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Fucnctional Differential Equations in Cell Growth Models

Thesis Info

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Author

Humiara Aziz

Institute

Virtual University of Pakistan

Institute Type

Public

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2019

Thesis Completion Status

Completed

Subject

Software Engineering

Language

English

Link

http://vspace.vu.edu.pk/detail.aspx?id=287

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676721014811

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A functional di erential equation for growth, ssion and loss of cells struc- tured with size is presented.Size refers to the content of DNA.Partial di er- ential equation explain the asymptotic functioning behavior of cell -growth models,are taken in to account.Here we discussed the symmetric fur- ther- more the asymmetric division of cell.Through probabilistic approach we ob- tained simple proof of existence of the steady size distribution and derivation of functional equation.We then move along the study of binary asymmetric cell division.Asymmetric cell division also takes to initial and boundary con- dition problem this relates to linear partial di erential equa- tion with two functional terms,which have order one.We consider the asymmetric binary cell division also show that the solutions for partial di erential equation converge to the separable solutions for large time.
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مولانا شاہ بدر الدین

مولانا شاہ بدرالدین

ابھی گزشتہ مہینہ کے معارف میں ہم نے حضرت امیر شریعت صوبہ بہار اور امارت شرعیہ صوبہ بہار کا تذکرہ کیا تھا، خیال میں بھی نہ تھا کہ اس کے ایک ہی مہینہ کے بعد ہم کو حضرت ممدوح کی دائمی مفارقت کا ماتم کرنا پڑے گا، حضرت مولانا شاہ بدرالدین سجادہ پھلواری اس عہد کے جنید و شبلیؒ تھے، ان کا زہد و ورع، نزاعت و ارتقاء، علم و عمل، صورت و سیرت، ہر چیز نمونۂ سلف تھی، کم و بیش چالیس برس تک یہ علم و عرفان کی شمع صوبۂ بہار میں روشن رہی اور اس کی روشنی دور دور تک پھیلتی رہی، ان کے شب و روز کے چوبیس گھنٹے ذکر و فکر اور مطالعۂ کتب کے سوا اور مشاغل میں کمتر صرف ہوتے تھے، ان کی نشست گاہ ایک کتب خانہ تھی، ان کے چاروں طرف کتابوں کا انبار لگا رہتا تھا اور اس کے بیچ میں یہ زندہ کتب خانہ جلوہ فرما رہتا تھا، اس عہد میں یہی ایک ہستی تھی جو ظاہر و باطن، علم و معرفت، حقیقت و شریعت کا مجمع البحرین تھی اور جس سے ہزاروں اور لاکھوں علم و معرفت کے پیاسے سیراب ہوتے رہتے ہیں، پھلواری کا سجادہ اس بزرگ ذات کی رونق افروزی سے چشمۂ خورشید تھا، افسوس کہ یہ آفتاب اب ہمیشہ کے لئے ڈوب گیا۔
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اردو میں عربی الفاظ کا املا: اختلافی مباحث کا تجزیاتی مطالعہ

Arabic language and literature has influenced Urdu language and literature in terms of fonts, grammar as well as orthography. Linguists have different opinions about orthography of Arabic words in Urdu. Some of them hold favorable opinion, some have opined against it, while some of the linguists have maintained a balance point of view in terms of orthography. The holy Qur’an is Arabic and perhaps that is the reason Muslims have spiritual affinity with Arabic. But language also sacred the way religion is? Can we relate languages with religion? Moreover, sociolinguistics cannot be ignored and that linguists provides concrete notions based on based on scientific study of languages. In this article, the author has analyzed and discussed the contradictory debates of different academic and applied in Urdu orthography of Arabic words in Urdu.  

Exploring Possibilities of Creating Gender Equitable Learning Environment in an Early Childhood Classroom

This study explored the possibilities of creating a gender equitable learning environment in one of the Early Childhood Education (ECE) classrooms in Karachi, Pakistan through a Collaborative Action Research (CAR). The actions, reflections and retrospections were guided by the Feminist poststructuralist theoretical lens throughout the study. Two ECE teachers and 43 five year old (23 girls and 20 boys) children participated in this collaborative action research which was conducted in a non-for-profit private school. Various data collection strategies were used throughout the study. This included in-depth interviews, dialogues, observations, pre and post observation discussions with the teachers and reflective dialogues during and after drawings, stories, play, games with children. The participating teachers and I maintained reflective journals as part of our commitment to reflexivity during the study. An analysis of the discourses and discursive practices of participating ECE teachers and children revealed that initially both the groups positioned themselves within the essentialist discourse of gender and viewed gender as part of biological sex determinism. However, feminist poststructuralist methods such as deconstruction through reading and discussing literature, dialogues, critical actions and reflections helped the participating ECE teachers to expand their theoretical and practical repertoire regarding gender equity in early childhood. This enabled the teachers to disrupt the processes of promoting stereotypical masculine and feminine traits and oppressive gender relationships among children in the classroom. Cross case analysis of the five focused children revealed that collaborative efforts, critical actions and reflections enabled us (teachers and myself) to destabilize the hegemonic ways of being boys; deconstruct femininity and celebrate gender risk taking among both girls and boys. Hence, the study indicated possibilities for transforming the classroom learning environment in the context of ECE in Pakistan. The cyclical process of critical actions and reflections in the study revealed that a combination of child initiated and teacher/researcher led activities worked as appropriate pedagogical strategies to create a gender equitable learning environment. The strategies such as storytelling, dramatization of stories, opportunities of cross gender play, group discussions, dialogues and conversations about gender were particularly illuminating for effectively engaging young children inside and outside the classroom. The research process further revealed that teachers' and children's gender discourses were highly influenced by the complex intersection of their multiple identities. Therefore, the study emphasized the importance of closer bonds with children's families to strive for transformational changes in children's feeling, thinking and practicing of gender differently in the patriarchal