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Fixed Point Theorems for Contractive Type Mappings in Distance Spaces

Thesis Info

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Program

PhD

Institute

Quaid-I-Azam University

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2018

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/9214/1/Fahim%20Ud%20Din%20PhD%20Thesis.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726212569

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Weoftencomeacrossnonlinearsystemsandtheirassociatednonlinearequa- tionsandbothpureandappliedmathematicsplayavitalroleindealing with suchkindofequations. When wetalkaboutnonlinearanalysis,itsfundamentalimportancein physical,biological,engineeringandtechnologicalsciencescanbeseenin the formulationandanalysisofvariousclassesofequation. As faras xedpointtheoryisconcerned,itsextensivenesscanbeseenby its applicationsinvarious elds.Theoremsthatareconcernedwiththeex- istenceandpropertiesof xedpointsareknownas xedpointtheorems. Thesetheoremsplayaveryimportantroleforprovingtheexistenceand uniquenessofsolutionsforvariousmathematicalmodels.Metric xedpoint theoryhastakenonnewdimensionssincetheinceptionofthewellknown Banachcontractionprinciple,andthiscontractionprinciplegivesusareally suitablebaseto nd xedpointforselfmappings.Themainaimofthis thesisistoaddsomemorewidelyapplicableresultstotheliterature.
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شاہ آفاق احمد ردولوی

حضرت شاہ آفاق احمد ردولویؒ
درگاہ شریف، ردولی۔
محترمی! تسلیمات
خدا کرے آپ کا مزاج اچھا ہو، اس سے پہلے بھی میں دو خط آپ کو تحریر کرچکا ہوں مگر جواب سے محروم ہوں۔ خدا معلوم وہ خطوط آپ تک پہنچے بھی یا نہیں، میرے حقیقی ماموں حضرت شاہ آفاق احمد سجادہ نشین درگاہ شیخ العام ردولی شریف کا ۲۵؍ جولائی ۸۰؁ء کو اچانک میڈیکل کالج لکھنؤ میں قلبی دورہ پڑنے سے انتقال ہوگیا، ان کو پہلا دورہ ردولی شریف میں پڑا تھا اس کے بعد تین دورے میڈیکل کالج لکھنؤ میں پڑے، ڈاکٹروں نے پیس میکر لگانے کو کہا وہ بھی لگادیا گیا۔ مگر موت کے آگے اور خداوند عالم کی مرضی کے آگے کوئی اختیار نہیں چلتا، چونکہ اکثر بیشتر وہ آپ کا تذکرہ فرمایا کرتے تھے اسی لئے ان کی بیماری کی اطلاع بھی ۳۰؍ جون کو آپ کو اور وسیم الحسن صاحب کو بھی دے دی تھی، اس کے بعد ۲۸؍ جولائی کو انتقال کی بھی خبر تحریر کردی تھی، اسی سال عرس شریف کی ۱۴؍ تاریخ کی شب کی محفل میں اپنے بڑے صاحبزادے تمیم میاں صاحب مرحوم جن کا بھی اچانک بقرعید میں انتقال ہوا تھا ان کے بڑے صاحبزادے نیرمیاں کی دستار بندی اپنے ہاتھوں کردی تھی اور خرقہ شریف بھی انہیں کو پہنا دیا تھا، چونکہ نیرمیاں ابھی طالب علم ہیں اور بی۔کام کررہے ہیں، اس لئے ماموں صاحب مرحوم نے اپنے چھوٹے صاحبزادے حسین میاں کو نیرمیاں کا ولی اور سرپرست مقرر کردیا ہے، جو نیرمیاں کی جگہ پر سجادگی کے فرائض انجام دے رہے ہیں، مگر ابھی دونوں صاحبزادگان بچے ہیں آپ حضرات ہی ان کے سرپرست اور بزرگ ہیں، اس کم عمری میں ان کے اوپر اتنی بڑی ذمہ داری آپڑی ہے، لہٰذا آپ حضرات کی شفقت دیرینہ ہی ان کی تسلی کا باعث ہوگی، چہلم...

Psychological morbidity in medical students after entering into clinical training Psychological morbidity among medical students

Psychological morbidity is emerging as animportant issue for medical students after entering clinical training due to extensiveworking hours. Students find themselves unable to balance competing demands on their time and cannot allocate appropriate time to family, spouses and even to themselves; this leads to complaints about exhaustion and lack of efficiency in their profession. Objective: To assess Psychological morbidity in interns, medical officers and residents Methods: a cross sectional study was conducted. A google form was designed with questions adopting from the three scales of the Maslach Burnout Inventory-General Survey (MBI-GS). Question from all three categories of MBI-GS such as emotional exhaustion, depersonalization and personal accomplishment were considered. The form was distributed via email and Whatsapp to 87 house officers, medical officers and residents of six public healthcare facilities in Lahore. Responses were captured from 73 participants who completed the General Health questionnaire. Seven of these forms were filled by nurses, so in the present study only the response ofthose 66 participants who conformed to the study cross-section were considered. The results were analyzedusing SPSS version 22 for descriptive statistics and chi-square association. Results: A significant association was found between long working hours and emotional exhaustion, depersonalization and personal accomplishment questions in particular. The findings suggests long working hours ruin the mental health of medical professionals, which ultimately produce psychological health impacts. Conclusions: It was concluded that these factors should be considered to reduce psychological morbidity in health professionals.  

Lithofacies, Petrography and Geochemistry of the Neogene Molasse Sequence of Himalayan Foreland Basin, Southwestern Kohat, Pakistan

The Himalayan Foreland Basin (HFB) is one of the largest and dynamic terrestrial basins, stretching between the northwestern and northeastern Himalayas before arching southward to the Arabian Sea in the west and the Indian Ocean in the east. Molasse sediments eroded from the Himalayan orogen, representing the post-Eocene sedimentary record of the collision of the Indian and Eurasian plates occur in this basin from Pakistan through India to Nepal. In Pakistan, this sedimentary sequence is well preserved and exposed in the Kohat and Potwar plateaus other than Sulaiman and Kirthar ranges. The source area, sedimentation pattern, drainage organization, tectonic and climatic conditions generally differ at sub-basin level. For present study, the Neogene molasse sequence of the southwestern Kohat plateau is selected, which constitutes the westernmost deformed part of the HFB. Here, the Neogene molasse sequence consists of the Kamlial, Chinji and Nagri formations. All these formations are composed of sandstones, mudstones and conglomerates. On the basis of field observations and presence of various sedimentary structures, different lithofacies of the Kamlial Formations are identified, namely; Channel Conglomerates Facies (K1), Cross-bedded Sandstone Facies (K2), Interbedded Mudstone, Sandstone and Siltstone Facies (K3) and Mudstone Facies (K4). In Chinji Formation, based on various sedimentary structures, lithofacies identified include; Cross-bedded Channel Sandstone Facies (C1), Cross-bedded and Cross-laminated Sandstone Facies (C2), Interbedded Mudstone, Siltstone and Sandstone Facies (C3) and Mudstone Facies (C4). Alike, lithofacies identified in the Nagri Formation include Channel Conglomerate Facies (N1), Cross-bedded Channel Sandstone Facies (N2), Interbedded Sandstone, Siltstone and Mudstone Facies (N3) and Mudstone Facies (N4). The above mentioned facies propose that the Kamlial Formation was possibly deposited by sandy bedload or major mixed load river, the Chinji Formation by mixed- load rivers with significant fine suspended sediment and the Nagri Formation by sandy bedload rivers. The floodplain deposits of the Chinji Formation seem to be deposited by suspended-load rivers during major flood events. Low lateral and vertical connectivity of the sandstone bodies suggests high subsidence rates. The change from thick channel sandstones of Kamlial Formation to dominantly overbank accumulation with minor, thin, channel-sandstone lenses of the Chinji Formation could either be due to a change in climate or palaeodrainage of the area. Again a major change from mudstone-siltstone facies-dominant Chinji Formation to channel sandstone facies-dominant Nagri Formation occurs, which might reflect one or more factors including (1) low subsidence rates, or (2) arid climatic regime and limited vegetation, or (3) strongly seasonal discharge resulting in flash flooding. Detailed petrographic studies of representative sandstone samples from three different sections reveal that the Kamlial, Chinji and Nagri formations contain abundant quartz with subordinate feldspars and variable proportions of lithic grains. Monocrystalline quartz dominates over polycrystalline quartz in all the three studied formations. The feldspar content mostly ranges from 18 to 30%, 24 to 28% and 16 to 36% in the Kamlial, Chinji and Nagri sandstones, respectively. The abundance of lithic grains shows a wide range of variation (4 to 35%). Although the lithics are mainly sedimentary, but fragments of volcanic and low-grade metamorphic rocks also occur in appreciable amounts. Micas, including both muscovite and biotite, are generally less than 10 % of the total detrital grains. The observed heavy minerals include epidote, monazite, apatite, garnet, zircon, rutile and brown hornblende. The crystals of zircon, monazite, rutile, epidote and mica also occur as tiny inclusions in quartz grains. viOn the basis of modal composition, sandstones of the Kamlial, Chinji and Nagri formations fall into the groups of feldspathic and lithic arenites indicating to be the products of feldspar-rich crystalline rocks and rugged high-relief source areas, respectively. The presence of appreciable amount of feldspars in the sandstone samples favors either high relief or arctic climate at the source area. The overall variation in the relative abundance of different types of quartz grains (monocrystalline including both non-undulatory and undulatory types and polycrystalline containing 2-3 and >3 subgrains) shows contribution from both medium-high grade and low-grade metamorphic rocks provenance for sandstones of the Kamlial, Chinji and Nagri formations, supported by the consistent presence of minerals like mica, epidote and garnet as well as relative dominance of polycrystalline quartz grains composed of 2-3 crystals (Qp 2-3 ). Alike, the presence of illite in mudstone also suggests a source area composed of metamorphic and sedimentary rocks. On the other hand, the average contents of different types of quartz grains from the Kamlial, Chinji and Nagri formations show granitic and/or gneissic source. The greater abundance of alkali feldspar than plagioclase further supports this conclusion. The relatively greater abundance of monocrystalline quartz also suggests that the presence of granitic and volcanic rocks in the source areas cannot be ruled out, or else the quartz grains have traveled a longer distance of transportation. Furthermore, the inter- sectional variation in modal composition and types of quartz grains in both the Kamlial and Chinji sandstones suggest a strong spatial control on their deposition. Petrographic results of the studied sandstones were also processed using different provenance discriminatory diagrams suggesting Magmatic arc, Recycled Orogens and a mixed provenance for the Kamlial, Chinji and Nagri formations. Similarly, geochemical data of the major element oxides of the sandstone was used for classification and provenance determination applying different tectonic discriminatory plots. Sandstone of the Kamlial, Chinji and Nagri formations predominantly classify as litharenite and Fe-sand. The shift of sandstone to various fields in classification is due to a wide range in the variation of relative proportion of matrix, feldspar and lithic components. Different provenance discriminatory plots suggest continental island arc and Active Continental Margin (ACM) provenance for the sandstone of the three studied formations of southwestern Kohat. Similarly, discriminatory plot of SiO 2 vs log (K 2 O/Na 2 O) indicate a dominant influx from ACM for the studied sandstone. Other geochemical parameters like Fe 2 O 3 +MgO, TiO 2 and Al 2 O 3 /SiO 2 and the contents of the major element oxides except MnO of the Neogene molasse sandstone show major provenance from continental island arc and partial influx from ACM settings. Furthermore, the Th/U ratio of the Neogene molasse sequence is lower than the UCC and PAAS, which also show that these sediments are first cycled in origin; however, Zr/Sc ratio proposes minor contribution from recycled sedimentary sources. In regional tectonic scenario of the study area, it is assumed that the recycled orogen sediments are sourced from the Himalayan tectonic units, the active continental margin orogen sediments from the Asian active continental margin (the Trans-Himalaya and Karakoram) and the magmatic arc orogen sediments from the Kohistan-Ladakh arc. Values of the Chemical Index of Alteration (CIA) of the Neogene sandstone (mostly 64 to 76) and mudstone (mostly 70 to 80) suggest moderate to slightly intense weathering of these sediments, respectively. However, Index of Compositional Variability (ICV) values and lower contents of Rb and Cs than UCC and PAAS of the mudstone indicate relatively moderate weathering. The more abundance of feldspar (plagioclase) than clay minerals in the mudstone suggests high denudation rates or high relief or limited chemical weathering in the source area(s). The presence of illite in the viimudstone suggests cold and dry glacier conditions whereas kaolinite indicates warm and humid conditions. This conclusion either favors a source region of vast area that had different climates in different parts, or major shifts in extreme climatic conditions. Red coloration of the Neogene mudstone of the Kohat Plateau most probably indicates deposition under hot, semi-arid and oxidizing diagenetic conditions. Furthermore, the values of the authigenic U, and ratios of U/Th, V/Cr, Cu/Zn and Ni/Co of the Neogene molasse sediments show that these sediments were deposited in oxidizing conditions. Greater abundance of alkali feldspar than plagioclase in the Neogene sandstone of the Kohat Plateau, and dominance of plagioclase in the associated mudstone suggest granitic and mafic/ultramafic sources for these sediments, respectively. However, the lower values of Zr, Nb and Y, and ratios of the Ba/Sc, Ba/Co, Cr/Zr, Sc/Th and Y/Ni in sandstone and mudstone indicate the consistent presence of basic/mafic phases in the source area, still values of La/Th, La/Sc, Th/Zr and binary plot of Th/Co vs La/Sc propose provenance similar to Upper Continental Crust (UCC)/Post Archaen Australian Shale (PAAS)/felsic rocks. Generally, there exist a significant positive correlation of TiO 2 , Zr, Rb and V with Al 2 O 3 indicating their association with clay minerals and associated phases." xml:lang="en_US