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Homogeneous sagbi basis

Thesis Info

Author

Sarfaraz, Sarah

Program

MS

Institute

Institute of Business Administration

Institute Type

Private

City

Karachi

Province

Sindh

Country

Pakistan

Thesis Completing Year

2015

Page

30

Subject

Mathematics

Language

English

Other

CallNo: 512.4

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676720937317

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n this thesis we will define Grobner basis, for ideals of multivariate polynomial ring, which solves the ideal membership problem. Then analogy of the theory of Grobner basis in subalgebra, the theory of Sagbi basis, is discussed. It is shown that Sagbi basis solves the subalgerba membership problem. The main goal is to present the theory related to homogeneous Sagbi basis and d-Sagbi basis. It is shown that homogeneous polynomial with a certain degree d, will, after s-reduction, yield a homogeneous polynomial, having degree within the bound d. Similarly, if a Ssagbi basis is homogeneous then the subalgebra generated by it, is also homogeneous. Lastly it is determined that Sagbi basis construction algorithm bounded by certain degrees, is less expensive for finding Sagbi basis, due to computations within those degree bounds. Moreover it is also presented that bounded algorithm from 0 to certain degree d, gives an outcome, known as d-Sagbi basis. This d-Sagbi basis is used to solve the subalgebra membership problem with a lot less computations as compared to solving it through Sagbi basis
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شاہ فخر عالم بھاگلپوری

شاہ فخر عالم بھاگلپوری
دینی اور علمی حلقوں میں شاہ فخر عالم بھاگلپوری کی وفات کی خبر بڑے رنج و افسوس کے ساتھ سنی جائے گی، ان کے نامور بزرگ سید ظہیرالدین ۱۲۷۹؁ء میں دہلی آئے اور حضرت نظام الدین اولیاء کے حلقۂ ادارت میں داخل ہوئے، انھوں نے حضرت بہاء الدین زکریا ملتانیؒ کے پوتے مخدوم رکن الدین رکن عالمؒ سے بھی اکتساب فیض کیا، اس طرح اس خاندان میں چشتی اور سہروردی دونوں نسبتیں جمع ہوگئیں، بعد کو یہ خاندان دہلی سے بہار آگیا، اور حضرت سید علی محمد (ڈمڑیا بابا) نے بھاگلپور میں قیام فرمایا، اس وقت سے یہ لوگ یہیں آباد ہیں، اور ان کی خانقاہ ڈمریا بابا ان کے نام سے موسوم ہے، شاہ فخر عالم مرحوم اسی خانقاہ کے سجادہ نشین تھے، وہ دینی مشاغل کے ساتھ علمی مذاق بھی رکھتے تھے، ان کا کتب خانہ ان کے علمی ذوق کا شاہد ہے، اﷲ تعالیٰ سے دعا ہے کہ وہ ان کو اپنی عنایتوں اور رحمتوں سے شاد کام کرے، اور ان کے جانشین سید شاہ شرف عالم ندوی کو اپنے بزرگوں کے نقشِ قدم پر چلنے کی توفیق عطا فرمائے۔
(عبد السلام قدوائی ندوی، جون ۱۹۷۶ء)

Harmony and Peace Education in Pakistan: Focus on Pctb Textbooks of History and Pakistan Studies

Textbooks produce specific minds so are believed the best way to promote peace and harmony in a society. Policymakers draw ideological lines for specific goals and educate the coming generations through the contents of the textbooks. Whatever agenda a nation has, peace and social harmony cannot be compromised so syllabi mean to promote nationalism along with integration. Although history and social studies textbooks address coexistence and tolerance but even then many writers share their reservations about some points. K K Aziz (1993) in Pakistan castigated the governments and the textbook authors on ‘distortion’ of the historical events and deleting important segments of history from the syllabi. Mariam Chughtai shared her reservation regarding the textbooks being published in Pakistan. Romila Thapar in India raised objections against the BJP government’s effort of ‘religionising the syllabi’ and tried her best to introduce non-communal approach based on social harmony in the textbooks while writing history books but her effort remained a mere desire because the ‘religiously’ extremist political party occupying the main corridor of the national government and having no compatibility with her ideas refused to accept the undisputed historical facts. Dr. Mubarak Ali opined while writing on the textbooks that ‘defective textbooks create a defective mindset. Ideology limits people from acquiring new knowledge in order to understand the fast changing world’ (Dawn, April 16, 2016). ‘National History’ reflects national point of view to produce a generation who represents some specific land, culture, religion, political ideology, art and social ethics. Children are taught to grow with their own culture, religion and social norms. This study finds that syllabus of the subjects of History and Pakistan Studies produced by the Punjab Curriculum and Textbook Board (PCTB) aims at educating the ‘national interpretation of history along with respect for other religious groups’ to the posterity therefore no gaps seem in the textbooks of History and Pakistan Studies. Criticism arises mostly on the old textbooks while the PCTB had revised the textbooks massively and all the historical periods including Indus Valley Civilization, ancient India, Sikh rule, etc. Are being taught at the school and college level. The ‘history textbook’ is not a ‘history’ rather it offers interpretation of the historical events. This article further pinpoints some issues such as communal interpretations in the British India, space in the textbooks, administrative, social, political and religious narrations, and the undeniable position on nationalism and patriotism which cannot be overlooked. The textbooks are playing their role in promoting social harmony and this policy has resulted in a coexistence, tolerance and peace in the society.

Effects of Intravenous Diclofenac on Postoperative Sore Throat in Patients Undergoing Laparoscopic Surgery at Aga Khan University Hospital, Nairobi: A Randomized, Double Blind Controlled Trial

Background: postoperative sore throat (POST) is the commonest complication after endotracheal intubation. The efficacy of intravenous non-steroidal anti-inflammatory drugs (NSAIDs) in alleviating postoperative sore throat has not been investigated. Objective: to evaluate the effect intravenous diclofenac sodium on the occurrence and severity of POST. Design: a randomised, double-blinded, controlled clinical trial. Setting: the operating theatres of the Aga Khan University Hospital, Nairobi, Kenya. Population: endotracheally intubated adult inpatients undergoing general anaesthesia for either general surgical or gynaecological laparoscopic surgery. Methods: forty two adult inpatients scheduled for laparoscopic surgery were randomized into two equal groups. The intervention group (referred to as the diclofenac group) received a single intravenous dose of 75mg diclofenac sodium in addition to standard care given at our hospital for the prevention of POST. The control group (referred to as the standard care group) received standard care only. All patients were interviewed postoperatively at two, six and eighteen hours. Data of the baseline characteristics, the occurrence and severity of sore throat were collected. If sore throat was present, a numerical rating scale (NRS) score was used to assess its severity. Results: the baseline characteristics of the participants were similar. The occurrence of POST at two hours postoperatively was less in the intervention group than in the standard care group, 15% and 30% respectively. However this difference did not reach statistical significance (p 0.26). There was no difference in the severity of postoperative sore throat between the intervention and standard care groups at two, six and eighteen hours postoperatively (p 0.360, 0.678 and 0.862 respectively) Conclusion: intravenous diclofenac sodium added to the standard care does not affect the occurrence or severity of postoperative sore throat.