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Black-Scholes Model for Finance

Thesis Info

Author

Amna Bibi

Supervisor

Fazeel Anwar

Department

Department of Mathematics

Program

BSM

Institute

COMSATS University Islamabad

Institute Type

Public

City

Islamabad

Province

Islamabad

Country

Pakistan

Thesis Completing Year

2015

Thesis Completion Status

Completed

Subject

Mathematics

Language

English

Added

2021-02-17 19:49:13

Modified

2023-01-08 02:17:15

ARI ID

1676720669719

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نسیم سخن اور صاحبِ کتاب

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حافظ محمد اکرم راشدؔ سے میرے دیرینہ اور دیر پا تعلقات ہیں ، یہ ایک علمی خاندان سے تعلق رکھتے ہیں۔ اِن کے بزرگوں کے دینِ اسلام کے میدان میں لگائے ہوئے شجر سایہ دار مسحور کن ماحول پیش کر رہے ہیں اور تشنگانِ علم کی پیاس بجھانے کے لیے دورانِ سفر طلباء کے راستے میں آنے والی جہالت اور کم علمی کی تپش اور دھوپ کو رفع کرنے میں مثالی کردار ادا کر رہے ہیں ۔ میں نے صرف کتاب اور صاحبِ کتاب کے بارے میں چند سطور ضبط تحریر میں لانے کے لیے اپنے قلم کو اذنِ خرام دینا ہے ۔موصوف قلم کے میدان کے شاہسوار ہیں ، ندائے حق کی ادارت ہو، منظور العارفین کی تدوین ہو ، یا منظورالعارفین ٹرسٹ کا قیام ہو، موصوف پیش پیش نظر آتے ہیں ،آپ ہمارے ادارے منظور العارفین ٹرسٹ کے ساتھ قلب و اذہان کی جملہ قویٰ کے ساتھ وابستہ رہے ہیں ۔ مُرور ایّام کے ساتھ پیرانہ سالی اور ضعف کا شکار ہو کر کچھ عرصہ سے گوشہ نشین ہیں تاہم تحریر سے عشق کی حد تک لگائو کی بنا پر کوئی نہ کوئی شاہ پارہ تخلیق کرتے رہتے ہیں ۔ آپ کالم نویس ہونے کے ساتھ ساتھ ایک عظیم خوش نویس بھی ہیں عارفوالااور اس کے مضافات میں خطاطی کے حوالے سے ان کا ایک نام ہے ۔ دنیوی اور دینی تعلیم کے امتزاج کے حامل ہیں اور اپنی ایک شناخت رکھتے ہیں ۔ سرکاری ادارہ میں رئیس مدرسہ کے فرائض سر انجام دے چکے ہیں ۔
مذہبی خدمات کے حوالے سے اِن کی خدمات مہر نیم روز کی طرح واضح ہیں ۔ مرکزی جامع مسجد -N بلاک عارفوالا کی امامت اور خطابت کے فرائض بحسن و خوبی سر انجام دے رہے ہیں۔صاحب ورع اور تقویٰ ہونا اِن کی...

عصر حاضر میں آرائش انسانی کے جدید سائنسی انقلابات اور اسلامی نقطۂ نظر

Every single thing made by Allah, the Creator of all things has its own essence of beauty and attraction to it. However, out of all the stunning creations of Almighty Allah, humans are the most superior creation which has the ability to gain knowledge. We, humans, have been given the power by Allah to explore the rest of his creations in nature and fully understand the beauty and functions of each and every aspect of it in order to take advantage of it. Islam is a religion based on nature and Shariah is a law which lays down rules for Muslims to follow which also allows us to move forward with the advancements in the world. It has a unique way of life for any person of any time to follow which cannot be found in any other religion. However, any development which takes place creates new problems and new obstacles which can only be manoeuvred by the researchers and scholars of that specific time who will decide the right use of that commodity and explain the commodity. This will allow the new invention to be utilised fully. Moreover, in this world many people want to look their best and feel their best and will be willing to go through many ways for their ideal look. With this desire, many jobs become associated with achieving this for people. Nonetheless, this leads to people putting their time, money and effort into something which can risk their entire life which can result in either an advantage or disadvantage. Moreover, they should know whether this is against their religious values. Those acts which cross your religious boundaries and are considered “haram”or not permitted are wrong. Thus, it is necessary for us to first consider whether it is crossing the boundaries and proving to be disadvantageous for you so that the wrong norms and values are not transmitted into the future generations.

Expression Analysis of Sonic Hedgehog in Breast Cancer and its Relationship With Metastasis

Expression Analysis of Sonic Hedgehog in Breast Cancer and its Relationship with Metastasis Involvement of Hedgehog pathway during embryogenesis and mammary development is well known. Salient members of this pathway include SHH, DHH, IHH, PTCH1, SMO and GLI1. Considering high prevalence and early onset of breast cancer among Pakistani population, reactivation of this developmental pathway is hypothesized. In the present study, expression profiling of Hedgehog pathway ligands (SHH, DHH, IHH), mediators (PTCH, SMO) and downstream effector (GLI1) in breast tumorigenesis was explored. The study was divided in two phases. The initial phase included screening of Hedgehog pathway molecules at mRNA and protein levels in Pakistani breast cancer patients. In the second phase, in-vitro models were generated for inhibition of SHH/GLI1 axis. Moreover, effect of SHH/GLI1 inhibition on EMT markers and metastatic cascade was investigated. In the first phase, expression of Hedgehog pathway molecules was evaluated using qRT-PCR and immunohistochemistry in tumor tissues (N=250) and adjacent noncancerous healthy tissues (N=250). SHH, DHH, PTCH1 and GLI1 were significantly overexpressed in tumors compared with respective controls. Significant correlation of SHH, DHH and GLI1 expression with advanced stage, grade, nodal involvement and distant metastasis was observed (p<0.05). Patients having high expression of SHH, DHH and GLI1 demonstrated poor overall survival in the cohort. Overexpression of SHH, DHH and GLI1 was observed to be significantly related with patients having early disease onset and pre-menopausal status. Moreover, Hedgehog pathway was frequently upregulated in luminal B or triple negative breast cancer affected patients. In addition, positive correlation was observed among aforementioned members of the pathway and Ki67 (r-value: 0.63-0.78) emphasizing their role towards disease progression. Expression of Vimentin and Snail was upregulated among SHH/GLI1 positive patients. Strong positive correlation of both Vimentin and Snail with SHH/GLI1 positive patients was observed. On the contrary, E-cadherin was downregulated in SHH/GLI1 positive patients and its correlation with SHH/GLI1 was also negative. xiii In the second phase, SHH knockout models were generated using CRISPR/CAS9 in MDA-MB-231 and MCF-7 cells. Additionally, both cancer cell lines were treated with GANT61 (GLI1 inhibitor) and its effect on cell viability and apoptosis was evaluated using CCK-8 and flow cytometry respectively. Effect of SHH knockout and GANT61 treatment was observed on EMT markers and Akt/ERK using qRT-PCR, western blot analysis and immunofluorescence staining. Invasion and migration assays were performed to investigate influence of SHH/GLI1 suppression on metastatic cascade. Treatment with GANT61 reduced cell viability (p<0.01) and induced apoptosis (p<0.01) in breast cancer cell lines. Expression of Vimentin and Snail was reduced in SHH knockout models and GANT61 treated cells. On the contrary, expression of E-cadherin was increased after inhibition of SHH or GLI1. Suppression of SHH/GLI1 axis also inhibited activation Akt/ ERK as well as reduced migration and invasion capacity in breast cancer cells. Based on these findings, SHH/GLI1 may be used as a prognostic marker in breast cancer patients. Moreover, inhibition of SHH/GLI1 axis provides a novel therapeutic target against aggressive breast cancer subtypes.