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Fourier Series and Orthogonal Functions

Thesis Info

Author

Saad Farooq

Supervisor

Saqib Zia

Department

Department of Mathematics

Program

BSM

Institute

COMSATS University Islamabad

Institute Type

Public

City

Islamabad

Province

Islamabad

Country

Pakistan

Thesis Completing Year

2018

Thesis Completion Status

Completed

Subject

Mathematics

Language

English

Added

2021-02-17 19:49:13

Modified

2023-01-06 19:20:37

ARI ID

1676720688473

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33. Al-Ahzab/The Allied Factions

33. Al-Ahzab/The Allied Factions

I/We begin by the Blessed Name of Allah

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

33:01
a. O The Prophet!
b. Remain conscious of Allah - The One and Only God of everyone and everything, and
c. do not yield to pressures brought about by the disbelievers and the hypocrites.
d. Surely Allah is All-Knowing of what they say and what their motives are and All-Wise.

33:02
a. Instead, follow what is being revealed on to you from your Rabb - The Lord.
b. Surely Allah is All-Aware of whatever you do: your deeds, dealings, and motives.

33:03
a. And trust Allah.
b. And Allah is Sufficient for you as a Guardian - to look after your affairs.

33:04
a. Allah has not placed two hearts in any person’s body.
b. And just as HE has never made your wives - whom you declare to be as your mothers’ backs - your biological mothers,
c. And, so too, HE has never made your adopted sons to be your biological sons.
d. These are merely phrases you utter from your mouths,
e. whereas Allah Speaks the truth in this and all matters.
f. And thus HE Guides you along the way of truth.

33:05
a. As for your adopted children, address them by the names of their biological fathers.
b. That is more just in the Sight of Allah.
c. But if you do not know the names of their biological fathers, then they are your brethren in faith and your protégés - so observe the due relationship within that social framework.
d. However, you will not be blamed for...

تاریخ کبیر میں امام بخاری کا رواۃ پر تنقید کے اسلوب کاجائزہ

Muḥadithīn have played a dynamic role in the preservation and compilation of Ḥadīth of the Prophet (SAW). Among them the contribution of Imam Bukhārī is unavoidable and remarkable in the field of Ḥadīth and its sciences. Since, he is known “Hafiz and Compiler” and considered as “Imam” and “authority” in the field of both higher and lower criticism. His book "Al-Tārīkh al Kabīr" (08 volumes) is considered as one of the ancient books in field of Ḥadīth and its sciences. This paper aims to describe the methodology of Imam Bukhārī in Al-Tārīkh al Kabīr. He described the biography of thirteen thousand seven hundred and seventy nine only (13779) in alphabetic order. Although his methodology was to mention names of the narrators alphabetically, but in respect with the Prophet (SAW), he gave place to eleven narrators among the companion whom names were started with the names of “Muhammad”. In the Methodology of Imam Bukhārī (RA), it is found that either the narrators are rejected or given authenticity, on the basis of not only his own examinations but he relied on the sayings of other Muḥadithīn as well. It is also pertinent to mention that he awarded degree to a little number of the narrators while left over most of the narrators undecided, because the main objective of the book was to portray the biographies of the narrators rather to make analysis of all the narrators.

Yield Forecasting of Wheat Triticum Aestivum L. for Different Irrigation and Nitrogen Levels Using Simulations and Satellite Imagery

Accurate and near real time wheat yield forecasting is important for policy makers and agricultural markets of Pakistan. Efficient and less labour intensive techniques of yield forecasting are required to support stakeholders. Wheat productivity depends upon irrigation water, fertilizer availability and rainfall in Pakistan. The per capita per annum water availability in Pakistan has reduced to less than 1000 m3 and is expected to reach severe scarcity level during next decade. Irrigating crops without measuring water and proper management practices is not a viable option anymore. The current study was conducted to address both above mentioned issues at Post-Graduate Agricultural Research Station (PARS), University of Agriculture Faisalabad for two years during 2012-2013 and 2013-2014. Reducing the amount of irrigation volume was expected to affect nitrogen availability. Therefore, response of varying levels of nitrogen was also studied for reduced volume of water per irrigation. There were four irrigation levels (control with 300 mm water for whole growing season, 80% of control, 60% of control and 40% of control) and four nitrogen levels (60,120,180 and 240 kg ha-1). The experiment was laid out in randomized complete block design with split plot arrangement. Irrigation treatments were randomized in main plots while nitrogen was kept as sub-plot factor and each treatment was replicated thrice. A model for forecasting wheat yield before time of harvest was developed and volume of water per irrigation was also optimized based on field experiment data. The results revealed that reducing irrigation volume from control to 80% did not reduce crop yield significantly. The response of nitrogen for 80% of control irrigation volume was same as for control treatment. Maximum wheat grain yield (4916 kg ha-1) was obtained with control irrigation and 180 kg ha-1 nitrogen (4743 kg ha-1) and it was at par with 80% of control irrigation with 120 kg ha-1 nitrogen (4461 kg ha-1) and 180 kg ha-1 nitrogen (4743 kg ha-1). To optimize both factors, DSSAT-CERES-Wheat was calibrated and evaluated. CERES-wheat model predicted the optimum level as 250 mm volume of water with 160 kg ha-1 nitrogen for whole growing season of wheat. The response of grain yield to nitrogen for different irrigation levels was quadratic. Quadratic equations predicted 240 to 242 mm water and 185 to 187 kg ha-1 nitrogen as optimum for whole growing season of wheat. The same experimental data was used for developing yield forecasting model of wheat before the time of harvest from Normalized Difference Vegetation Index (NDVI). Three satellites (QuickBird, Pleiades and GeoEye-1) and handheld Green Seeker were used to calculate NDVI. Random Forest was used to for modeling using grain yield as dependent variable while weather elements, irrigation, nitrogen and NDVI as independent variables. DSSAT-CERES-Wheat, calibrated on experimental data of 2012-13 was also used to forecast yield for 2013-14. The mean error percentage of grain yield prediction was less than 10% and 17.1% for remote sensing and CERES-Wheat, respectively. Random forest was further used to forecast yield of different districts of Punjab and Punjab province using MODIS NDVI and weather elements as independent variables in eight different ways. RMSE of the forecast results of the whole Punjab Province was 147.7 kg ha-1 and 148.7 kg ha-1 with mean error less than 5% using average and generic random forests, respectively. Forecasts of individual districts showed R2 of 0.95 with RMSE of 175.6 kg ha-1 and mean error of 5.86%. It is concluded from the study that reducing irrigation volume by 20% has no significant effect on grain yield of wheat and was helpful to save water. Near real time wheat yield forecasting using satellite imagery and crop models would be helpful for policy makers and stakeholders. Remote sensing using NDVI with random forest methodology and DSSAT-CERES-Wheat were good tools to predict wheat yield and both could be used in Pakistan.