Search or add a thesis

Advanced Search (Beta)
Home > New Results in the Artin Approximation Theory and the Construction of General Neron Desingularization

New Results in the Artin Approximation Theory and the Construction of General Neron Desingularization

Thesis Info

Access Option

External Link

Author

Kosar, Zunaira

Program

PhD

Institute

Government College University

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2019

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/12582/1/Zunaira%20Kosar%20Maths%202019%20gcu%20lhr%20prr.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726753193

Asian Research Index Whatsapp Chanel
Asian Research Index Whatsapp Chanel

Join our Whatsapp Channel to get regular updates.

Similar


If everyfinitesystemofpolynomialequationsoveraring R has asolutioninthe ring R if andonlyifithasasolutionin ˆR where ˆR representsthecompletionof R, then wesaythatthering R has the Artinapproximationproperty. M.Artinsetin a numberofconjectures,thefollowingtheoremsolvedoneofthemwhichsays,“an excellentHenselianlocalringhasthepropertyofArtinapproximation”.General Neron Desingularizationisthebaseoftheproof. Let R and R0 beNoetherianrings,foraspecial(thatisregular)morphism u : R ! R0, any R-morphism '' : S ! R0 with afinitetype R-algebra S, factors through an R-algebra T whichissmooth R-algebra, thatis, '' is acomposite Rmorphism of S ! T and T ! R0. The R-algebra T is calledaGeneralN´eron Desingularization (shortlyGND). In ourthesiswegivetheconstructiveproofofGeneralNeronDesingularization for thecasewhen R and R0 are localringsofdimension m and S has abigsmooth locus,wealsogiveauniformGeneralNeronDesingularizationforlocalringsofdi- mension m along withthealgorithmstoconstructtheN´eronDesingularizationin these cases.Anothercontributionisthat,wegivethenestedstrongArtinapproxi- mation.
Loading...
Loading...

Similar Books

Loading...

Similar Chapters

Loading...

Similar News

Loading...

Similar Articles

Loading...

Similar Article Headings

Loading...

103. Al-Asr/The Time

103. Al-Asr/The Time

I/We begin by the Blessed Name of Allah

The Immensely Merciful to all, The Infinitely Compassionate to everyone.

103:01
a. By the Passage of Time.

103:02
a. Indeed, human being is in a constant danger of great
loss -

103:03
a. except for those who:
- believe, and
- practice righteousness, and
- motivate one another to the truth, and
- urge one another to steadfastness during the trials that befall.

Reconciliation Process in Afghanistan and Pakistan as Cardinal Player

Afghanistan is in state of war for almost 40 long years but the political dynamics got changed after 9/11. Since the war on terror started facets of peace talks launched without meaningful end. The reconciliation process in Afghanistan had immediately started after establishment of Afghan interim government in 2001. Till 2016 mid, four different reconciliation /reintegration processes were launched by the USA and Hamid Karzai government with Afghan Taliban. The new elected president Ashraf Ghani ended all such processes in 2016 but showed willingness again in 2018 for direct peace talks between USA and Taliban clerics. In the current political scenario, Afghan reconciliation process is back on track with direct peace talks between USA, Taliban and Afghan Government along other international actors. However, Taliban were not ready to sit with the Afghan Government and this is where the Pakistan played as key to Afghan peace process. The focus of this research article is to find the challenges and opportunities of this peace process; Pakistan’s role as cardinal player can consolidate the peace process in Afghanistan. Furthermore, this research will give future recommendations for the peace process in Afghanistan.

Culture of Gun Violence: Impact of Proliferation of Small Arms and Light Weapons on Pakistans Internal Security

The number of people killed or affected by firearms or light weapons each year is far greater than those killed by the atomic explosions in August 1945. Yet, in comparison to the weapons of mass destruction– which bear signature characteristics of indiscriminate mass annihilation and destruction - small arms and light weapons (SALW), or firearms have been viewed as less significant, less lethal and more manageable. This unfortunately is just one of the many myths that surround the destructive potential of these seemingly innocuous tools of violence and destruction. In case of Pakistan, the availability and continued proliferation of small arms, has not only made the country violence-prone but has also led to the violent framing of its politics. The acceptability of guninduced violence is becoming part of the political culture and more so than ever before, poses a direct and dangerous threat to the internal cohesion of the Pakistani state and society. Romancing the gun has been a salient feature of the Pakistani tribal culture for generations, where for centuries people have not only wore the gun as part of their dress code but have also taken pride in their ingenuity to manufacture weapons as a cottage industry. Across the country irrespective of ethnic or sectarian identity, the increase in licensed and unlicensed firearms ownership as well as indiscriminate usage and tolerance towards SALW has been manifold This study examines the role of SALW in the violent framing of Pakistani politics in the aftermath of the Soviet-Afghan war. It attempts to shed light on how small arms proliferation and use contributed to the rise in societal violence, perpetuated widespread insecurity and instability in the country and undermined the ability of Pakistani State to stem the rising tide of armed violence. It is not wrong to say that there is both a vertical as well as horizontal spread of weapons across the country which corresponds with the failing state of law and order and writ of government. The key questions to be addressed in this study are - what is the relationship between small arms and the sources of domestic insecurity and violence in Pakistan? Have SALW contributed to the fragility or failure of the state? Has the traditional culture of gun wearing and romancing with guns contributed to the increased violence in the country? What were the policy imperatives that motivated successive administrations in Pakistan to tolerate the emergence of illicit arms market? What is the negative fallout of these policies over the years, and why is the Pakistani state now feeling the impact of these weapons more than ever before? What more needs to be done, keeping in mind the increased international efforts at seeking a monumental arms trade treaty and other legislations to curb proliferation of small arms at both state and non- state level. Lastly, were the various remedial measures undertaken by the Pakistani state to redress domestic security concerns internally - motivated or these were acts undertaken to appease outside actors?