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پنڈت وجے لکشمی

پنڈت وجے لکشمی
اسی ماہ میں ایک دوسرا حادثہ ٔ جانکا ہ ملک کوپنڈت وجے لکشمی کابھی پیش آیاہے۔ محترمہ جواہرلال نہرو کی ہمشیرہ تھیں۔لیکن وہ خودبھی بڑی قابلیت کی مالک تھیں۔ صحیح بات کہنے میں وہ کبھی نہیں چوکیں، چاہے اس کے لیے ان کو اپنے خاندانی افراد ہی سے ناراضگی کیوں نہ لینی پڑی ہو۔ایمرجنسی کی مخالفت میں وہ اپنی بھتیجی شریمتی اندرا گاندھی کے خلاف میدان میں کودپڑیں۔
وہ بڑی بہادر خاتون تھیں اورایک اچھی مقرر بھی تھیں۔ بھارت کی نمائندگی کرتے ہوئے انہوں نے غیر ملکوں میں بھی اپنی قابلیت کالوہا منواتے ہوئے اپنے ملک کانام روشن کیا۔یو۔این۔ او میں ان کی صلاحیتوں کابرملا اعتراف واظہار کیاگیا۔ان کے انتقال سے ہندوستان نے اپنی ایک بڑی محسنہ کوکھودیا ہے۔ان کی کمی کوہمیشہ ہی محسوس کیاجائے گا۔ہندوستان کی سیاست میں___ایسا ہماراایقین ہے۔ [دسمبر ۱۹۹۰ء]

 

EFFECTS OF MULLIGAN ROTATIONAL MOVEMENT VERSUS MEDIAL GAPPING TECHNIQUE ON PAIN, RANGE OF MOTION AND DISABILITY IN PATIENTS WITH KNEE OSTEOARTHRITIS

Background and Aim: To compare the effects of mulligan rotational movement and medial gapping technique on pain, range of motion and disability in knee osteoarthritis patients. Methodology: This study was a Randomized Clinical Trial. The data was collected using a convenience sampling technique. Data was collected from Jinnah Hospital Lahore, from 15th December – 30th June 2022.36 subjects (males and females) were recruited in two groups. The first group received Mobilization with movement along with a conservative treatment protocol. The second group received the Medial gapping technique along with conservative treatment protocol. Each group was treated for four weeks in which three sessions per week were given. Numeric pain rating scale and the disability index were used as outcome measures. Data was analyzed through statistical package for the social sciences (SPSS) version 25. Results: Within-group comparison by paired t-test showed the p-value was significant <.05, indicating that both treatment was effective in improving symptoms. Between groups, comparison by independent t-test showed that Mulligan Mobilization Technique is more effective than the medial gapping technique in improving pain disability and quality of life. Conclusion: The study concluded that Mulligan Mobilization Technique provides more clinical benefits regarding pain, disability and range of motion in osteoarthritis patients than Medial Gapping Technique.

Exact and Approximation Riemann Solutions of Nonlinear Hyperbolic Conservation Laws

This thesis project focuses on the numerical solutions of selected nonlinear hyperbolic sys tems of partial differential equations (PDEs) describing incompressible and compressible flows. Such type of PDEs are used to simulate various flows in science and engineering. The underlying physics of such systems of PDEs is very complex and some mathematical and computational issues are associated with them. For instance, they may contain non conservative terms or may be weakly hyperbolic. The strong nonlinearity of the systems could generate sharp fronts in the solutions in a finite time interval, even for smooth initial data. Moreover, accurate discretization of the non-conservative terms is a challenge task for the numerical solution techniques. In the presence of non-conservative terms, well balancing, positivity preservation and capturing of steady states demand special attention during the application of a numerical algorithm. In this thesis project, we develop exact Riemann solvers for the one-dimensional Ripa model, containing shallow water equations that incorporate horizontal temperature gradients and considering both flat and non flat bottom topographies. Such Riemann solvers are helpful for understanding the behavior of solutions, as these solutions contain fundamental physical and mathematical characters of the set of conservation laws. Such solvers are also very helpful for evaluating performance of the numerical schemes for more complex models. Afterwards, third order well-balanced finite volume weighted essentially non-oscillatory (FV WENO) schemes are applied to solve the same model equations in one and two space dimensions and a Runge-Kutta discontin uous Galerkin (RKDG) finite element method is applied to solve this model in one space dimension. In the case of compressible fluid flow models, an upwind conservation element and solution element (CE/SE) method and third order finite volume WENO schemes are applied to solve the dusty gas and two-phase flow models. The suggested numerical schemes are able to tackle the above mentioned associated difficulties in a more efficient manner. The accuracy and order of convergence of the proposed numerical schemes are analyzed qualitatively and quantitatively. A number of numerical test problems are considered and results of the suggested numerical schemes are compared with the derived exact Riemann solutions, results available in the literature, and with the results of a high resolution central upwind (CUP) scheme.
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