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Foliation and Isometric Embeddings Ψ 2 S of Schwarzschild Spacetime

Thesis Info

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Author

Faridi, Muhammad Ayub

Program

PhD

Institute

University of the Punjab

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2010

Thesis Completion Status

Completed

Subject

Physics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/1417

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726222133

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Last decades have witnessed remarkable progress in using numerical tools in solving Einstein Field Equations. For qualitative and quantitative analysis of black hole spacetime, the tools of ’Foliation of Spacetime’, ’Effective Potential for the geodesics of particles’ and ’Isometric Embeddings’ are discussed in an elaborative manner with particular reference to the work of Brill et al. Using compactified Kruskal-Szekeres coordinate transformations, complete foliation has been performed with Constant Mean Extrinsic Hypersurfaces (K-Surfaces) and Free Falling Hypersurfaces (ψN - Hypersurfaces). K-Surfaces and ψN -Hypersurfaces which smoothly pass through r = 2m, are helpful for the procedure of canonical quantization of massive scalar fields. Isometric Embeddings for a variety of K-Surfaces and Effective Potentials for the geodesic of massless and massive particles by using all values of K, are numerically calculated and displayed graphically. These tools and methodology would be helpful in research on the geometries of many other curved spacetimes.
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حکیم شیر محمد شیر

حکیم شیر محمد شیر(۱۸۷۴۔۱۹۶۰) داغ دہلوی کے شاگرد اور لسان الاعجاز پنڈت میلا رام وفا کے استاد گرامی تھے۔ اقبال کی طرح آپ بھی خط و کتابت کے ذریعے مرزا خاں داغ دہلوی سے شاعری میں اصلاح لیتے تھے۔ داغ کی وفات کے بعد آپ نے سید احمد حسن میرٹھی کو اپنا کلام دکھانا شروع کر دیا۔ آپ کا کلام ہندوستان کے معروف رسائل میں چھپتا رہا۔ تین ضخیم دیوان لکھے مگر انہیں غربت کی وجہ سے شائع نہ کروا سکے۔ (۱۵۷) شیر نے غزلیں بہت کم لکھی ہیں۔ نظم‘ قصیدہ‘ مرثیہ‘ سلام اور صنف تاریخ کو تو وہ بچوں کا کھیل خیال کرتے تھے۔ بہت کوشش کے باوجود شیر کے مسودات دریافت نہیں ہو سکے۔ ’’سرزمینِ ظفر وال‘‘ کے تذکرے کے ذریعے راقم الحروف نے شیر کا کچھ کلام بازیاب کیا ہے۔ آپ نے اپنی ساری زندگی اپنے آبائی وطن ظفر وال(سیالکوٹ) میں گزاری۔ آپ کے کلام میں دیگر موضوعات کے ساتھ ساتھ مقامیت کے عناصر دیکھے جا سکتے ہیں۔ اس حوالے سے ان کی نظم ’’قصبہ ظفر وال‘‘ ملاحظہ کی جا سکتی ہے۔ اس نظم میں مقامیت کے ساتھ ساتھ ماضی و حال‘ تقسیمِ ہند اور ہندوستانی تہواروں کا ذکر بھی ملتا ہے۔ اس نظم کی زبان بہت سادہ اور سلیس ہے کچھ اشعار ملاحظہ ہوں:

اب ظفر وال ہے شکستہ حال                        آ گیا ہے اس آئینہ میں بال

رہ گیا ہے صرف عکس مو اس میں                 خوبیاں ہیں نہ خوبرو اس میں

چشمہ مہر میں وہ آب نہیں                            خم گردوں میں وہ شراب نہیں

وہ زمیں اب وہ آسمان نہ رہا                          ہم نے دیکھا تو جو سماں نہ رہا

حسنِ شہری سے یہ جا محروم                          اکثر اوقات بولتا ہے بوم

رہ گیا ماند قصبہ جاتی حسن                             ملگجا ہے کچھ دیہاتی حسن

نہیں سیپوں...

OCCURRENCE OF LOWER EXTREMITY MUSCULOSKELETAL INJURIES DURING THE LOCKDOWN IN ATHLETES

Background of the Study: Lockdown was implemented worldwide to limit the spread of COVID-19. This sudden implementation of lockdown causes significant lifestyle changes for every individual. Along with the general population, it also has psychological, behavioral, and physical consequences on athletes. The study objective is to determine the occurrence of lower extremity musculoskeletal injuries during the COVID-19 lockdown in athletes. Methodology: Retrospective cross-sectional study design was used, and participants were recruited by a non-probability convenient sampling technique. A sample size of 147 was taken as calculated by the Raosoft software, and the study was completed 6 months. Both male and female athletes between the age group of 18-35 years, participants who did not participate in any official training session during the lockdown and registered at domestic level for at least 2 years were recruited from Pakistan Sports Board and Wapda Sports Complex Lahore. Data was collected using a semi-structured questionnaire. Nordic Musculoskeletal Questionnaire was used to identify the problematic painful areas of body. Data entry, analysis, and interpretation were done by using SPSS software version 22.0. Results: The mean age and BMI of participants were 25.6531±4.49 (years) and 23.28±3.24 (kg/m2) respectively. From the total, 39.5% of participants reported lower extremity musculoskeletal injuries. And most reported problematic areas include lower back and knee. 75% of participants continue to do workouts at home as a prevention strategy against injury occurrence. Conclusion: This concluded that the occurrence of lower extremity musculoskeletal injuries during the lockdown was moderate.

Studies of Production and Beneficial Effects of Bacillus Species As Probiotics on Poultry Birds

This study was conducted for the production of probiotics for poultry birds from spore forming Bacillus species and its efficacy on poultry birds. For this purpose soil samples were collected from all over Pakistan to isolate spore forming Bacillus bacteria by heat shock method. Total 120 soil samples were collected. On the basis of morphological characteristics colonies were considered. Further, various biochemical tests were carried out and 120 colonies were confirmed as Bacillus species. Some physical tests were also conducted like growth of isolates on different pH, time period, different concentrations of NaCl and different temperatures. The isolates showing more growth and colony forming unit CFU/ml at same parameters like pH, time, temperature, inoculums size and age, were selected. Thus 3 isolates were selected on priority basis which gave more CFU and activity against Micrococcus leuteus but three other strains which gave nearest growth to first 3 selected isolates were also selected for safe side and future use. Species level determination was carried out by ribotyping in which 16S rDNA was amplified, sequenced and verified through BLAST. Out of 6 isolates, strain Zii12 Bacillus licheniformis accession No. KT443923 was finally selected for probiotics production on the basis of biochemical tests, physiological tests, molecular identification, antibacterial activity against bacteria (Micrococcus leuteus) and number of CFU/ml. In shake flask method 1 (g) cell mass per liter of Bacillus licheniformis KT443923 with antibiotic activity (22.37 mm zone of inhibition and CFU 5.1 × 1010 ) was obtained but in scale up studies where we used batch fermentation method, it was 4 gm per liter, 3 times enhancement. The bacterial culture was centrifuged and lyophilized; the product in dried powdered form was indicated in grams. The activity and CFU/g were re checked the results were same as before. Now the product was supplemented in the poultry feed to check its efficacy, for this purpose two different types of poultry trials were conducted. For rural poultry trials, aseel birds were used and growth parameters and mortality were studied. The encouraging results with increased body weights (g) for birds fed with feed supplemented with probiotics in comparison to antibiotic and control group. After six weeks the results obtained in three groups 197.48±5.11, 172.48±5.81, 146.98±4.86, weight gain (g) 156.15±4.96, 132.25±5.56, 106.69±4.80, folds of weight gain 4.82±0.14, 20 4.34±0.16, 3.72±0.14, Feed intake (g) 711.46±22.58, 653.92±29.74, 595.79±28.94, feed conversion ratio FCR 4.57±0.25, 4.92±0.24, 5.55±0.34, mortality 0.28, 0.84, 1.25% respectively. In another trial of commercial broiler (Cobb 500) strain was used. Growth performance, mortality, slaughtering characteristics, histology, blood parameters and prevalence of pathogens in broiler meat were studied. In commercial broiler, best results obtained in birds that were fed with feed supplemented with probiotic. At the age of 5th weeks, body weight (g) of broiler birds fed with feed supplemented with probiotic, antibiotic and control were 2155.11±30.79, 1978.40±57.02, 1840±0.71; total weight gain 2133.98±36.90, 1946.12±63.00, 1805.23±24.50 feed intake (g) 3305.96±11.44, 3370.05±44.15, 3496.67±8.17 maximum folds of weight gain 4.50±0.02, 4.23±0.14, 4.32±0.10 FCR 1.47±0.03, 1.64±0.03, 1.86±0.01 mortality 0, 0.74, 1.48% respectively. After a successful study, 54 birds were slaughtered according to their body size and sex wise. Live weight, slaughtered weight, dressed weight, pancreas weight and heart weight of high body size was high in males that used feed supplemented with probiotic. No difference was found in bursa weight of all the slaughtered birds. Gizzard, liver, spleen and weight and intestinal among all groups was approximately not significant. Less abdominal fat (17.50±0.84 g) was observed in probiotic group. pH of small intestine was almost not significant in birds of al groups. Blood parameters results were also satisfactory. Cholesterol level in probiotic group was very low (119.07±0.44 mg/dl) in comparison with other groups. Pathogens like E.coli, Campylobacter and Salmonella were not found in the meat of probiotic groups but low or high percentage was found in other groups. High villus length of ileum (1439.11±22.83 mm) was also found in probiotic group. Similarly, maximum quantity of goblet cells (167.55±4.55) was found in the ileum of probiotic group. The manure of all type of treated birds was applied separately to lentil crop to check the efficacy of every group. Maximum growth of plant and high seed yield (1243.93±8.99 kg ha-1) was found in probiotic treated plots. Less or nil pathogen prevalence was found in probiotic group manure and soil. Bacillus licheniformis probiotic was concluded as the better feed additive for poultry as compare to antibiotic.