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پروفیسر محمد سرور جامعی

پروفیسرمحمد سرور جامعی
۲۰/ستمبر۱۹۸۳ء کومولانا عبیداﷲ سندھیؒ کے سوانح نگار اوراُن کے فکر کے شارح پروفیسر محمد سرور جامعی ابوظہبی میں جہاں وہ اپنے بیٹے سے ملنے گئے ہوئے تھے۔ ۷۹ سال کی عمر میں انتقال کرگئے۔ ان کی میت تدفین کے لیے لاہور گئی۔نماز جنازہ ڈاکٹر اسراراحمد نے پڑھائی اورانھیں لاہور کی ایک نئی بستی ٹاؤن شپ کے قبرستان میں سپرد خاک کیاگیا۔
سرور صاحب نے’’مولانا عبیداﷲ سندھیؒ حالات، تعلیمات اورسیاسی افکار‘‘ اور’’افادات وملفوظات حضرت مولانا عبیداﷲ سندھیؒ‘‘کے عنوانات سے دو بلندپایہ کتابیں اپنی یادگار چھوڑی ہیں۔
مرحوم بڑے بلندپایہ صحافی تھے۔ وہ مختلف اوقات میں روزنامہ وفاق، المعارف اورماہنامہ زکوٰۃ کے مدیر رہے ہیں۔ان کی زبان میں قدرے لکنت تھی اس لیے تقریر کی بجائے تحریر پرزیادہ توجہ دیتے رہے۔
مرحوم تقسیم ملک سے قبل جامعہ ملیہ اسلامیہ دہلی میں استادتھے۔وہاں انھیں ڈاکٹر ذاکر حسین خاں،ڈاکٹر عابد حسین اورپروفیسر محمد مجیب کے ساتھ سالہا سال تک کام کرنے کاموقع ملا۔ مرحوم ان کے بڑے مداح اور ان کے سیاسی نظریات سے بڑے متاثر تھے۔
’’افادات وملفوظات مولانا سندھی‘‘ کے بارے میں علمی حلقوں میں یہ بات مشہور ہے کہ اس میں مولانا سندھی کے نظریات کم اورسرور صاحب کے زیادہ ہیں۔واﷲ اعلم بالصواب۔سرور صاحب بڑے محنتی اورمخلص انسان تھے۔اﷲ تعالیٰ ان کی خطاؤں سے درگزر کرتے ہوئے ان کی مغفرت فرمائے۔
[مارچ۱۹۸۴ء]

 

Sleep Quality in relation with Perceived Stress and Physical Activity in the Students of Pakistani Medical Colleges

Background: Sleep is an essential function of our body. Many surveys have reported the prevalence of poor sleep in university students, especially in medical students.  Objectives: The objective of the study was to evaluate the effect of physical activity and stress on sleep quality among medical students in Pakistan. Materials & Methods: An observational cross-sectional study was conducted on medical students of private medical colleges in Lahore. A convenient sampling technique was used and 210 students were selected. The Pittsburgh Sleep Quality Index (PSQI), Godin Shephard Leisure Time Physical Activity Questionnaire (GSLTPAQ), and Perceived Stress Scale (PSS 10) were used for data collection. We used SPSS version 20 to analyze data and applied statistical tests: Chi-square test and Logistic Regression.  p-value < 0.05 was taken to establish significance. Results: Among the study participants 91(43.3%) were males and 119 (57.7%) were females. There was a significant effect of stress level on sleep quality (P=0.000*). The frequency of good sleepers was seen to increase by almost three times with increasing physical activity, however, this difference remained non-significant (p=0.07). The logistic regression test showed a significant relationship between poor sleep and stress (p=0. 008**) while no significant relationship was seen between sleep quality and physical activity. Conclusion: There was a significant association between poor sleep and high-stress levels and an increase in physical activity showed an increase in the frequency of good sleep, however, this difference was non-significant. It can be inferred that this positive effect of increasing physical activity on the quality of sleep could be indirectly due to its relieving effect on stress.  

Numerical Analysis for Stochastic Models

Stochastic differential equation (SDE) is a differential equation in which some of the terms and its solution are stochastic processes. Stochastic differential equations can be formulated from given ordinary differential equations by introducing stochastic perturbations in it. SDEs play a central role in modeling physical systems like finance, biology, engineering to mention some. In modeling process, the computation of the trajectories (sample paths) of solutions to SDEs is very important. However, the exact solution to an SDE is generally difficult to obtain due to non-differentiability character of realizations of the Brownian motion. There exist approximation methods of solutions of SDEs. The solutions will be continuous stochastic processes that represent diffusive dynamics, a common modeling assumption for financial, biological, physical and environmental systems. This thesis presents a comprehensive survey on numerical methods for stochastic differential equations. Standard numerical methods, Euler Maruyama, stochastic Euler, stochastic Runge Kutta methods are well described. These methods have certain limitations and do not behave well in certain scenarios. A reliable stochastic non-standard finite difference (SNSFD) scheme is proposed which remains consistent for all choice of parameters. In this thesis, we described formulation of nonparametric perturbation techniques for stochastic models. The formulation is based on epidemiological model of humans, animals and plants. Also, this idea is extended for computer virus transmission and smoking models. A comparison of proposed stochastic non-standard finite difference (SNSFD) method with standard stochastic numerical methods is also presented. Explicit methods, such as Euler Maruyama, stochastic Euler, stochastic Runge-Kutta methods are widely used in solving systems of stochastic differential equations. It is well-known that solving stochastic differential equations with explicit finite-difference schemes such as Euler Maruyama, stochastic Euler, stochastic Runge-Kutta methods can result in contrived chaos and non-physical oscillations caused by numerical instability for certain values of the discretization parameters. Such scheme-dependent numerical instabilities can be avoided by using small time steps but the additional computing cost incurred when examining the long-term behavior of a dynamical system. To avoid unnatural chaos and other scheme dependent numerical instabilities, implicitly-driven explicit scheme with certain additional desired properties are generally preferred. The numerical integration of systems of stochastic differential equations over very long-time intervals requires the use of time steps which are the largest possible, keeping in mind accuracy and stability. In the present research work, we developed and investigated such reliable numerical method for the solution of stochastic models, which remains consistent with the continuous dynamical systems. This method will numerically analyze the behavior of solution of the models, stability analysis of the steady states and threshold criteria for the physical systems. The proposed method could be used with arbitrarily large time steps, thus making them more economical to use when integrating over long time periods and could be restore all the essential properties like dynamical consistency, positivity and boundedness of the corresponding dynamical systems.
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