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Some Iterative Methods for Solving Nonlinear Equations

Thesis Info

Author

Farooq Ahmed Shah

Supervisor

Muhammad Aslam Noor

Department

Department of Mathematics

Program

MS

Institute

COMSATS University Islamabad

Institute Type

Public

City

Islamabad

Province

Islamabad

Country

Pakistan

Thesis Completing Year

2008

Thesis Completion Status

Completed

Subject

Mathematics

Language

English

Added

2021-02-17 19:49:13

Modified

2023-01-06 19:20:37

ARI ID

1676720752182

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اب انھیں ڈھونڈ چراغِ رخِ زیبا لے کر

اب انہیں ڈھونڈ چراغِ رخِ زیبا لے کر

آغا شورش کا شمیری ایک دن بھٹو صاحب کے پاس گئے تو بھٹو مرحوم نے کہا :آکسفورڈ یونیورسٹی میں میری لڑکی اور لڑکا دو نوں پڑھتے تھے ۔آپ بھی اپنی لڑکی اور لڑکے کو بھیج دو ،حکومت وظیفہ دے گی ۔

شورش نے کہا میں مشرقی طرزکا آ دمی ہوں ۔مغربی تہذیب میں اولاد کو بھیج کر خراب نہیں کر نا چاہتا ۔

تو بھٹو مرحوم نے کہا کہ شادمان کا لونی ،لاہورمیں دو پلاٹ پڑے ہیں ،تم کم ریٹ پر حکومت سے خرید لو اور ایک کو بیچ کر اپنا پلاٹ بنا لو ۔تو شورش نے جواب دیا :جناب سر چھپانے کے لیے جگہ موجود ہے ۔میں کوٹھی نہیں بنا نا چاہتا ۔

شورش اپنے گھر واپس آئے اور سارا قصہ اپنی بیٹی کو سنا دیا ۔تو بیٹی نے کہا کہ :ابو بھٹو صاحب پلاٹ دے رہے تھے تو لے لیتے ،سرکاری زمین ہے ہم پیسے جمع کرا دیتے ہیں بات صرف اتنی ہے کہ وہ کوئی اور لے جائے گا ۔بس ہمیں رعایت ہی مل جاتی ۔آپ نے ہمارے مستقبل کے ساتھ زیادتی کی ہے ۔

تو جواب میں شورشؒ نے فرمایا کہ :دنیا یہیں رہ جائے گی ۔میں بھٹو صاحب سے ایک ایسا تحفہ لے کر آ یا ہوں جو قبر میں مجھے کام آئے گا بس یہ بات کہنی تھی ۔

تحریک ختم نبوت کے اکابرین بھٹو مرحوم اور شورش ؒ کے درمیان کی گفتگو سے بالکل ہی لا علم تھے ۔کچھ ہی دنوں بعد شورشؒ بیمار ہوئے اور انتقال فر ما گئے ۔جنازے میں حضرت مفتی محمود صاحب ؒ مولانا غلام غوث ہزاروی ؒ ،مصطفی کھر ،کوثر نیازی ،معراج خالد ،حفیظ پیرزادہ اور دیگر حضرات شریک...

Running Musharakah Product of Islamic Banks: An Alternative of Running Finance

Islamic banking system is growing day by day. The new era of Islamic banking is very successful as new products are being introduced by Islamic banks to cater the demands of customer under Shariah guidelines, there was demand of a product for working capital as an alternative to the conventional product of running finance. Running Musharakah Product has been introduced as substitute to Running Finance Product. In this paper the concept of Running Finance as well as Running Musharakah is described, the practical steps of running Musharakah are also illustrated to examine the viability of the product.

Export-Led Growth and its Supply Determinants in Pakistan: A Disaggregated Empirical Analysis

This study is an attempt to investigate the export-growth nexus and the impact of supply-side factors on the export performance of Pakistan at a disaggregated level. It has identified major export categories of Pakistan and constructed a novel time series data set of each of these categories from 1971 to 2014. The principal objective of the study is to examine the impact of disaggregated exports on economic growth and determine how much of the variance in economic growth can be explained by various export categories in Pakistan. It allows us to classify exports in terms of their contribution to the long-term economic growth of Pakistan. In addition, the study also discovers the role of prices, cost, production capacity and domestic demand pressure in determining Pakistan’s exports. Using autoregressive distributed lag (ARDL) model, the empirical results show that there is a significant long-term equilibrium relationship between output growth and aggregate, and disaggregated export categories. Moreover, the long-run dynamics indicate that aggregate, manufactured and services exports have significant positive effects on the long-term output growth while primary and semi-manufactured exports showed insignificant effects on non-export GDP in the long-run. However, with further decomposition, the analyses of primary export categories show an individual impact on non-exports GDP which is positive and significant. The long run growth impact of food exports such as rice, fruits, fish and fish preparation is stronger compared to raw materials exports. In addition, the estimation results also indicate that all sub-categories of manufactured exports have a significant positive influence on the non-export GDP in the long-run though with few qualifications. However, the value-added manufactured goods exports have the potential to contribute more to the long-term aggregate output in Pakistan’s case. The results of the Granger causality test based on vector error correction model also confirmed that aggregate, manufactured, and services exports Granger causes the non-export GDP, while no causal link is found from primary and semi-manufactured exports to non-export GDP in both the short- and the long-run. In the case of sub-categories of primary and manufactured exports, the findings showed a causal link from only food items and value-added manufactured exports to non-export GDP in both the short- and the long-run. Similarly, the variance decomposition analysis also confirmed that manufactured and services exports have significant effects on non-export GDP, while shock in primary and semi-manufactured exports are found to be insignificant in explaining variation in non-export GDP. However, when primary and manufactured exports divided into sub-categories, then the shocks in value-added exports and food items exports are found to be significant in explaining movement in non-export GDP. To sum up, the results of all three tests suggest that export-led growth hypothesis cannot be rejected for Pakistan in most cases in both the short- and the long-run. However, the services, food items, and value-added manufactured exports are much more important for the output growth in the case of Pakistan. With respect to the determinants of export supply, the empirical results based on ARDL model show a cointegrating relationship between aggregate exports, disaggregated export categories and other important variables under study. In addition, long-run estimates indicate that aggregate exports are highly elastic to changes in prices and production capacity while inelastic to changes in the cost of production and domestic demand. When aggregate exports are disaggregated into several primary and manufactured export categories, however, major export categories respond differently to changes in various factors of export supply. For instance, the relative prices have a larger impact on the export performance of raw materials and value-added manufactured products. Similarly, the cost of production has higher effects on the growth of value added manufactured and cotton waste exports. On the contrary, production capacity and domestic demand pressures have significantly influenced the export supply almost all manufactured and primary export categories in the long-run. In the short-run, the relative price, cost of production and production capacity showed mixed effects on the export supply of majority primary and manufactured export categories, while the domestic demand pressure hypothesis is valid almost in all cases of primary and manufactured export categories in the short-run. This implies that the export supply almost of all primary and manufactured export categories significantly depends on the domestic demand pressure in the short-run in Pakistan’s case. Apart from this, the study also empirical verified that that domestic demand pressure has a negative and significant effect on export supply at both aggregate and disaggregated levels, implying that along with traditional factors, domestic demand pressures are also relevant for modeling the export supply for Pakistan at both aggregated and disaggregated levels. Finally, the study concludes that export-led growth hypothesis is relevant to Pakistan. However, there are large differences in the effects of exports on non-export GDP across various export categories. Services, food items, and value-added manufactured exports can contribute more to the aggregate output in the long-run in Pakistan’s case. Therefore, it is suggested that Pakistan should pursue the export promotion policy with a greater emphasis on services, food items, and value-added manufactured exports to contribute sufficiently to the economic growth of the country in the long run.In addition, the disaggregated analysis also clarifies that the factors determining the export supply have changed over time and across the various categories of exports.Hence, the government must revisit the export policy and make the new policy in line with new sectoral realities in order to expand the export sector of the country as well as to ensure the economic prosperity of the country on a sustainable basis.