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U/U Expansion Method for Solitary Wave Solutions of Partial Differential Equations and System of Equations

Thesis Info

Author

Qaisar Shahzad Khan

Supervisor

Bashir Sadiq

Institute

Riphah International University

Institute Type

Private

Campus Location

Faisalabad Campus

City

Faisalabad

Province

Punjab

Country

Pakistan

Thesis Completing Year

2016

Thesis Completion Status

Completed

Page

vii, 78 . : ill. ; 30 cm.

Subject

Mathematics

Language

English

Other

English; Call No: 510 QAI

Added

2021-02-17 19:49:13

Modified

2023-01-06 19:20:37

ARI ID

1676712123623

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کینیڈی

کنیڈی
گذشتہ مہینے مسٹر کنیڈی کاقتل دنیا کاسب سے زیادہ الم انگیز واقعہ بھی ہے اور خصوصاً اس ملک کے حکمرانوں کے لیے سبق آموز و عبرت انگیز بھی! الم انگیز اس لیے کہ مسٹر کنیڈی اپنے دل ودماغ کے غیر معمولی اوصاف وکمالات کے باعث ایک نہایت وقیع اور بلند پایہ شخصیت کے مالک تھے۔اُن کے یہی وہ کمالات تھے جنھوں نے دوبرس کے اندر ہی کم عمر وجوان ہونے کے باوصف ان کو بین الاقوامی دنیا کاہر دلعزیز ہیرو اور لیڈر بنادیا تھا اور سبق آموز وعبرت انگیز! وہ اس لیے کہ ایک طرف دنیا کی سب سے زیادہ طاقت ورمتمول اور ترقی یافتہ حکومت کاجوان وکم سال سربراہ ہے جس کے لیے عیش وتنعم کی زندگی بسرکرنے میں نہ کوئی رکاوٹ ہے اور نہ اُس کے اسباب کی کمی ۔مگراس کے باوجود اپنے ملک کی مظلوم ومقہور اقلیتوں کی دادرسی کااُس نے جو عزم اوراعلان کیاہے اُس میں وہ اس درجہ سچا، پختہ اوراستوار ہے کہ اُس کی اپنی قوم سخت منحرف ہوکر اُس کی جان کی دشمن ہوگئی ہے لیکن اسے اس کی ذرا پروا نہیں، وہ جوکہتا ہے اُسے کرگزرتا ہے۔یہاں تک کہ اسی راہِ حق وصداقت میں وہ جان بھی دے بیٹھتا ہے اور دوسری طرف اس ملک کے حکمراں ہیں کہ اقلیتوں کے دستور ی حقوق کی حفاظت و نگرانی کے بلند بانگ دعوے کرتے ہیں مگر اکثریت جس کی حمایت اُن کے اقتدار کاسہارا ہے اُس کی ناراضگی کے ڈرسے بہت سے زبانی اور کاغذی وعدے خوابِ پریشاں سے زیادہ کوئی حقیقت نہیں رکھتے۔ وہاں فرض شناسی ہے اور یہاں خودغرضی۔ وہاں ایمان داری، حق گستری اوراس کے لیے جاں سپاری ہے اور یہاں بے ایمانی کوتاہ نظری اور بزدلی ۔ فاعتبرویااولی الابصار۔
[دسمبر ۱۹۶۳ء]

 

ڈاكٹر فضل الرحمن (م۱۹۸۸ء) کے آرا ء كا ایجابی اور سلبى پہلو

The government of General Ayub Khan (Former President of Pakistan) established an Institution in 1960, in the name of Idarah Tahqeeqat Islami (Islamic Research Institute). Dr, Fazlur Rahman, was the visiting professor at the institute remained on the rank of director of the year 1961 to 768 in seven years. And later, he serves as an advisor to the Islamic Ideology council. The writer who was published by the Institute of Islamic Research was the first editor of "Fikr-o - Nazar”. The scholars were considered as 'expertise of logic and philosophy' as 'interpretation of the Qur'an'. It is mentioned in the various verses of the Prophet (peace and blessings of Allah be upon him). The slaughtering of zakat in 'zakat' animal slaughtering 'basic laws and family planning' matters of marriage and Sunnah, such as the month of revelation, and their opinions have earned great reputation. And because of which they were accused of denying the heavenly nature of the Qur'an. Therefore, the first step towards Islamic thinking regarding the Islamic idea was to put an eye on Islamic law and religious beliefs on Islam. According to their plan, the difference between the Quranic verses and the verses and the laws of the law, is the difference. Regarding the meanings, his axis received: The beginning of the tradition and the meaning of 'the law of the law' is the word and the law. Islamic Laws' Principles Concernedly speaking about issues like Fiqh and Qa'as and al-Azai speak.

Pharmacological Rationale for the Use of Aegle Marmelos. L and Pyrus Cydonia. L in Cardiovascular Disorders

The crude extracts, fractions and isolated marmelosin were investigated to rationalize the therapeutic potentials in cardiovascular disorders. Heart and aorta were isolated from Wistar rat for working and Langendorff’s heart and aortic ring preparations. Preliminarily, Langendorff’s heart determined the following studies. Firstly, working heart was performed at fixed preload of 15 cmH2O and afterload of 80 cmH2O. Secondly, variable preload 5, 10, 15, 20 and 25 cmH2O was employed, whereas, afterload was fixed at 80 cmH2O. In Ca++ paradox; Ca++ free KH perfused the heart, afterwards, firstly normal KH, secondly normal KH plus Am.Cr and thirdly Ca++ free KH plus Am.Cr and normal KH plus Am.Cr. In Langendorff’s heart Am.Cr and Pc.Cr increased the left ventricle (LVP) and systolic pressures (SP). This determined the path to study in more detail. Am.Cr; exhibited biphasic effect on dP/dt(max) dose-dependently in working heart. Am.Cr increased the AoF and EF dose-dependently. Am.Cr increased the dP/dt(min), DP and EDP. The SV and CP were increased at higher doses. CE was decreased while SP, PASP and RPP were unaffected. In aorta Am.Cr inhibited PE and high K+-induced contractions in both +veEnd and -veEnd, showing VDCCs and ROCCs blocking effect and release of Ca++ from sarcoplasmic reticulum.Am.Cr shifted the Ca++CRCs to the left at lower and to the right at higher doses showing agonists and antagonistic effect on Ca++ channels. At variable preload the heart was pretreated by 3.0, 30.0 and 100 mg/mL of Am.Cr. The AoF, LVP and CVR were increased by acute preload reduction that followed by load-dependent increase. The CE was decreased dose- and load-dependently. The dP/dt(max) and HR were decreased, whereas dP/dt (min) showed dose- and load-dependent increase. The CO increased variably while PASP and MW were unaffected. In calcium paradox experiments; Ca++ free perfusion decreased the contractility whereas, Am.Cr increased the contractility whether it was added in Ca++ free or normal KH solution at various series of experiments. Aq.Fr.Cr decreased the dP/dt(max) and RPP significantly in working heart. It increased AoF, DP, CO and CP. The dP/dt(min) was reduced.Aq.Fr.Cr caused dose-dependent minimal reduction in CE. The EDP, SP, PASP, EF and SV were unaffected. Aq.Fr.Cr induced dose-dependent relaxation of PE- and high K+-induced contractions in +veEnd aortic rings. In -veEnd rings; it inhibits PE-induced contraction only, whereas in high K+-induced contraction Aq.Fr.Cr failed to relax. The cumulative addition to the L-NAME pre-incubated and PE pre-contracted +veEnd rings did not show relaxation. This explains endothelium-dependent vasorelaxation through NO/cGMP pathway. At variable preloads; pretreatment ofthe heart with 1.0, 10.0 and 30.0 mg/ml of Aq.Fr.Cr; increased the AoF, LVP and CVR by acute preload reduction while preload increment caused load-dependent increase. The dP/dt(max) and HR were decreased by acute preload reduction and was not affected by preload increase. The dP/dt(min) was decreased by acute preload reduction while increasing preload caused load-dependent increase. CE was decreased at all changes in preload. The PASP, MW and CO were minimally affected during preload changes. But.Fr.Cr increased dP/dt(max), dP/dt(min), AoF, SP, CP and CO in working heart. The PASP, EF, SV and RPP were decreased. CE was decreased significantly and dose-dependently. In aorta; But.Fr.Cr induced inhibitory effect in both +veEnd and -veEnd ring pre-contracted by PE and high K+. This shows blockade of ROCCs, VDCCs and release of Ca++ from sarcoplasmic reticulum. But.Fr.Cr at lower concentrations caused leftward and at higher concentrations rightward shift of Ca++ CRCs showing calcium channel agonists and antagonistic activities. At variable preload; the heart was pretreated by 0.01, 0.1 and 1.0 mg/mL of But.Fr.Cr. The AoF, LVP and CVR were increased by acute preload reduction and continued by increasing preload. The dP/dt(max) and dP/dt(min) were decreased by preload reduction and not affected by increasing preload. HR was decreased by acute preload reduction and continued during increase in preload. The PASP, MW and CE were decreased at all preloads. The CO was less affected. ISD Marm increased the AoF, CO and CP in working heart. The dP/dt(max) was decreased minimally while dP/dt(min) and HR were decreased significantly at higher doses. CE decreased dose-dependently. The SP, DP, PASP, EDP, EF and RPP were not affected. STD Marm reduced the CE and increased the AoF, CO, CP, SV and EF comparatively more than ISD Marm. The dP/dt(max), dP/dt(min), HR, SP, DP, EDP and RPP were reduced whereas SV was not affected. In aorta; STD Marm induced dose-dependent relaxation in both +veEnd and -veEnd PE precontracted rings. This was significant at higher doses in +veEnd rings. Whereas in high K+ precontracted +veEnd and -veEnd rings it showed insignificant effect. The cumulative addition to L-NAME pre-incubated and PE pre-contracted +veEnd rings it showed partial but significant dose-dependent relaxation. At variable preloads; pretreatment of the heart by 1µM, 10 µM and 100 µM of ISD Marm; increased the AoF, LVP and CVR by acute preload reduction while preload escalation showed load-dependent increase. The CO and MW were increased by acute preload reduction, whereas preload increment led to attenuation of CO and MW. The dP/dt(max), dP/dt(min), HR, CE and PASP were decreased by acute preload reduction and continued during preload increment. Thus, this study may rationalize the therapeutic potential of A.marmelos and P.cydonia possesses cardiotonic effect. The crude extract of A.marmelos, its fractions and isolated marmelosin exhibited numerous effects on the heart and aortic muscle mediating through multiple pathways that pointed out that though crude extract showed most of the activities, but it appears as no single compound can be a true representative of the plant. Because, it constitutes multiple compounds with different properties which can be exploited for various therapeutic purposes. Further studies would establish the clinical significance of A.marmelos in the management of cardiovascular disorders and promising chemical agent may be identified.