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Stanley Decompositions and Localization

Thesis Info

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Author

Nasir, Sumiya

Program

PhD

Institute

Government College University

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2005

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/1634

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727233505

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In Chapter 1, some basic definitions and results from commutative algebra are given. In Chapter 2, we study the behavior of Stanley decompositions under the opera- tion of localization with respect to a variable. We prove how prime filtrations behave under localization. We observe that pretty clean filtrations under localization are still pretty clean filtrations. In Chapter 3, we introduce the concept of Stanley decompositions in the local- ized polynomial ring Sf where f is a product of variable, and show that Sf has a canonical Stanley decomposition and that the Stanley depth does not decrease upon localization. Furthermore it is shown that for monomial ideals J ⊂ I ⊂ Sf , the number of maximal Stanley spaces in a Stanley decomposition of I/J is an invariant of I/J. We also introduce the Hilbert series of Zn -graded K-vector space.
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آیاتِ استفہام اور فہم عقیدہ آخرت

کائنات کے نظام کا مطالعہ کرنے سے پتہ چلتا ہے کہ یہاں کسی چیز کے لئے کبھی ہمیشگی نہیں ہے، سب کی ایک عمر مقرر ہے وہ اپنی عمر مکمل کرنے کے بعد ختم ہوجاتی ہے، اس کائنات کو کمال درجہ حکمت سے بنایا گیا ہے جس کی ہر شئے میں ایک قانون کار فرما ہے۔ دنیا میں نیکی و بدی، ظلم و عدل اور تعمیر و تحریک کرنے کے بعد مٹی میں مل جانا یہ حقیت نہیں ہے بلکہ ہر اچھائی اور برائی کا بدلہ ضرور ملے گا۔

حافظ عمران ایوب لاہوری اپنی کتاب ’’آخرت کی کتاب‘‘ میں لکھتے ہیں کہ:

 "آخرت ان تمام امور کا نام ہے جو مرنے کے بعد انسان کو پیش آئیں گے آخرت کے لیے کہا گیا ہے کہ یہ دنیا کے بعد آنے والی ہے آخرت پر ایمان پر قائم ان میں سے ایک اہم رکن ہے کہ جب تک آخرت کے متعلق اللہ تعالی کی بتلائی ہوئی ہر خبر پر دل ایسا مطمئن نہ ہو جائے کہ کسی قسم کا شک و شبہ باقی نہ رہے تب تک ایمان بالآخرت کا حصول ممکن نہیں اور ایسا اعتقاد رکھنے والا ہی حقیقی مومن ہے اس کے علاوہ آخرت پر ایمان کا یہ فائدہ ہے کہ اس سے رغبت، خوف اور اعمال صالحہ کی بجاآوری کے ذریعے رب العالمین کی خوشنودی حاصل کرنے کا جذبہ پیدا ہوتا ہے ہر جاندار نے موت کا ذائقہ چکھنا ہے اور جو بھی ذی روح اس دنیا میں آیا ہے اس نے بالآخر یہاں سے رخصت ہونا ہے کوئی بھی موت سے نہیں بچ سکتا چاہے وہ خود کو مضبوط قلعوں میں بند ہی کیوں نہ کرلے اس لئے موت کو ہمیشہ یاد رکھنا چاہیے نبی صلی اللہ علیہ وسلم نے نصیحت فرمائی ہے کہ موت کو کثرت سے...

Youth Perception on Climate Change and Its Impact on Health (Islamabad)

Climate change is a global issue characterized by a shift in regular weather patterns over decades or longer, such as rising temperatures, more precipitation, or decreased humidity. Pakistan is experiencing the consequences of climate change, with increased glacier melt, droughts, and warmer winters and early summers. Pakistan does not make a significant contribution to global warming or climate change. It is, nevertheless, the seventh most severely affected country. In the last century, the average temperature of Pakistan increased by 0.6°C. Pakistan’s government has already initiated the Ten Billion Trees Tsunami Project, one of the world’s most ambitious endeavors to extend and repair its forests. The objective of this study was to investigate the perceptions of youth of Islamabad on climate change and its impact on human health. The mixed methodology (qualitative and quantitative) is used to get better results in apprehensive research work. Our research found that a large percentage of people in the capital city believe climate change is happening and is caused by global warming and deforestation. The youth are aware of climate change and its effects on humans, but they require further education on the subject and guidance on how to mitigate climate change. The government should do something at the national or university level to raise awareness about climate change.

The Study of Shortcomings in Conventional Banking System: A Maqasid-E-Shariah Perspective

It is unanimous quote that the life blood of development is the sound economy of a country. The trend reveals the fact, all the developed countries across globe are symbols of cited above quote. Contrary to the said saying, countries deficient of it are still striving for survival and the world ranks them in the list of under developed countries. It is also pertinent to mention that along with other relevant factors to boost up the economy, banking sector play a very keen role in providing the smooth ground one way or other. The fact beyond it is quite clear as this Industry has depth involvement in almost all life businesses. Nobody can deny the importance of this sector that is why the fast growth has been observed in Banking Industry so for as comparative to other economic sectors. Similarly, the financial history depicts the datum about gray aspect of this sector. The downfall of financial industry leads towards the collapsing of entire economy as almost all the core economic activities based on this industry directly or indirectly. In last centuries, financial crises has been observed numerous time affecting the global economies and put the adverse impact on routine economic cycles for long time. The economist played a vital role in evaluating these financial crises and presented thousands of research papers and reports aimed to explain the issue and causes of its occurrences. Likewise different surveys has been conducted in order to get core and real causes of these disasters but all in vain. After practicing a large number of remedial measures and opting thousands of suggestion in this regard results almost same consequences. The world economy faced huge financial disaster on average after decade or two like Wall Street Crash of 1929 and Great Depression, Oil Crises in 1973, Latin American Debt Crises in 1982, Black Monday in1987, U.S Saving and Loan Crises in 1989, Japanese Asset Bubble in 1990, Mexican Peso Crises in 1994, Asian Financial Crises in 1997, Russian Financial Crises in 1998 and Dot-Com bubble in 2000. The worst case occurred in 2008 that affect the world economy severely. Almost all the dollar base countries felt the shocks of these crises. The summary of almost all recommendations towards its healing and to bringing them in a streamline of rationality shows that all are primarily made on derived assumptions of mankind and based theoretical phenomena’s constantly leaving the space for individual’s curiosity and interest which leads the system to repeat itself in year or decade in the shape of new financial disaster or financial crises. Important to mention that after the use of bulk of energies and utilization of all type resources, why the economist are unable to explore the solid and firm system to accomplish the financial objectives of humanity and why the world used to face such disaster in a cyclic manner and why the financiers remains in risk of “anything may happen anytime” and in fear of uncertainty. The only answer to all raised question is very clear that we always construct our system on man-made policies and procedures rather than opting the divine rules and orders. “An interesting irony that every dollar note has the admission: “In God we trust”, but when it comes to develop theories to earn dollars or to distribute or spend them, trust is placed only on human ideas based on personal assessments; God is held totally out of picture, as being irrelevant to economic activities’. [Taqi Usmani, 2009].This is the quandary that high financial experts and economist didn’t realize and nobody confer attention towards it to know the root cause of downfall. Manmade theories are always limited to specified era and restricted to particular setting. That is why the world economy consistently running with high risk. So there is dire need felt to observe the banking system in the light of divine rules to ensure its smooth operations with full confidence of sound and firm procedures from customer to organizations along with reliance of all stakeholders operating in the said system directly or indirectly. This research study will mainly covers the identification of shortcomings in conventional banking system with respect to sharia’s principles and laws only. Those products, trends, policies and dealings of it violating the cultural norms, international accounting or auditing standards and any other sort of disrespect and lacking is not the considerable part of this research. Along with that, it also focus on describing the remedial measures of the loopholes in order to eliminate them from the system to ensure the smooth flow of financial operations and to protect it from adverse violations and exploitations. The study will present the some in vogue practices of Islamic banking system in the form of portraying the detail discussion of mostly used modes of financing like Mudarabah, Murābaḥa, Ijarah, and Diminishing Musharakah along with their procedural documentations and patterns exist in the Islamic Banks as sample that how these modes are free from all such lacking and weakness what the conventional Banks have which is the need of the day to address properly in order to bring the entire system in full conformity of divine standards and laws. For the said purpose, the study includes all the sources of Shariah i.e. Qura’n, Sunnah, Ijma and Qias classical literature and contemporary financial reports, surveys and procedural laws of different financial Institutions special emphases on conventional Banks. On the basis of findings of the study, the suggestions will be stated to bring the deviations in accord with the mainstream Sharia.