سید مرتضیٰ علی
افسوس ہے اس مہینہ میں ہمارے ایک نہایت عزیز اور مخلص دوست سید مرتضیٰ علی نے بھی دہلی میں وفات پائی۔ مرحوم نواب صدیق حسن خاں صاحب مرحوم کے نواسی داماد تھے۔حکومت ہند کے محکمہ دفاع میں اعلیٰ افسر تھے۔تقسیم کے بعد بھی یہیں رہے۔دلّی کی جامع مسجد کے قریب ان کا آبائی مکان تھااُسی میں رہتے تھے اورجامع مسجد میں نماز اس پابندی سے ادا کرتے تھے کہ وفات سے پہلے سخت مجبوری کے باوجود انھوں نے نمازباجماعت ترک نہیں کی۔ادارہ ندوۃ المصنفین کے شروع سے محسن اوراس کے کاموں کے بڑے قدردان تھے۔ اسلام کی محبت اورعشق میں سرشار رہتے تھے۔بڑے خلیق،متواضع،صاحب ِخیر، غیور و خوددار اور حد درجہ پابندِ وضع تھے۔اﷲ تعالیٰ ان کوغریق رحمت فرمائے اور پسماندگان کوصبر جمیل کی توفیق ارزاں ہو۔آمین [جولائی۱۹۵۶ء]
COVID-19 is a disease that cause respiratory illness due to novel corona virus. It was reported to WHO on December 31,2019 for the first time. The outbreak of this disease started from Wuhan city, China. Now COVID-19 pandemic is spreading worldwide mostly in Europe and North America, these regions have high prevalence of obesity. In the pathogenesis of COVID-19 disease, obesity assumes a significant job. Theinsusceptible framework, which is official in the pathogenesis of COVID19, assumes asignificant job in weight instigated fat tissue aggravation. In the fat tissue the irritationbrings about metabolic brokenness conceivably prompting dyslipidemia, type 2diabetes mellitus, insulin obstruction, hypertension and cardiovascular sickness. Obesity has been expanded the vulnerability to contaminations. In this pandemic, a large number of obese individual with Covid-19 are reported. Infection rate in obese is greater due to poor immunity, comorbidity and inadequate nutritional needs. Statistical analysis showed that about 41.7% patients reported in New York city were obese. Whereas 40% obese have been reported in United State of America with Covid-19. A report from UK indicated that 38% obese were admitted in ICU with Covid-19. According to Chinese researchers, obese individuals are 3-timesmore prone toward the development of Covid-19. So recent analysis indicated that obesity is the major risk factor of Covid-19. In COVID-19, overweight and obese patients have high danger of metabolic difficultiesand eternal infections that stoutness works. More nutrition care is required for such patients. As nutrition is a key factor for keeping up human wellbeing, for example, denseimpervious framework and satisfactory admission of supplements and dietaryenhancements. Tolerant with COVID-19 create contamination from slight to seriousindications bound to the dietary status. Consequently, assessing wholesome status ofindividuals with contamination turns out to be increasingly significant. Through dietaryhelp, we can bring down the danger of oxidative pressure, infection contamination andexpands invulnerability framework among obese people especially.
The main purpose of this thesis is to study the existence, uniqueness and Ulam’s typestabilityofsolutionsofimpulsivedelaydynamicsystemsontimescale. First, westudytheexistence,uniquenessandUlam’stypestabilityofsolutionsofimpulsive delay differential equations and then we extended it to impulsive delay dynamic systems on time scale. More specifically, the integral impulses of fractional orderareutilizedforthestudyoffirstordernon–lineardelaydifferentialequations and then the results are extended to system of non–linear delay differential equations with instantaneous and fractional integrable impulses on time scale. Also, theresultsarethengeneralizedtonon–linearimpulsiveVolterraintegro–delaydynamicsystemandnon–linearimpulsiveHammersteinintegro–delaydynamicsystem on time scale. Furthermore, the mixed impulsive integro–dynamic system on time scale is also studied. The main tools for obtaining the existence, uniqueness and Ulam’s type stability results are Gr¨onwall’s inequality, abstract Gr¨onwall’s lemma, Banach contraction principle and Picard operator. For our results, some assumptions are made along with Lipschitz conditions. Some examples are also presented to support our results.