Search or add a thesis

Advanced Search (Beta)
Home > Some Applications of Convolution Operator in Geometric Function Theory

Some Applications of Convolution Operator in Geometric Function Theory

Thesis Info

Access Option

External Link

Author

Murtaza, Rashed

Program

PhD

Institute

COMSATS University Islamabad

City

Islamabad

Province

Islamabad

Country

Pakistan

Thesis Completing Year

2017

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/8245/1/Some%20Applications%20of%20Convolution%20Operator%20in%20Geometric%20Function%20Theory.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727191446

Similar


Some Applications of Convolution Operator in Geometric Function Theory Geometric Function Theory on comprehensive spectrum deals with the geometric properties of analytic functions. In the study of analytic functions, image domains are of prime importance. Analytic functions are categorized into different classes on the basis of geometry of image domains. The core objective of present research is to study some applications of the convolution operator in Geometric Function Theory. We define some new subclasses of analytic functions by using the convolution operator. Several other operators with reference to these classes also under discussion. Our main focus is to generate some new results like inclusion results, integral preserving properties, arc length, rate of growth of coefficients, necessary condition for univalency, closure under convolution with convex functions and some radii results with the convolution operator. We also use some special functions to study properties of the convolution operator. Some application of this operator related to the conic domains is also discussed. The recently developed techniques that are convolution and differential subordination are used to explore some geometrical and analytical properties. The results obtained in this dissertation are also connected with the previously existing results in the literature of the subject.
Loading...
Loading...

Similar Books

Loading...

Similar Chapters

Loading...

Similar News

Loading...

Similar Articles

Loading...

Similar Article Headings

Loading...

ایک تو ہے صدمات نے گھیرا

ایک تو ہے صدمات نے گھیرا
اس پہ اپنی ذات نے گھیرا

کیسے ہوش سنبھالوں اپنے
غم کی ہے بہتات نے گھیرا

ہم کو یاد تھے ہم ہی آئے
پیروں کو جب پات نے گھیرا

اپنی ذات نفی میں ڈالی
ہم کو جب اثبات نے گھیرا

اک مفلس کی شامت آئی
کچا گھر برسات نے گھیرا

اس نے کبھی پھر دن نہیں دیکھا
جس کو ہجر کی رات نے گھیرا

Islamic Studies and Private Universities in South-West Nigeria: Challenges and Prospects

Islamic Studies is one of the core and pertinent courses offered and taught at both private and public universities in Nigeria. The subject prepared its graduates to have potentialities, capabilities man power in teaching, administration, politics, economic, legislation and judiciary in Nigeria. Despite these significant contributions, the subject has confronted with a lot of deprivations in the enrollment of students, recruitment of staff and availability of physical and instructional materials. Based on these, the paper therefore, intends to explore the teaching and learning of Islamic studies in the south west Nigeria private universities, identify problems facing its teaching and learning and proffer solutions to these predicaments. The methodology adopted is analytical with information from both oral interview and written sources from libraries in Nigeria. Among the findings of the study are that the Subject-Islamic studies needs more experts to teach its core courses in private universities in Nigeria and students who wish to enroll for the subject should have rudiments of the discipline before admission.   

Environmental Sustainability Analysis of Water Footprints of Peshawar Basin, Pakistan.

Water is a fundamental resource for sustainable social and economic development of any country. Freshwater resources are becoming scarce due to inevitable demand for food, industrial development and growing urban and rural population. Over the last few decades, demand for the agricultural products has been increased due to the population and economic growth. This has exerted immense pressure on the available water resources. Pakistan is located in the arid region of the world with an average annual rainfall less than 240 mm.Being an agriculture based economy the availability of fresh water is essential for sustainable economic development. The goal of this research was to analyze the environmental sustainability of blue, green and grey water footprint in Peshawar Basin during the period 1986 to 2015. The basin is located in the northwest of Indus Basin at longitude of 710 15/ and 720 45/ E and latitude 330 45/ and 340 30/ N in Khyber Pakhtunkhwa province of Pakistan that covers an area of 5617 km2 and has 9.78 million inhabitants. Blue and green water scarcity was selected as an indicator to assess the environmental sustainability of water footprints. Further, the study was aimed to assess the potential impact of dam on Kabul river water pollution. The water pollution level was estimated under normal and reduced runoff scenarios for an increased upstream use of water from Kabul River in Afghanistan. The annual blue and green water availability and scarcity was calculated following global water footprint assessment standard during the period 1986-2015 and annual blue and green water footprints of crops were estimated using AquaCrop model. The AquaCrop output was post-processed to separate incoming and outgoing water fluxes and soil water content into blue and green water components; considering blue water fluxes from irrigation and capillary rise. Consequently, evapotranspiration (ET) originating from irrigation water, capillary rise and rainwater was tracked out. Grey water footprints is used as an indicator to assess environmental sustainability related to nitrogen (N) and phosphorus (P) pollution in Peshawar Basin, Pakistan. The N and P pollutants load from artificial fertilizers, animal manure, household and industrial sources were considered during 1986 to 2015. The results showed that per capita water availability dropped from 1700 m3 per in 1986 to 600 m3 in 2015. In terms of per capita water availability the basin has turned from “water stressed” in 1986 to “water scarced’ in 2015. Further, both the blue and green water footprint of agriculture has decreased from 2139 million m3 in 1986 that reduced to 1738 million m3 in xi 2015. Similarly, the green water flow from agricultural land was 1231 million m3 in 1986 which reduced to 1104 million m3 in 2015. The domestic water footprint has increased from 13 million m3 in 1986 to 29 million m3 in 2015.The average of 30 years blue water footprint of maize, rice, tobacco, wheat, barley, sugar cane and sugar beet were 7077, 3932, 2176, 1913, 1561, 181 and 174 m3/ton, respectively. The mean values of green water footprint were 2744, 2254, 1985, 1535, 1603, 67 and 45 m3/ton, respectively. The 30 years average annual blue water consumption of sugar cane, maize, wheat, tobacco, sugar beet, rice and barley was 655, 623, 494, 57, 32, 14 and 11 million m3, respectively while green water was 308, 236, 391, 52, 8, 8, and 11 million m3, respectively. The average annual blue and green water consumption of agricultural sector in Peshawar Basin was 1886 and 1014 million m3 respectively.Average of 30-years N-related WFgrey showed that artificial fertilizer contributed 61%, livestock manure 36%, household sources 2% and industries 1% while for P-related WFgrey, the contribution from artificial fertilizer, livestock manure and household sources were 50%, 49% and 1%, respectively. Averaged 30-years N and P associated WFgrey of the basin were 50´108 m3/y and 50´109 m3/y respectively. The water pollution level was estimated under normal and reduced runoff scenarios for an increased upstream use of water from Kabul River in Afghanistan. N-related WPL was within the sustainability limit of 100% while Prelated WPL exceeded sustainable limits in every year under normal runoff and were worse in each reduced runoff scenarios.This study shows that the blue and green water scarcity are less than 100% and are low water scarcity level. It provided a baseline information for the sustainability, food security and water productivity of crops. This would be helpful for policy makers for efficient irrigation management and water conservation in Peshawar valley. The study further shows the deterioration of water quality of Kabul River and the findings may be helpful for future planning and management of the basin