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Existence and properties of the solutions of evolution inclusions

Thesis Info

Author

Shamas Bilal

Department

Department of Mathemetics

Program

PhD

Institute

Government College University

Institute Type

Public

City

Lahore

Province

Punjab

Country

Pakistan

Degree Starting Year

2015

Degree End Year

2018

Subject

Mathematics

Language

English

Other

CD is also available at PG Library

Added

2021-02-17 19:49:13

Modified

2023-01-06 19:20:37

ARI ID

1676711073879

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جوشؔ ملیح آ بادی

جوشؔ ملیح آبادی
پاکستان ہی میں اردو کے مشہور شاعر جوش ملیح آبادی کی وفات ہوئی، انھوں نے اردو شاعری کی صنف نظم گوئی کو بڑی ترقی دی، غزل کے بجائے نظم گو کی حیثیت سے زیادہ مقبول ہوئے، ان کے مداح ان کے فن اور شاعرانہ مہارت کے بڑے قدردان رہے، مگر ان کے کچھ ناقد ایسے بھی ہیں، جو ان کی شاعری ہی میں خیالات کی بلندی اور پاکیزگی کے بجائے صرف گھن گرج اور چیخ و پکار زیادہ پاتے ہیں، دینی حلقوں میں تو اپنے ملحدانہ اور رندانہ طرز فکر کی وجہ سے اچھی نظر سے نہیں دیکھے جاتے، مگر جب کبھی اردو شاعری کی تاریخ لکھی جائے گی تو اس میں ان کے شاعرانہ فن کی وجہ سے ان کو نمایاں جگہ دی جائے گی۔ (صباح الدین عبدالرحمن، اپریل ۱۹۸۲ء)

Computer Aided Instruction For Preschoolers In Mathematics

Computers are increasingly a part of pre-schoolers to professional lives. The use of multimedia in education has significantly changed people’s learning processes.  Computer technology holds promise for improving student performance and quality of teaching education program at all levels. Today, development has been rapid and technology has been acknowledged as an additional teaching tool. Results from a number of research studies indicate that appropriately designed multimedia instruction enhances students’ learning performance in mathematics, and literacy. The purpose of the present paper was to discuss research avenues employing computers as a learning tool and to analyse the results obtained by this method at the pre-schoolers learning level.

Conservation Issues and Restoration Strategies for Japanese Oak in the Himalayan Region of Pakistan

This study was conducted in order to detect the current conservation status and related issues and to recommend conservation measures for protection of Quercus glauca Thunb in the Himalayan region of Pakistan. This species is a member of the family Fagaceae, a dicot family. Extensive field surveys were carried out in already known locations and unknown potential sites from 2014-2017. Population size, geographic ranges, phytosociological attributes, germination capacity, physiological aspects, morphological characters, ethnobotanical studies and molecular studies were carried out. Future predictions regarding habitat shift of the species were also made using Maxent Modeling. Average leaf length in all the sampling sites ranged from 19.5 cm to 12 cm, while average leaf width ranged from 6.5 cm to 3 cm. The dominant leaf margin was partial dentate being observed in 46 sampling sites. The dominant veination type was alternate observed in 36 sampling sites. The inflorescence was catkin and flowers were monoecious. Seeds were acorns partially embedded in ringed cupule. The number of rings was 6 observed in almost all sites. The localities hosting Q. glauca were traced lying in the Lesser Himalayan region of Pakistan in three districts viz., Mansehra, Battagram and Muzafarabad (AJK). The total number of sampling localities was 29, while total sampling sites were 51. The floristic composition in association with Q. glauca comprised of 144 plant species belong to 66 families. Habit-wise, herbs were dominant comprising 80 species (55.55%) followed by trees 42 species (29.16 %) and shrubs 22 species (15.27%). Family-wise, Poaceae was dominant family with 13 species (9.02 %) followed by Astracea and Rosaceae with 11 species (7.63%) share of each. The altitude in the sampling sites ranged from 718 to 1417.32 m. In the 51 sampling sites, collectively 164 mature individuals were observed with total DBH value of 15587.7 cm. The cluster analysis /dendrogram divided the Q. glauca populations into three associations based on presence and absence data. These associations were (1) (Themeda anathera, Quercus glauca and Oxalis corniculata), (2) (Themeda anathera, Quercus glauca and Cynodon dactylon), (3) (Themeda anathera, Quercus glauca and Oxalis corniculata). The slope aspect, altitude and soil physico-chemical composition were more significant among variables. The germination and further survival of the seedlings was found dependent on the development of mycorrhizal fungi in their root system. Four species of mycorrhizae belonging to three genera were isolated and identified in the molecular analysis i.e. Scleroderma bovista Fr, S cepa Pers, Boletus impolitus Bertault and Tomentella affbadia species in two samples. Our findings revealed that along with the availability of suitable habitat and climatic conditions, germinating seedlings must develop mycorrhizae for absorption of sap for active growth and survival of the species Significant differences were found in viability results among the seeds collected from selected sampling sites. Higher viability was found in the seeds collected from Gadda (District Battagram) (95.23%) than those collected from Tandali (Muzafar Abad District) i.e. 88%. Least viability (33.33%) was foud in the seeds collected from Afzal Abad (District Mansehra). The stratification of seeds for 15 days was found to be the most effective in breaking dormancy in Q glauca having 95.45 % germination having average germination time (AGT) of 12.42 days as compared to the control (22.22%) germination with AGT of 27.5 days. Seeds with dehisced seed coat also showed poor germination, seeds germinated at 10% at Jaba (Mansehra) and Chorlanga (Battagram) with AGT of 30 and 32 days respectively. Seeds with bores in their seed coat showed poor germination, only 10% seeds germinated with AGT of 32 days in seeds collected from Jaba (Mansehra), while were unable to germinate collected from sites.