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On Some New Subclasses of Analytic Functions

Thesis Info

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Author

Shahid, Humayoun

Program

PhD

Institute

COMSATS University Islamabad

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2018

Thesis Completion Status

Completed

Subject

Physical Sciences

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/10879/1/Humayoun%20Shahid_Maths_2019_Comsats_PRR.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676724889907

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Geometric Function Theory is a branch of complex analysis which deals with the geometric properties of image domain of an analytic function and this research is rationalized with the advanced trends in this area. The main focus of this study is to define new subclasses of analytic functions using conic domains and Janowski functions. The technique of convolution and differential subordination is used to solve most of our results. We will use the concept of dual sets and quantum differential operator to study properties of these new subclasses. Some analytic and convolution properties such as inclusion results, radius problems and invariance under certain integral operators are studied. Several of the results are shown to be best possible. The connection of the results proved is established with already known ones.
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73. Al-Muzzammil/The Enwrapped

73. Al-Muzzammil/The Enwrapped

I/We begin by the Blessed Name of Allah

The Immensely Merciful to all, The Infinitely Compassionate to everyone.

73:01
a. O Al-Muzzammil!
b. O The Enwrapped - Muhammad!

73:02
a. Stay up in worshipful meditation through the late nighttime,
b. except for a little while,

73:03
a. - half of it,
b. or a little less than that, up to a third,

73:04
a. or even a little more, up to two-thirds.
b. And recite The Qur’an in a slow and distinct recitation.

73:05
a. Indeed, soon WE are going to entrust a heavy burden on you - awe-inspiring –
b. - The Qur’an.

73:06
a. Surely, the getting up by late nighttime for worshipful meditation is very demanding,
b. yet very rewarding for subduing one’s soul, and
c. making recitation more effective -

73:07
a. - for, indeed, during the daytime you have extended schedule of engagements.

73:08
a. But recite The Sacred Name of your Rabb - The Lord,
b. and devote yourself to HIM exclusively in wholesome devotion.

73:09
a. HE is Rabb - The Lord of the east and the west.
b. There is no worshipful entity except HIM.
c. So take HIM as your Guardian and Guarantor.

688 Surah 73 * Al-Muzzammil

73:10
a. And bear with patience over what they allege against you and your Divine Mission,
b. and keep a distance from them in a gracious manner.

73:11
a. And leave it to ME to deal with the beliers and deniers who have been given the good...

Buddhism In Gandhara

The present study entitled “Buddhism in Gandhara” focuses on the religious faith of Gandharans during the Kushan Empire, especially during Kanishka Reign when Buddhism became popular. This research focuses on the religious art works flourished during the regime, including stone sculpture of Gandhara and Mathura reflect the Hellenistic style of Gandharan Buddhist art. It also deals with the artifacts, coins, inscriptions, narrative sculptures from Kushan to ascertain Gandharan Buddhist tradition as documented in art, archaeology, and epigraphy, which comes mainly from the region. The Study can be distinguished as a special case study of its own nature for being conducted in the geographical boundaries, where Kushan and Gandhara art was experimented and practiced which afterwards achieved a status of the full-scale culture of the area. The main aim of the research was to study the religious aspects of the inhabitants of the Kushan period, which was prominent in the living patterns of different social classes, structural design of the buildings, attires and cultural outfits of various segments of the society as well as personal features like ornaments, headdresses, and social rituals in shaping the cultural contours of Gandhara art. The study, based on empirical data collected from various museums and archaeological sites, particularly from excavated areas around Taxila valley, which reflect a special understanding of religious artwork during the regime of Kushans supporting a close link with the Kings and Princess during their control of South Asian region. This paper concludes that Buddhism was a thriving religion during the Greek regime and was supported by the state.

To Study the Effect of Salts and Complexes of Lead and Arsenic Metals on the Status of Thiols in Blood Components, Pharmacological and Toxicological Perspectives

Heavy and transition metals have been widely known for their toxicities for centuries. Arsenic and Lead are highly valued in terms of toxicity to living systems due to their high affinity for sulfhydryl (-SH) containing residues. The chemical interactions of Arsenic and Lead with thiols (–SH rich molecules) results in numerous ill-health effects. As a part of this PhD thesis, the chemical status of GSH was determined in the presence of inorganic and organic complexes of lead and arsenic employing simple spectrophotometric analysis and 1H NMR methods. The behavior of Ellman’s reagent towards the metal-thiol chemistry was initially investigated to begin with the study of the changed status of thiols resulting from metal-thiol coordination. Chapter 2 describes the use of NMR methods to study the species in solutions. 1H NMR allowed us to identify additional components of the reaction mixture, their relative abundance and consequently the involvement of these additional Ellman’s based species in the spectrophotometric errors associated with the use of Ellman’s reagent. Using 1H NMR methods we are able to show that Ellman’s reagent can exchange with thiolates previously coordinated with lead and arsenic. In the context of this 1H NMR study, some limitations were found to be associated with the use of Ellman’s reagent in our study. Ellman’s reagent was found able to react with the thiols being previously attached with arsenic and lead, leading to an over estimation of the thiols in the solution systems. 4,4′-dithiodipyridine (DTDP) was adapted instead of Ellman’s reagent for the spectrophotometric determination of the mixtures involving metal-thiols complexes in aqueous solution and biological mixtures after establishing limitations associated with the use Ellman’s reagent in this capacity of the study. Chapter 3 describes the 1H NMR carried out to study the conditions and ratios of the complexed thiolates (complexes of both arsenic and lead with some important low molecular weight thiols (Glutathione, N. acetyl cysteine and D-Penicillamine). 1H NMR study presented in this chapter provides detailed information about the changes in the chemical status of GSH that might be the basis of this chemical change observed spectrophotometrically in the form of depletion. 1H NMR methods confirmed metal-thiol adducts (i.e., As-SG3 and Pb-SG2) to be the mechanism behind the GSH depletion in the presence of these metal compounds. After establishing the limitation associated with the use of Ellman’s reagent, 4,4′- dithiodipyridine was used for the spectrophotometric determination of the unbound thiols in the presence of complexed thiolates in aqueous solutions. In the course study presented in XII chapter 4, we have spectrophotometrically investigated the reactions of arsenic and lead with sulfhydryl containing thiols i.e., Glutathione, N-Acetyl cysteine and D-Penicillamine in aqueous solutions. In this chapter, the effects of arsenic (Sodium arsenite and Methylarsonous acid) and lead (Lead acetate and Lead acetyl acetonate) on low molecular weight thiols (Glutathione, N. acetyl cysteine and D-Penicillamine) have been spectrophotometerically quantitated in aqueous solutions. Employing influential variables (i.e., different metal concentrations, incubation times and pH ranges) to the study in aqueous solutions, prominent and regular decrease in the thiol levels were caused by each of the inorganic and organic compounds of arsenic and lead in spectrophotometric analysis. Chapter 5 describes the spectrophotometric estimation of important and most abundant low molecular weight thiol (Glutathione) in the whole blood and blood components (cytosolic Fraction and plasma) of human volunteer. In order to improve our understanding of the coordination chemistry of arsenic and lead in whole blood, cytosolic fraction and Plasma, a systematic study of the changes in glutathione (GSH) levels in these biological samples of healthy human volunteers, has been carried out. The effects of the inorganic and organic compounds of arsenic and lead on glutathione status in these biological samples have been spectrophotometerically evaluated by 4,4′-dithiodipyridine. Chapter 6 describes the spectrophotometric estimation of Glutathione in WBCs (Lymphocytes and Monocytes) isolated from human blood, while the study carried out in chapter 7 describes the estimation of Glutathione in liver isolated from rabbits. Chapter 8 describes the exchange of arsenic (AsIII) and lead (PbII) between Proteins (Albumin) and low molecular weight thiols (Glutathione, N. acetyl cysteine and D- Penicillamine). In addition to thiol disulfide exchange reactions, the exchange of arsenic and lead between Proteins (Albumin) and low molecular weight thiols (Glutathione, N. acetyl cysteine and D-Penicillamine) has also been investigated by Column chromatographic methods using Ellman’s reagent. The exchange behaviour of arsenic and lead between proteins and low molecular weight thiols have been analyzed spectrophotometrically by making use of Ellman’s reagent. Column chromatographic methods have been used to collect complexed proteins. The sulfhydryls present on the pure and complexed proteins have been estimated spectrophotometerically. The study regarding the thiol disulfide exchange reactions resulted that the low molecular weight thiolates (Reduced glutathione and N-acetylcysteine) take off As(III) and Pb(II) species which are attached to proteins. XIII Results from multiple studies presented in this PhD thesis are consistent to conclude and anticipate that lead and arsenic species are dynamic in nature as in the case of using Ellman’s reagent, thiolates could be removed from the coordination sphere of the arsenic and lead in As(SR)3 and Pb(SR)2 respectively and in the case involving albumin, the slow exchange of lead and arsenic species bound to cys-34 is the basis for a mechanism by which toxic species can become widely distributed around the body.