Search or add a thesis

Advanced Search (Beta)
Home > Subalgebra Bases in Local Rings and its Efficient Computation in Polynomial Rings

Subalgebra Bases in Local Rings and its Efficient Computation in Polynomial Rings

Thesis Info

Access Option

External Link

Author

Khan, Junaid Alam

Program

PhD

Institute

Government College University

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2006

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/1010

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727411082

Asian Research Index Whatsapp Chanel
Asian Research Index Whatsapp Chanel

Join our Whatsapp Channel to get regular updates.

Similar


In Chapter 1, there are given some necessary definitions and results about monomial orderings, Standard basis and Sagbi basis in polynomial ring over the field along with a description on the Gr ̈obner walk algorithm and Gr ̈obner basis under composition. In Chapter 2 we develop a theory of subalgebra basis analogous to Standard basis for ideals in polynomial rings over a field. We call this basis Sasbi Basis, standing for Subalgebra Analogue to Standard Basis for Ideals. Sasbi bases may be infinite. In this chapter we consider subalgebras admitting a finite Sasbi basis and give algorithms to compute them. Sasbi basis theory is given in my paper [22]. In Chapter 3, we present an algorithm which converts the Sagbi basis with respect to one ordering to the Sagbi basis with respect to another ordering, under the as- sumption that the subalgebra admits a finite Sagbi basis with respect to all monomial orderings. We called it Sagbi walk algorithm. Sagbi Walk algorithm is given in my paper [20]. Composition is an operation of replacing variables in a polynomial by other poly- nomials. In Chapter 4, we study the behavior of Sagbi basis under composition. Some related results are from my paper [21].
Loading...
Loading...

Similar Books

Loading...

Similar Chapters

Loading...

Similar News

Loading...

Similar Articles

Loading...

Similar Article Headings

Loading...

مولانا عبدالسلام رامپوری

مولانا عبدالسلام خاں رام پوری
اخباروں سے یہ افسوس ناک خبر ملی کہ ۱۳؍ اپریل کو مولانا عبدالسلام خاں رام پوری نے اس دنیائے فانی کو الوداع کہہ دیا، اِناﷲ وَاِنا اِلَیہ رَاجِعُون۔
ان کے ساتھ ہی دارالسرور رام پور کی وہ امتیازی شناخت بھی رخصت ہوگئی جس کی وجہ سے رام پور کو بخارائے ہندی کہا جاتا تھا، رام پور کی ریاست کی علم پروری اور سخن نوازی کی داستانیں ہماری علمی و ادبی تاریخ کا بڑا دل کش حصہ ہیں لیکن فلسفہ و کلام و منطق جیسے علوم معقولات میں اس ریاست کی روایت کی بات ہی کچھ اور ہے، اٹھارہویں صدی کے اواخر میں نواب فیض اﷲ خاں کے فیض سے جب وہاں مدرسہ عالیہ قائم ہوا اور اس کے پہلے صدر مدرس کی حیثیت سے مولانا عبدالعلی بحرالعلوم فرنگی محلی کا تقرر ہوا تو جیسے معقولات کی بہار آگئی، مولانا فضل حق خیرآبادی اور مولانا عبدالحق خیرآبادی جیسے ائمہ فلسفہ اسی فصل گل کی یادگار ہوئے، مولانا عبدالسلام خاں نے جب رام پور کی اس فضا میں ۱۹۱۷؁ء میں پہلی سانس لی تو گو پہلا سا رنگ نہیں تھا لیکن رونق اب بھی باقی تھی، ان کے ہم عصر ساتھیوں میں مولانا وجیہ الدین خاں، مولانا ابوالوفاء شاہ جہاں پوری، مولوی عبدالوہاب خاں، مولانا امتیاز علی عرشی جیسے اصحاب فضل و کمال کے نام ملتے ہیں، ان کے اساتذہ میں ایک نام جیراج پور اعظم گڑھ کے مولوی عبدالودود ندوی کا بھی ہے، مولانا عبدالسلام خاں کی غیر معمولی لیاقت ہی تھی کہ ان کو کم عمری میں اس مدرسہ عالیہ کا متولی یعنی پرنسپل بنایا گیا اور یہ ان کی صلاحیت تھی کہ وہ ۱۹۷۵؁ء تک یعنی قریب تیس سال تک اس عہدے پر فائز رہے لیکن ان کی اصل شہرت ان کے قلم کی رہین منت ہے جس نے...

مزاح کے انسانی نفسیات پر اثرات اسلامی تعلیمات کی روشنی میں Effects of humor on human psychology in the light of Islamic teachings

Every branch of art leaves a deep impact on the human psyche, but the immortal fact is that the reason for their creation is also to reduce the tension of the human mind. The most representative theory of humor in philosophy and psychology and even in physics. Is the idea of ​​well-being, comfort or well-being? Broadly speaking, this suggests that humor (which has an obvious physiological effect) has effects on the nervous system and allows different levels of stress to be released. In other words, laughter and good humor have the ability to release stored nervous energy. Humor is included in human nature and man has a strong desire for this thing that there should be such means for him to express joy and expansion. Because through them, man is blessed with mental and physical peace and comfort. In these things, he considers the survival of his self-respect. Islam not only allows humor, sports and entertainment, but also sets rules and regulations within which human beings can fulfill their natural needs. Its cultural traditions should also be propagated. As the head and governor of the Islamic state, the Holy Prophet (ﷺ) made the best arrangements for his state, the taste of the people and their entertainment, and set an example for the rulers that, like other matters, oppression in this not to be taken for granted, fun and humor are part of human nature. He (ﷺ) allowed fun and laughter and He (ﷺ) himself used to be cheerful. Islam admires cheerfulness and cheerfulness, and encourages it so that people can be refreshed and perform their duties in an auspicious manner. Through this paper, it will be clarified that what are the effects of humor on human psychology and what are the teachings of Islam and the Prophet of Islam in this regard. Key Word:    Fine Arts, Humor, Human terms, Human humor

Evaluation of Solid Breast Masses Using Sonographic Acr Bi-Rads Lexicon Descriptors

Purpose of the study: To which of the ACR sonographic BIRADS lexicon descriptors can be used reliably to differentiate benign from malignant solid breast masses. Objectives: 1.Main Objective: To determine the association of sonographic ACR BI-RADS descriptors and solid breast masses 2. Specific Objective: To determine the predictive probabilities of sonographic BI-RADS lexicon descriptors Methodology: This was a 15 months prospective cross sectional study in which 125 consecutive patients who met the inclusion criteria were enrolled. The study was carried out at theAga KhanUniversity hospitalradiology department between October 2008 and December 2009 inclusive. The scans were performed in ourradiology department by residents and consultant radiologists. The sonographic BI-RADS descriptors were then assigned to the lesions based on the consensus arrived at between the principal investigator and the consultant radiologist. The findings were then correlated with the histological/cytological diagnosis which was the gold standard. The study was approved by the University Research and Ethics Committee Results: 66% (n=82) of the patients turned out to have benign lesions while 34% (n=43) had malignant breast lesions. All the sonographic BI-RADS descriptor variables demonstrated significant association with the histology results apart from vascularity. The predictive probability of malignancy was lowest (8.36 %) for lesions with parallel orientation and well circumscribed margins and highest (73.89%) for masses with non parallel and poorly circumscribed margins. Conclusion: There is a significant association between all the sonographic ACR BI-RADS lexicon descriptors and solid breast masses apart from one descriptor: vascularity. Lesions with both non parallel orientation and non circumscribed margins have the highest predictive probability for malignancy.