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On a Class of Variational Inequalities

Thesis Info

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Author

Latif, Rafia

Program

PhD

Institute

COMSATS University Islamabad

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2018

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/13086/1/Thesis.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726792083

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A novel generalization of variational inequalities, which is called strongly mixed variational inequalities, is introduced and investigated. It is shown that the minimum of a sum of differentiable convex functions and nondifferentiable strongly convex functions can be characterized by strongly mixed variational inequalities. Auxiliary principle technique is used to investigate the existence of the unique solution of strongly mixed variational inequalities. This technique suggests us to propose some iterative schemes for solving strongly mixed variational inequalities. It is shown that strongly mixed variational inequalities are equivalent to fixed point problem and the resolvent equations under some conditions. These equivalent formulations can be used to examine the existence of a solution of the strongly mixed variational inequalities as well as used to develop new iterative schemes for solving strongly mixed variational inequalities. Convergence criteria of proposed methods is analyzed under some conditions. Dynamical systems related to strongly mixed variational inequalities is introduced. This approach is also used to examine the existence of the solution of strongly mixed variational inequalities. The error bounds for a solution of the strongly mixed variational inequalities using the merit function technique are derived. Moreover various special cases have also been discussed. System of strongly mixed variational inequalities involving two different operators is considered.
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۴۴۔ نجانے کس لیے

نجانے کس لیے

سحرِ حزیں،مسائے الم،شبِ ملُول،دلِ غمگیں

حسرتِ مسکیں،ادا س راہیں ،کھوئی کھوئی نگاہیں

بنا ہم سفر،نگر نگر دربدر

سانسیں بے قرار ،پا فگار

بے رنگ آسماں ،دھواں ہی دھواں

آرزئوں کے جال میں

حسرتِ وصال میں،گم کسی خیال میں،کسی کے ملال میں

بھیگی ہے آستیں، یارم نہیں قریں

ذاتی ملکیت میں کچھ آنسو،اس کا وجود نہیں جس کی جستجو

دلِ منتظر اداس ہے ،کوئی آس نہیں پھر...

Price Fixation in Islamic Law

Adl and Qisṭ is indeed a manifestation of God’s mercy, rather, it may also be seen as a principal objective of Shariʿah. The origin or sources of administration of justice in Islām are the Quran, Sunnah of the holy Prophet, consensus of opinions of the jurists of Islamic jurisprudence and Analogy (Qiyās). Justice is a sacred obligation of supererogatory. It is obligatory upon the Muslim rulers to appoint judges for the dispensation of justice to attain equality, to protect the human rights from their violation, to safeguard the lives and properties, and to maintain law and order in society. As a judge is supposed to accomplish a very important and noble task being a regent of Allāh, hence, some vital merits and criteria regarding the conditions and qualifications for the appointment of the Qāḍī or judge in the light of the Qur’ān, Sunnah and Islamic jurisprudence and the code of conduct for the Pakistani judges must be observed at all costs. The author of this paper has discussed these conditions and qualifications in this article. There are some unanimous conditions for the appointment of judges, while some others are not agreed upon. While presenting the difference of opinions of the Islamic jurists, the author tried to explain, reconcile the opinions and at some places presented her own view in the light of her analysis and arguments. These conditions are around thirty, but the author according to her own discretion chose some of the most important ones to discuss in this paper.

An Analysis of the Clinical Practice of Emergency Medicine in Public Emergency Centres in Kenya

Objectives: To describe the case mix, interventions, procedures and management of patients in public accident and emergency departments (A&Es) in Kenya. Methods: This was an observational study of patients who presented to 15 A&Es from 1 October to 31 December 2010. The study was conducted across Kenya in two national referral hospitals, five secondary level hospitals, and eight primary level hospitals. All patients presenting alive to the A&E during the 24 hour study period that were seen by a doctor or clinical officer were included in the study. A data collection form was completed by the primary investigator at the time of the initial A&E consultation documenting patient demographics, presenting complaints, investigations ordered, procedures done, initial diagnosis and outcome of A&E consultation. Results: Data on 1887 patient presentations were described with adults (≥13 years) accounting for the majority (70%) of patients. There were two peak age groups, 0-9 and 20–30 years accounting for 27% and 25% of the patients respectively. Respiratory and trauma presentations each accounted for 21% of presentations with a widespread of other presentations. Over half (58%) of the patients were investigated in the department and an equal number (56%) were treated and discharged from the A&E. Only one in three patients admitted or transferred to specialist units received any immediate therapy. Conclusions: Public accident and emergency departments in Kenya provide care to a widespread undifferentiated patient population yet most of the immediate therapy is provided only to patients with minor conditions who are subsequently discharged from the A&Es. Sicker patients have to await transfer to the wards or specialist units to start receiving treatment.