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Some Properties of Non-Commutative Multiplication Semi-Groups

Thesis Info

Author

Nazli Sanam

Department

Deptt. of Mathematics, QAU.

Program

Mphil

Institute

Quaid-i-Azam University

Institute Type

Public

City

Islamabad

Province

Islamabad

Country

Pakistan

Thesis Completing Year

2006

Thesis Completion Status

Completed

Page

61

Subject

Mathematics

Language

English

Other

Call No: DISS/M.Phil MAT/534

Added

2021-02-17 19:49:13

Modified

2023-02-19 12:33:56

ARI ID

1676717751652

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مسٹر تلک

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            ہندوستان کے لئے ماہ گذشتہ کا اہم ترین حادثہ مسٹر تلک کا انتقال تھا، اپنی سیاسی حیثیت سے قطع نظر کرکے مسٹر تلک ملک کی علمی زندگی کے بھی ایک بہت بڑے عنصر تھے، وہ سنسکرت زبان کے ماہر اور ہندوؤں کے علوم قدیمہ کے ایک زبردست عالم تھے، قدامت وید کے متعلق انہوں نے جو فاضلانہ مقالہ پہلی اورینٹل کانفرنس کے سامنے ۱۹۲۰؁ء میں پیش کیا تھا، اسے مستشرقین کے حلقہ میں خاص وقعت کے ساتھ دیکھا گیا۔ اس کے بعد سے مسٹر تلک نے ویدوگیتا کے متعلق بلندپایہ تصانیف و مضامین سنسکرت اور انگریزی میں شائع کئے، اور ماہرین فن ان کی وسعت نظر و تبحر علمی کا ہمیشہ اعتراف کرتے رہے، ہندوستان اپنی بزم علمی کے اس رکن رکین کے اٹھ جانے پر جس قدر بھی تاسف کرے بجا ہے۔ (ستمبر ۱۹۲۰ء)

 

قرآنی طرز زندگی کے مطابق قیادت و رہبریت کی شرائط

Islam teach us complete way of life. It guides human to face any circumstance from birth to death such as clothing and appearance etc, Beard on male face is one of those guidance, through which male can be differentiated from female. Quran and Sunnah, Ijma and Qiyas (four principles of sharia) has made beard a part of human and Islamic nature. Due to this beard is obligatory and not having beard on face and large mustaches on face is the appearance of non-Muslims. And we are ordered to oppose that appearance. And by leaving beard less than one hand is forbidden, and group of many sins. And Hazrath Muhammad (SAW) also hate them. And according to sharia having beard on face have a lot of benefits for health and not having beard on face is much harmful for health. And cutting beard more than one hand is allowed and as well evident that it is Sunnah and Mustahib, because it is the original quantity of beard. And also it is based on the principles of nature and common sense instead of copying.

Three Wave Interactions in Non- Degenerate and Degenerate Magneto-Plasmas

In this thesis we study the parametric decay instability problem (three wave interactions) in classical andquantummagneto‐plasmas.Twocombinationsofthethreewaveinteractionshavebeen investigated.First,theparametricdecayinstabilityofupperhybridwaveintolow‐frequency electromagnetic shear Alfven wave and Ordinary mode radiation has been solved in an electron‐ion plasma immersed in uniform external magnetic field. Incorporating quantum effect due to electron spin, the fluid model has been used to investigate the linear and nonlinear response of the plasma species. It is shown that the spin of electrons has considerable effect on the three‐wave coupling interactions even in classical regime. Secondly,theelectronspin‐1/2effectsontheparametricdecayinstabilityofobliqueLangmuir waveintolow‐frequencyelectromagneticshearAlfvenwaveandleft‐handedcircularlypolarized wave(LHCP)hasbeeninvestigatedinanelectron‐ionquantumplasmaimmersedinuniform external magnetic field. Incorporating the quantum effects due to electron spin, Fermi pressure and Bohmpotentialterm,thequantummagneto‐hydrodynamic(QMHD)modelhasbeenusedto investigatethelinearandnonlinearresponseoftheplasmaspeciesforthree‐wavecoupling interactionina quantummagneto‐plasmas.Nonlineardispersionrelationsandgrowthrateshave been derived analytically. It has been shown that the spin of electrons has considerable effect on the growth rate of parametric instability problem even when the external magnetic field B0 is below the quantum critical magnetic field strength BQ = 4.4138 ×1013 G. Finally,theparametricdecayinstabilityofobliqueLangmuirwaveintolow‐frequency electromagnetic shear Alfven wave and LHCP have also been investigated in high density (quantum) and low density (classical) magneto‐plasma environments. QMHD model has been used to find the linear and non‐linear response of the high density quantum magneto‐plasma, and to compare the (h → 0, Pe → Pte ) results with the low density classical plasma we have used classical limit in the results of QMHD model. Nonlinear dispersion relations and growth rates of the problem have been derived analytically. The growth rate both for quantum and classical magneto‐plasma environments has been plotted. The normalized growth rate as a function of number density in the high density degeneratemagneto‐plasmasincreasesexponentiallywhileinthelowdensityclassicalmagneto‐ plasmas it increases logarithmically.