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Generalized Exponential Estimator for Multiphase Sampling in the Presence of Non-Response Using Multi Auxiliary Variables

Thesis Info

Author

Irsa Zafar

Supervisor

Zaheer Ahmad

Institute

Allama Iqbal Open University

Institute Type

Public

City

Islamabad

Country

Pakistan

Thesis Completing Year

2012

Thesis Completion Status

Completed

Page

105 .

Language

English

Added

2021-02-17 19:49:13

Modified

2023-01-06 19:20:37

ARI ID

1676710103661

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49. Al-Hujurat/The Residential Rooms

49. Al-Hujurat/The Residential Rooms

I/We begin by the Blessed Name of Allah

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

49:01
a. O The Faithful!
b. Do not put your opinions ahead of that of Allah and HIS Messenger.
c. Rather, be mindful of Allah in awe, reverence, and piety,
d. for Allah Listens to your sayings, and Knows everything of your intensions and behavior.

49:02
a. O The Faithful!
b. Do not raise your voices above the voice of The Prophet Muhammad,
c. and do not be loud to him in speaking like the loudness of some of you to others, lest your
good deeds be wasted for a reward without your even realizing it.

49:03
a. Surely, those who lower their voices in the presence of Allah’s Messenger, those are the ones whose hearts Allah has chosen – after testing - for reverence and righteousness.
b. For them is going to be Allah’s forgiveness and a great reward: Paradise.

49:04
a. Surely, those who call you aloud - O The Prophet - from outside your residential rooms, most of them do not have any sense of manners.

49:05
a. And it would indeed have been better for them if only they had waited patiently for you to come out to them and met them,
b. Yet Allah is Ever-Forgiving to those who were unaware of these manners, Most Merciful
to them too when they become aware of it.

49:06
a. O The Faithful!
b. If a known troublemaker comes to you with some news/information, then investigate it and ascertain its truth before you share it with others and act...

حالات و زمانہ کی رعایت سے متعلق جمہور فقہاء کرام کی تصریحات (عصر حاضر کے تناظر میں ایک مطالعہ)

Human life is the subjective of change with the changing circumstances. If we look at the condition of our late grandfather or great – grandfather and look at the contemporary situation; it will not be difficult to understand this change. The rules about some important issues had been changed with the passage of time. In the initial descendants of Adam the marriage of brothers and sisters was allowed, after the flood of Noah, due to the scarcity of animals, the meat of all kinds of animals was allowed, two sisters were married to Hazrat Yaqub (A.S) at the same time, but the rules had been reversed afterwards. Even in the time of the Holy Prophet and the rightly guided caliphs, such changes took place and they were associated with the changing conditions. Initially it was banned to visit the graves and the sacrificial meet was not allowed to keep for more than three days and it was mandatory upon the women to attend the congregational prayer but afterwards the permissions were granted contrarily. Fortunately, we have a body of jurisprudence in the light of which not only contemporary issues can be solved but also guidance can be provided for the future. Our leading Jurists, who are followed, have done a remarkable job in this regard. The following article reviews the teachings of the three jurists, namely Imam Shafi’i, Imam Malik, and Imam Ahmad ibn Hanbal and teachings of their glean jurists. It will make clear that under changing circumstances these jurists seemed to agree on change. Therefore, by using the efforts of these jurists, we can try to resolve the problems of our contemporary changes and requirements throughout the Muslim World.

Analysis and Application of Optimal Homotopy Asymptotic Method and the Use of Daftardar- Jaffery Polynomials

In this thesis, we use the standard optimal homotopy asymptotic method for the analytical solution of higher order ordinary differential equations with two or multi- point boundary conditions, a nonlinear family of partial differential equations with an initial condition and Integro-differential equations. The results obtained are compared with the results obtained by the application of Adomain decomposition method, homotopy perturbation method, variational iteration method, differential transform method and homotopy analysis method etc. The optimal homotopy asymptotic method uses a flexible auxiliary function, which controls the convergence of the solution and allows adjustment in the convergence region where it is needed. Moreover, the procedure of this method is simple, clearly well-defined and the built- in recursive relations are explicitly worked out for easy use. Numerical results obtained by the optimal homotopy asymptotic method reveal high accuracy and excellent agreement with the exact solutions. Apart from the application of optimal homotopy asymtotic method, we develop a new scheme by using Daftardar-Jafari polynomials in the homotopy of optimal homotopy asymptotic method to solve nonlinear problems more effectively. This scheme is almost as simple as the optimal homotopy asymtotic method but its results are more accurate than the usual optimal homotopy asymptotic method. To show the effectiveness of this scheme, we solve different bench mark problems from literature and compare the results with those obtained by the standard optimal homotopy asymptotic method. To determine the convergence control parameters of the auxiliary function, two well known methods are followed: The Least squares and the Galerkin methods. We also explore and use a variety of the forms of auxiliary functions that results more accuracy and shows flexibility and reliability of the methods. For symbolic computation, we use Mathematica 7. The work presented in chapters 2, 3 and 4 of this thesis has been published in different reputed international journals and the work presented in chapters 3, 5, 6 and 7 is submitted for possible publication. The details of published/submitted work are included in the list of publications.