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Computing in Singularity Theory

Thesis Info

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Author

Binyamin, Muhammad Ahsan

Supervisor

Gerhard Pfister

Program

PhD

Institute

Government College University Lahore

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2012

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/1530

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676725780799

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The aim of the thesis is to study, develop and implement algorithms to compute in- variants in singularity theory. A very important part is a parallel and very efficient implementation in computer algebra system SINGULAR. Three different and inde- pendent problems have been considered: • The computation of the signature of a surface singularity defined by z N + g(x, y) = 0. • The computation of resolution graph and related invariants for plane curve singularities. • The classification of simple function germs with respect to right equivalence in characteristic p > 0 and the implementation of a classifyer.
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ڈاکٹر ذاکر حسین خان

آہ ذاکر صاحب !
ڈاکٹر ذاکر حسین صاحب کی ناگہانی وفات ہندوستان کا بہت بڑا قومی حادثہ ہے، وہ اسکا گوہر بے بہا تھے، ان کی موت سے وہ ایسی دولت سے محروم ہوگیا جس کی تلافی نہیں ہوسکتی، کم سے کم مسلمانوں میں ان کا بدل پیدا ہونا بہت دشوار ہے اور اب وہ اس نقصان کو محسوس کریں گے، وہ اپنے علمی کمالات ، فہم و فراست، قومی و تعلیمی خدمات، ایثار و قربانی اور اخلاق و سیرت کے لحاظ سے بہت بڑے انسان تھے، انھوں نے سیاست کے میدان میں کبھی قدم نہیں رکھا، لیکن اپنی بصیرت سے بڑی بڑی سیاسی گتھیوں کو آسانی سے سلجھا دیتے تھے، پنڈت جواہرلال نہرو کے بعد بین الاقوامی دنیا میں ہندستان کا وقار اُن ہی نے قائم رکھا۔
ان میں ابتدا سے غیر معمولی صلاحیتیں تھیں، ان کا آغاز ہی ان کے روشن مستقبل کا پتہ دیتا تھا طالب علمی ہی کے زمانہ سے ان کا قومی خدمت کا ولولہ اور ایثار و قربانی کا جذبہ تعلیم یافتہ نوجوانوں اور قومی کارکنوں کے لیے نمونہ تھا، اس زمانہ اور اس عمر میں جب ہونہار نوجوانوں کا منتہائے نظر اور ترقی کی سب سے بڑی معراج سرکاری عہدے اور تعیش کی زندگی تھی، انھوں نے ان کی طرف آنکھ اٹھا کر بھی نہ دیکھا، اور ان کے مقابلہ میں قومی خدمت اور غربت کی زندگی کو ترجیح دی اور اس راہ میں عمر کا بہترین حصہ صرف کردیا، ان کا زندہ کارنامہ ہندوستان کی پہلی آزاد قومی درسگاہ جامعہ ملیہ ہے، گو اس کے بانی حضرت شیخ الہند حکیم اجمل خاں اور مولانا محمد علی وغیرہ تھے۔ لیکن اس کے اصلی معمار وہی تھے، اور ان ہی نے جامعہ کو جامعہ بنایا اور اپنی زندگی میں اپنے لگائے ہوئے پودے کو ایک تناور درخت بنا گئے، اور آج...

عرب اسلامی روایت کے برصغیر پاک و ہند میں تفسیر نگاری پر اثرات: عہد رسالت تا خلافت عباسیہ کے تناظر میں اختصاصی مطالعہ

It is an established fact that the mainthrust driving force  of all Islamic disciplines is the personality of Prophet Muhammad (PBUH) who appeared in the Arab Peninsula, spreading the rays of divine wisdom throughout the globe. He emerged and prevailed the Prophetic message in such a vivid style that the whole humanity confessed his lasting impressions. The Indian sub-continent has also been one of the impressed territories despite of having no direct social, cultural or religious relationships, yet some approaches from Indian sub-continental Rajas and presentations of gifts to the Prophet (PBUH) have been recorded in the history. Historians have expressed the reality that before Muhammad bin Qasim, a numbers of companions of Prophet reached India and played a pivotal role in making the suitable ground for embracing Islam. Hence, the Arab epistemological tradition engraved in the core of Indian hearts which consequently, reappeared and emerged in the classical exegetical literature of sub-continental scholars, such as Shah Waliullah and his off shoots both in India and Pakistan. This paper has been specifically articulated to explore the Arab impression on exegetical writings in the sub-continent

Efficient Computer Diagnostic System for Early Detection of Cancer

Breast cancer is considered to be one of the most fatal types of cancer among women. The early detection of breast cancer increases the survival probability. Computer Aided Diagnosis (CAD) system for detection and classifying of masses in mammograms is essential. In this thesis, new pre-processing techniques for mammograms have been proposed. First, an improved segmentation technique using image pre-processing and modified reaction diffusion based level set method is developed. The mammogram is passed through morphological operations, contrast enhancement and interpolation algorithm. The pre-processed image is then passed through a modified reaction diffusion based level set algorithm for accurate breast boundary segmentation. In Second pre-processing technique, pectoral muscle is suppressed by the proposed technique based on geometry and contrast variance between the breast tissues and pectoral muscles. Simulation results verify the significance of proposed schemes visually and quantitatively as compared to state of art existing schemes. Three class classification based on deep learning techniques i.e. CNN and RBMs is proposed. In the CNN-DW method, enhanced mammogram images are decomposed as its four subbands by means of two-dimensional discrete wavelet transform (2D-DWT), while in the second method discrete curvelet transform (DCT) is used. Proposed methods have been compared with existing methods in terms of accuracy rate, error rate, and various validation assessment measures. Simulation results clearly validate the significance and impact of our proposed model as compared to other well-known existing techniques. Last but not the least, a novel three-class classification technique for a large dataset of mammograms using a deep-learning method of restricted Boltzmann machine (RBM) is proposed. The augmented dataset is generated using mammogram patches. The dataset is filtered using a non-local means (NLM) filter to enhance the contrast of patches. These patches are decomposed using (2D-DWT) and (CT). The proposed method is compared with existing methods in terms of ROC curve, accuracy rate and various validation assessment measures. The simulation results clearly demonstrate the significance and impact of our proposed model compared to other well-known existing techniques.