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Home > A Study of Soft Rings and Their Generalizations: M. Phil Mathematics

A Study of Soft Rings and Their Generalizations: M. Phil Mathematics

Thesis Info

Author

Muhammad Irfan Siddique

Supervisor

Muhammad Faisal Iqbal

Program

Mphil

Institute

Allama Iqbal Open University

Institute Type

Public

City

Islamabad

Province

Islamabad

Country

Pakistan

Thesis Completing Year

2020

Thesis Completion Status

Completed

Page

vi,39p.

Language

English

Other

Classification: 512.4 IRS

Added

2022-07-09 15:11:20

Modified

2023-02-19 12:33:56

ARI ID

1676729774553

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چلے چلو کہ منزل ابھی نہیں آئی

چلے چلو کہ منزل ابھی نہیں آئی
نحمدہ ونصلی علی رسولہ الکریم امّا بعد فاعوذ بااللہ من الشیطن الرجیم
بسم اللہ الرحمن الرحیم
معزز اسا تذہ کرام اور میرے ہم مکتب شاہینو! آج مجھے جس موضوع پر لب کشائی کا موقع مل رہا ہے وہ ہے:’’چلے چلو کہ منزل ابھی نہیں آئی ‘‘
صدرِذی وقار!
منزل کے حصول کے لیے جدوجہد ہر ذی روح کی خواہش رہی ہے، ہر کس و ناکس اس کے لئے کدوکاوش کرتا ہے، اس کی زندگی کا ہر لمحہ حصولِ منزل کے لئے وقف ہوتا ہے، ہمہ قسم لوگ شبانہ روز اس مقصد کے حصول کی خاطر کوشاں رہتے ہیں ، حصول منزل میں ہر آنے والی رکاوٹوں کو ختم کرنے کے درپے ہوتے ہیں، اور پھر یونہی ان کے لمحاتِ زیست گزرتے رہتے ہیں۔
جنابِ صدر!
حشرات الارض سے لے کر انسان تک ہر ایک اپنی منزل کی طرف گامزن ہے، ہر ایک کی اپنی ایک منزل ہے، مورومگس کی منزل اور ہے، گل لالہ کی منزل اور ہے، جوئے نغمہ خواں کی منزل اور ہے، حر یرو پر نیاں کی منزل اور ہے، زمین پر رینگنے والی مخلوق کی منزل اور ہے، گل لالہ کے گردبھنبھنانے والی شہد کی مکھی کی منزل اور ہے، غلاظت پر چکر لگانے والی مکھی کی منزل اور ہے۔
صدرِ محترم!
گلستان میں عندلیب خوش الحان کی منزل اور ہے، برگد کے درخت پر موجود بوم کی منزل اور ہے، آبادی میں شجر سایہ دار کی منزل اور ہے، ویرانے میں خشک تنے والے درخت کی منزل اور ہے، فضاء میں محو پرواز عقاب وشاہین کی منزل اور ہے ،مُردار کے گرد چکر لگانے والی گدھ کی منزل اور ہے۔
پرواز ہے دونوں کی اسی ایک فضا میں
کرگس کا جہاں اور ہے شاہیں کا جہاں اور
جنابِ صدر!

الإعجاز البلاغي في قصة إبراهيم عليه السلام

The topic, "Eloquence of the Discourse in the Narrative of Ibrāhīm” is selected to meet the desire to examine the Quranic eloquence of the selected discourse. The Quranic narrative is selected for the present study for its significant position in the Quranic text. Most of its artistic elements are based on the Quranic rhetorical inimitability. In Sūrah Shua‘rā’, there are the famous dialogues of Ibrāhīm with the polytheists. He invites his nation to abandon the worship of different gods and pay their adoration to the One and the Only God: the Sustainer of the worlds. Then, comes his invocation (Du‘ā) for himself, his nation and for the Prophet Muḥammad (S. A. W). Also, this article discusses the condition of the polytheists and their dispute with their leaders in the hell, those leaders, who diverted them from the right path. The article discusses the narrative, and studies the Quranic eloquence of the discourse in the story of Ibrāhīm. It shows how the Qur’ān deals with the said story from Rhetoric, syntactic and morphological point of view.

Proactive Strategies to Improve Link Stability under Topology Changes in Mobile Adhoc Networks

Improving link stability under topological changes arise due to link/node failures under uniform speeds and random trajectories of mobile nodes, is a significant problem that must be addressed to improve routing performance in mobile adhoc networks (MANETs). Under random characteristics of wireless channels, there must be a unified model based on proactive strategies to improve link stability under topological changes for stable and robust communications among neighboring nodes. This thesis addresses the problem of link stability under topological changes by presenting proactive strategies for faster failure detection, robustly maintaining link stability, effective link stability estimation, and efficient traffic estimation. First, a novel faster failure detection (FFD) strategy is proposed for link re-connectivity under link/node failures using a Hello messaging scheme. FFD is modeled through a Continuous Time Markov Chain (CTMC) based approach to proactively detect link/node failures under topological changes in MANETs. The FFD strategy minimizes delay incurred as a result of link re-connectivity, optimizes adjacency establishments among neighboring nodes, and enables energy efficiency to improve network connectivity. Second, a novel dynamic link connectivity (DLC) strategy for maintaining link stability among neighboring nodes. DLC is modeled through CTMC by taking into account continuous time analysis of dynamic link connectivity and stationary probability distribution between neighboring node pairs. The DLC strategy examines stability of network nodes and calculates probabilities of connection and disconnection states on the basis of transition rate estimation between these states. The DLC strategy robustly maintains link connectivity for future communications among neighboring nodes inside a cluster. Third, novel link connectivity metrics (LCM) and path distribution analysis (PDA) strategies are presented for effective link stability estimation in MANETs. LCM and PDA are modeled using CTMC under random movement of network nodes and topology trigxxii gered path duration statistics as a function of effective link stability estimation. The LCM and PDA strategies collectively enhance robustness and stability of a network by making it less prone to connectivity failures for future communications among network nodes. Finally, the fourth contribution is a novel efficient traffic estimation (ETE) strategy using Hello messaging among neighboring nodes inside a cluster. ETE is modeled through periodic exchange of transmitted Hello messages under local link connectivity between neighboring node pairs, which follows a CTMC model. The ETE strategy estimates optimum Hello messages traffic through local link connectivity. Simulation and analytical results demonstrate that the proposed strategies improve link stability under topological changes and can be deployed as effective tools for maximizing routing performance in MANETs.