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Some Subclasses of Analytic Functions Related With the Generalizations of Functions With Bounded Boundary Rotation

Thesis Info

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External Link

Author

Bukhari, Syed Zakar Hussain

Program

PhD

Institute

COMSATS University Islamabad

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2011

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/1564

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727210619

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Some Subclasses of Analytic Functions Related with the Generalizations of Functions with Bounded Boundary Rotation Geometric Function Theory on broad spectrum mostly deals with the geometric properties of univalent, multivalent, meromorphic functions etc. and Theorists paid much of their attention to the classes of these functions. Various subclasses of analytic functions related with the Carathéodory functions along with their generalizations were studied systematically in various aspects in the literature of the subject. The main focus of this study is to define certain new subclasses of analytic functions related with the functions of bounded boundary rotation and their generalizations. We use the idea of convolution and subordination along with the concepts of bounded Mocanu variation, Robertson functions, multiplier transformations etc. in defining these classes of analytic as well as multivalent functions. We also investigate and explore these classes and study various results like coefficient bounds, radius problems, inclusion results, integral and convolution preserving properties etc. and their relationships with the previously known results.
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ارادھنا(کرونا وائرس کے تناظر میں)

ارادھنا
(کرونا وائرس کے تناظرمیں)
اے خالق عصر۔۔۔اے مالک ’’کن‘‘۔۔۔!
مسجدوں کے دروازے بند ہیں
مندروں میں ہُو کا عالم ہے
آنسوئوں سے بھیگی صدائوں میں!
قاتل ہوائوں میں!
بچے گلیوں میں نکلتے نہیں۔۔۔کرفیو کا نفاذ بھی نہیں
اہلِ زباں۔۔۔حسن بیاں کے پھول کھلتے نہیں
اے خالق ارض و سما۔۔۔!
عنکبوتی تاروں کی طرح وبا کی موجودگی میں!
اسلوب کنعان میں ڈوبی جوانیاں،
موج زلیخا کی دلفریب روانیاں۔۔۔!
روایاتِ اذیت سے ڈرتے ہوئے گھروں سے نکلتی نہیں
اے ازل کے مالک۔۔۔اے ابد کے خالق۔۔۔!
یہ دنیا تیری ہی بنائی ہوئی ہے
جس کے سر پر وبا موت بن کے چھائی ہے
نشاط روح، سرور ازل ، وعدئہ اول کو یاد کرتے ہوئے!
شبنمی گلابوں پر اُداسی چھائی ہوئی ہے
کوئلیں ، فاختائیں اور عندلیبانِ چمن۔۔۔!
نہ جانے کن گمنام جزیروں کی طرف نکل گئی ہیں
اے رب دو جہاں۔۔۔کچھ معلوم نہیں
رحم فرما ۔۔۔رحم فرما ۔۔۔اے حافظ حفیظ رحم فرما
بہلول مسکراتے ہوئے بولا۔۔۔ اچھا تم نثری نظم لکھتے ہو۔ عہدِحاضر کی اک معروف شخصیت جسے ریاض مجید کہتے ہیں۔ وہ اسے نثم کے نام سے یاد کرتا ہے۔ اس صنف کے لیے دونوں نام بہتر ہیں۔ لیکن میں ’’نثم‘‘ کو ذاتی طور پر پسند کرتا ہوں جو اس نام کو پسند نہیں کرتے ، نثری نظم پر بضد ہیں ۔مجھے اُن سے بھی اختلاف نہیں۔
ادبی دنیا میں اک مندائیت کی شکل میں فرقہ ہے جو اس صنف کو آج بھی نہیں مانتا۔
تم جانتے ہو۔۔۔مندائیت کیا ہے؟
میں نے نفی میں سر ہلاتے ہوئے جواب دیا، اور خاموش رہا۔ کیونکہ بہلول دلچسپ شخصیت کا مالک تھا اور میں اُسے صرف سننا چاہتا تھا ، کہ وہ کیا کہتا ہے۔
اُس نے میری طرف دیکھتے ہوئے ،بولنا شروع کیا۔۔۔!
مندائی ایک فرقہ ہے۔ جو آدمؑ ،شیثؑ ، نوحؑ، سامؑ اور ادریسؑ کو مانتا ہے۔
یوحنا اصطباغی...

Anatomy & Surgery: A love hate relationship

Introduction: Anatomy is still taught in medical schools as a basis for studying pathophysiology and surgery. Lack of integration of basic and clinical disciplines reduced teaching hours, and poor teaching methodologies have a significant effect on anatomical knowledge and medical education standards. Objectives: To evaluate the perspectives of undergraduate students of MBBS, fresh MBBS graduates, teaching faculty of anatomy, and consultants on the importance and reconstruction of the anatomy curriculum. Materials & Methods: A total of 600 subjects participated in this cross-sectional study. A feedback form was used to collect data regarding time allocation, clinical relevance, integration, and clear viewpoints in basic histology, embryology, and gross anatomy. The form included free text, binomial, and 5-point Likert scale replies. Results: Analysis of the results revealed that all stakeholders universally preferred integrated anatomy teaching throughout the academic years of medical school instead of demanding block during the early two years. According to the study, students experienced inadequacies in their anatomical knowledge when they started their clinical training. Conclusion: This study contributes further to the ongoing discussions in anatomical sciences education by revealing that new doctors believe that anatomical instruction should be prioritized regardless of their career goals.

Strategies for Enhancing the Quality and Shelf Life of Mango Mangifera Indica L. Fruit Grown under the Environmental Conditions of Dera Ismail Khan

The mango fruit not only has wonderful taste, flavor and nutritional values but also has anticancer and anti-viral activities. It is therefore, very popular and is recognized as king of the fruits. Mango fruit is also one of the cash crops of Pakistan that stands at 5 th position among the main mango producing countries. However, its pre and postharvest wastage is quiet high due to short shelf life and vulnerable to various microorganism. Therefore, the objective of this work was to prolong the shelf life and to improve the quality of the fruit by applying various strategies. For the purpose two commercial varieties of mango namely, Langra and Samar Bahisht Chaunsa were selected for the study. The impact of controlled atmosphere ripening was explored by harvesting the fruit at hard green stage and stored at 20, 30 and 40°C till ripening. The results obtained for various quality parameters (QP) as well as shelf life of the fruit were compared with the fruit ripened at the tree (under normal conditions). It was observed that the tree ripened fruit was better in quality than the fruit ripened at different storage temperature after harvesting. The fruit took longer time for its ripening at the tree compared to storage at 30 and 40°C, irrespective of the variety. The shelf life was longest for the mangoes stored at 20°C compared to others, including tree ripened fruit. However, the waste percent was highest at tree ripened fruit as compared to stored fruit, irrespective of temperature and variety. These parameters were significantly different in most of the cases under the limit P < 0.05. xxii The results obtained for various quality parameters of the fruit harvested at hard green stage of maturity from different (orientation) side of the tree East, West, North and South showed that the quality was best and waste percent was lowest for the fruit harvested from south (sun exposure time for the fruit was maximum) orientation of tree; the shelf life was longer and weight loss percent was lower for North direction compared to others, irrespective of the variety and storage temperature. The values of QP for the fruit harvested from South were significantly different from other treatments in most of the cases under the limit P < 0.05. The fruit was harvested three (6.30 am , 1.30 pm and 8.30 pm) times a day and was stored at 20, 30 and 40°C till ripening. It was concluded that the quality of the ripened fruit was highest for 8.30 pm harvest time and stored at 40°C. The fruit harvested at 6.30 am and stored at 20°C had lowest quality and weight loss but longest shelf life, whereas the fruit harvested at 1.30 pm and stored at 40°C had shortest shelf life and highest weight loss, irrespective of the variety. On the other hand, the waste percent was highest for fruit harvested at 1.30 pm and 20°C storage temperature and lowest for 6.30 am harvest time and stored at 30°C, irrespective of the variety. However, the quality and the shelf life were improved by coating the fruit with calcium chloride, respective of harvest time plus storage temperature and irrespective of the variety. The impact of harvest stages and storage conditions over the postharvest quality and shelf life of mango fruit was explored by measuring the QP for the fruit harvested at 80 (early stage), 95 (mid stage) and 110 (late stage) days after the fruit setting and stored at three different storage temperature showed a significant impact over the quality characteristics. xxiii The waste percentage, weight loss, pH, total soluble solids, carotenoids and total sugar were increased with the storage time/ ripening process, irrespective of maturity stages; while the percentage of acidity and vitamin-C was decreased with storage time. The total sugar contents were highest in later stage whereas, vitamin C and acidity were highest in fruit harvested at early stage whereas; the waste percentage was lowest for mid stage harvest. The weight loss was higher and shelf life was longer for early stage harvest. The ripening rate increased and the shelf life decreased with rise in storage temperature. The total soluble solids, sugar contents and carotenoids had positive correlation with the skin color, irrespective of stage, variety and temperature. The contribution of cooling of the fruit towards the enhancement of quality and prolonging the shelf life was explored by harvesting the fruit at hard green stage of maturity and maintaining at 15 ○ C (by keeping in cold water and/ or in cold air) for different time periods. The fruit was then stored at 20, 30 and 40 o C till ripening. The quality parameters obtained were correlated with pre-storage cooling treatment. It was concluded that the impact of heat removed of the fruit was significantly different in most of the cases under the limit of P < 0.05. It was also observed that the removal of heat from the fruit enhanced the quality, prolongs shelf life and minimize wastage, irrespective of the variety and storage temperatures. The quality of mango fruit was investigated as related with pedicle (stalk) lengths of the fruit. The fruit was harvested at hard green stage of maturity with 0.5, 2.5, 4.5 and 6.5cm pedicle (stalk) lengths and stored at 30 ○ C till ripening. The result showed that the fruit harvested with 4.5cm stalk length was better among the investigated treatment for quality and shelf life. The weight loss and waste percent during ripening process of mango fruit xxiv was higher for 0.5cm stalks and lower for 4.5cm stalk, irrespective of the variety and storage temperature. The impact of coating over the quality and shelf life of mango (Langra and Samar Bahisht Chaunsa) fruit was investigated in detail. For this purpose, several coating materials like starch, olive oil, beeswax, sodium benzoate, coconut oil, natural ghee (clarified butter) and potassium metabisulphite were evaluated. The fruit was harvested at hard green stage of maturity, coated and stored at various temperatures with control till ripening. The data showed that the coating had significant impact over the quality and shelf life of the fruit in most of the cases under the limit of P < 0.05. Shelf life was longest with minimum weight loss and waste percent in natural ghee (clarified butter) and beeswax. Quality was higher in case of natural ghee and starch based coating than others, irrespective of the variety and storage temperature. Overall the shelf life was longest and waste percent was lowest in Samar Bahisht Chaunsa as compared to Langra mango variety, irrespective of the treatment.