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Estimation of Variance under Different Sampling Schemes

Thesis Info

Author

Musarat Sardar

Supervisor

Javid Shabbir

Institute

Allama Iqbal Open University

Institute Type

Public

City

Islamabad

Country

Pakistan

Thesis Completing Year

2014

Thesis Completion Status

Completed

Page

xii, 62.

Subject

Mathematics

Language

English

Other

Call No: 519.5 MUE; Publisher: Aiou

Added

2021-02-17 19:49:13

Modified

2023-01-06 19:20:37

ARI ID

1676710017487

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ابتدائے وحی

ابتداء ِوحی
وحی کی ابتدارویا ئے صادقہ سے ہوئی جو کچھ آپ خواب میں دیکھتے اسی طرح وہی ظہور میں آتا ۔ یہ مقدمات نبوت کا ظہور ہو رہا تھا اس وقت آپ کی عمر چالیس سال کے پیٹے میں تھی ۔ رویائے صادقہ چھ ماہ تک رہے آخر کا ر ایک روز غار حرا میں مراقب تھے کہ جبرائیلؑ فرشتہ آپ ﷺ کے پاس اللہ کا پیغام لے کر آیا اور کہا : اقراء (پڑھو) آپ نے فرمایا مَااَنَا بقاَریِِ ( میں پڑھنے والا نہیں ہوں ) فرشتہ نے آپ ﷺ کو سینہ سے لگا کر بھینچا پھر اقراء کہا : آپ نے فرمایا ’’ ما انا بقاری‘‘ فرشتہ نے دوبارہ بھینچا اور کہا اقراء ، تیسری بار فرشتہ نے کہا : اِقرَابِاِِاسِم ِ رَبَّکَ الذَّی خلق‘‘ آپ نے ان کلمات کو پڑھا( اقراء با اسم ربک الذی خلقo خلق الانسان من علقoاقراء وربک الاکرم o الذی علم با لقلم oمالم تعلم o ) آپ پڑھیے اپنے رب کے نام کے ساتھ جس نے پیدا فرمایا ، پیدا کیا انسان کو جمے ہوئے خون سے ، پڑھیے آپ کا رب بڑا کریم ہے جس نے علم سکھایا قلم کے ذریعے سے ، اس نے سکھایا انسان کو جو وہ نہیں جانتا تھا ۔‘‘
مستشرقین ایسی چیزوں کی تلاش میں مصروف رہتے ہیں جن کو بنیاد بنا کر اسلام اور پیغمبر اسلام ﷺاور ان کے اصحاب کو نشانہ تنقید بنا سکیں ۔ بد قسمتی سے انہیں اپنے موقف کے لیے مواد بھی ہمارے اپنوں کی تحریروں سے ہاتھ لگ جاتا ہے پھر انہیں مزید غلط رنگ دے کر اور خوب نمک مرچ لگاکر شکوک و شبہات کے علاوہ فی نفسہ ِ واقعہ کو غلط ثابت کرنے میں ایڑی چوٹی کا زور لگاتے ہیں ۔ اسی طرح وحی کے متعلق عجیب و غریب باتیں کرتے ہیں ۔...

ولادت النبیﷺ سے متعلق سیرۃ کی چند روایات کا تحقیقی جائزہ

Allah sent Hadrat Muhammad (SAW) as last Prophet and preserved his all aspect of life for the complete guidance of mankind. Love with the Holy Prophet (SAW) is a part of the Faith. But it has become the standard of his love that all the things which are attributed to him either authentic or unauthentic are accepted without research. Regarding the S╚rah (life) of Holy Prophet (SAW) numerous authentic narrations are exist, but on the other hand some fabricated narrations also mentioned by the story-teller historians, so be careful while propagating these narrations. Some narrations are very famous regarding the birth of the Holy prophet (SAW) which are far away from the reality. In this article some narrations regarding the birth of the Holy prophet (SAW) are scholarly reviewed in the light of the views of the scholars of Jarh-o- Ta‘d┘l in order to find their legal status.

Nonlinear Coherent Structures in Multi-Component Degenerate Plasmas

The propagation characteristics of nonlinear coherent structures involving the solitons, shocks and rogons (rogue waves) are studied in a degenerate dense plasma, which has strong relevance not only to compact astrophysical bodies such as white dwarfs, magnetars, neu tron stars, etc., but also in high density laser-induced plasmas. In superdense plasmas, the quantum corrections due to quantum degeneracy, quantum diffraction, relativistic degener acy and degenerate particle trapping strongly modify the nonlinear properties of the waves and instabilities. In Chapter 3, a multi-dimensional propagation and stability for ion-acoustic (IA) soli tary waves are discussed in a magnetoplasma, containing degenerate relativistic trapped electrons and classical anisotropic ions. By using the Chew Goldberger and Low (CGL) the ory alongwith quantum magnetohydrodynamic (QMHD) equations, a Zakharov-Kuznetsov (ZK) equation is obtained, which admits a solitary solution in the form of potential pulse. The stability parameter Si is analyzed by a k-expansion method, which reveals the stable and unstable solitons in the domains Si < 0 and Si > 0, respectively. Numerically, it is found that trapped electrons and ionic pressure anisotropy support the formation of taller and wider solitons in a degenerate relativistic anisotropic plasma. Chapter 4 presents the linear and nonlinear analyses of magnetosonic (MS) solitary and shock waves in a degen erate relativistic magnetoplasma. For this, we have solved the QMHD equations with the aid of reductive perturbation technique to study a Korteweg-de Vries (KdV) solitons and Korteweg-de Vries-Burger (KdVB) shocks. For linear study, a plane wave solution is used to obtain a linear dispersion relation for MS waves. It is revealed that relativistic electrons reduce the rapid variations in the wave frequency due to intensification of external mag netic field. In nonlinear analysis, the relativistic electrons strongly favor to excite taller and narrower localized solitons and amplify the shock strength. In Chapter 5, one-fluid QMHD model is utilized to investigate the characteristics of low frequency MS envelope solitons in a dense magnetized plasma. By using a multiscale reductive perturbation technique, the nonlinear Schro¨dinger (NLS) equation is derived to account for degenerate relativistic electrons and associated quantum diffraction effects. It is examined that these effects play a vital role to excite modulationally stable excitations, such as the dark and grey solitons in dense magnetoplasma. These solitons only exist under the condition PQ > 0, where P and Q are the dispersion and nonlinearity coefficients, respectively. These results are useful for analyzing the propagation characteristics of MS excitations in dense astrophysical plasmas, where quantum and relativistic effects modify the wave properties and stability. Chapter 6 describes the evolution of weakly nonlinear dust-ion-acoustic (DIA) bright solitons and rogons in a degenerate dusty plasma containing degenerate relativistic electrons, and dynamical degenerate ions with static dust. To examine numerically the modulational instability (MI) and unstable modes on ion-timescales, the effects of relativistic electrons and degenerate ions are examined on the profiles of MI and localized DIA excitations (bright solitons and rogons). It is found that the instability domain becomes widen for varying the relativistic parameter and ionic degeneracy. Finally, in Chapter 7, we have extended our work to nonlinear evolution of extremely low frequency dust-acoustic (DA) solitons and rogons in a nonplanar cylindrical plasma accounting for Thomas-Fermi distributed electrons and ions. The fluid equations are evolved into the cylindrical Kadomtsev-Petviashvili (CKP) and cylindrical nonlinear Schro¨dinger (CNLS) equations for studying the formation of solitary and rogue excitations. It is found that cylindrical plasma leads to radial deviation of solitons and modification of the growth rate associated with modulationally unstable wavepackets. The results are important to understand the nonlinear DIA and DA potential excitations in dense dusty plasmas where dust particulates modify the characteristics scales and affect the properties of stable and unstable wave modes.