose of BTH. However, POD was accelerated after combined dose of BTH & SA. Protease, MDA and SOD were raised after weekly dose of BTH and single spray of BTH+SA. While CAT and APX activity was elevated by weekly dose of BTH+SA. Activity of pigments was shifted with little margins in the tunnel experiment. Overall conclusion can be drawn that, combine application of BTH and SA gave better protection to tomato against CMV and provided efficient vector control. This protection was accompanied by various physico-chemical alterations with promising benefits for defence activity in host plants.