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Home > A Classifier for Isolated Complete Intersection Singularities of Modality ≤ 1

A Classifier for Isolated Complete Intersection Singularities of Modality ≤ 1

Thesis Info

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External Link

Author

Deeba Afzal

Program

PhD

Institute

Government College University

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/bitstream/123456789/2292/1/2519S.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676725391894

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The aim of the present thesis is to study, develop and implement certain algorithms in order to find the type of singularities for isolated complete intersection singularities w.r.t contact equivalence of modality ≤ 1 defined over an algebraically closed field K. The new investigation is that we do not compute the normal form of a given singularity because this would be space and time consuming. We present a charac- terization of the different types of singularities in terms of certain invariants and use the characterization to identify the singularities. We describe our implementation in computer algebra system Singular. Therefore, we discuss three problems in this thesis. • Problem 1 deals with the classification of hypersurface singularities with respect to contact equivalence when the characteristic of the field p > 2 by using blowing up as a new tool. • Problem 2 studies the classification of simple complete intersection singularities in terms of certain invariants when the characteristic of the field p = 0. • Problem 3 includes to find the complete list of unimodular complete intersection space curve singularities and the characterization of these singularities in terms of certain invariants when the characteristic of the field p = 0
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مراتب اختر کا ادبی مقام و مرتبہ(نامور ادیبوں اور دانشور وں کی نظر میں)

مراتب اخترکا ادبی مقام و مرتبہ

نامور ادیبوں اوردانشوروںکی نظر میں

 

                مراتب اختر کا شمار اُن شعرا میں ہوتا ہے جنھوں نے جدید شاعری میں ایک نئے رجحان کو متعارف کروایا اور اُن کے اس فن کی تمام ناقدین قدر کرتے ہیں۔مراتب اختر کی شاعری کے رکھ رکھائو اور ڈِکشن کے حوالے سے معروف نقاد افتخارجالب لکھتے ہیں:

مراتب اختر نے جو شاعری کی ہے اس میں رکھ رکھائو، ڈِکشن کی ملائمت، نفاست اور مروّجہ شعریت نہیں ہے۔ سب کچھ اُکھڑا اُکھڑا دکھائی دیتا ہے۔ یہ خرابیاں کہ اِمکان سے نابلداندھے، اور بے مغز لوگوں کو گراں گزرتی ہیں، درحقیقت مراتب اختر کی خالص خوبیاں ہیں۔ ان خوبیوں سے مستفید وہی ہو سکتا ہے جو شعر کی منزہ صورت کو پہچان سکتا ہو۔اِمکان کے اِمکانات تک جن کی رسائی نہیں ان کے لیے مراتب اخترکی شاعری کوئی لذت اورمعنی نہیں رکھتی۔اس شاعری کے لیے کہ اِمکان کے اِمکانات پرایمان کو پہلی شرط قرار دیتی ہے، زندہ اور تواناہونے کے ساتھ ساتھ شعر کو ڈِکشن کی موجودگی اور عدم موجودگی دونوں صورتوں میں پہچاننے کی صلاحیت ہونی چاہیے۔

                مراتب اختر کی شاعری درحقیقت یہ تقاضا کرتی ہے کہ آپ بھی مراتب اختر ہوں۔ آپ کے اور اس کے اِمکانات یکساں نہیں تو مماثل ضرور ہوں تاکہ آپ یہ جان سکیں کہ کتنے ہی اِمکانات ہیں:حقیقت میں تبدیل ہوتے ہوئے، نئے اِمکانات کو ضم دیتے ہوئے:رائج الوقتی سے بے نیاز، نامراد و کامگار! کیا آپ اس تقاضے پر پورے اُترتے ہیں؟ اگر نہیں، تو نہیں، کبھی بھی نہیں، مگر نہیں شاید!(۱)

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Relationships have value, the impact of Leader Member Exchange on Affective Commitment

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