A space efficient flexible pivot selection approach to evaluate determinant and inverse of a matrix

This paper presents new approaches for finding the determinant and inverse of a matrix. The choice of pivot selection is kept arbitrary and can be made according to the users need. So the ill conditioned matrices can be handled easily. The algorithms are more efficient as they save unnecessary data storage by reducing the order of the matrix after each iteration in the computation of determinant and incorporating dictionary notation (Chvatal, 1983) in the computation of inverse matrix. These algorithms are highly class room oriented and unlike the matrix inversion method (Khan, Shah, & Ahmad, 2010) the presented algorithm does not need any kind of permutations or inverse permutations

A Phenomenological Analysis of Challenges and Benefits of Online Learning Transformation in the Masters of Health Professions Education

Learning that challenges preconceived notions and inspires the development of fresh perspectives on the world has been referred to as transformative learning. This study offers a thorough analysis of how changes in learning have been reflected, including how they have an impact on curricula, in order to guide the master of health professions education’s potential field applications. Through purposive sampling, 15 students of MHPE from Islamic International Medical College, Rawalpindi, Pakistan have been chosen. The study design is phenomenological in nature. A semi-structured interview has been used. All the interviews were audio-recorded and separately transcribed. The transcribed interviews were then imported into NVivo software version 11 for analysis. A thematic analysis has been done and six themes are generated. The applications of distance learning positively related to teaching and learning practices and students identified a change in their attitudes toward distance learning. Major factors recognized were student-centered learning, small group discussions, peer-assisted learning, technology awareness, personal grooming, and motivation. About three-fourths of the sample population experienced a transformation in their distance learning after going through a Master’s in Health Professionals Education. The impact of hands-on activities and small group discussions turned out to be the strongest factors that caused the transformation in distance learning

Unsteady Flow of an MHD Tangent Hyperbolic Nanofluid Over a Stretching Sheet

Abstract The recent article addresses the unsteady flow of MHD incompressible tangent hyperbolic fluid with Nanofluid particles in the direction of a stretching surface. Nano-fluid is related to thermo-phoretic and Brownian movement. With proper help through the transformation procedure, the set of non-linear (PDEs) is re-framed into (ODEs). The initiate expressions of momentum, temperature field, and nano-particle concentration are composed into groups of nonlinear equations. That consequential terminology is computed shooting system. The impact of fundamental parameters on the flow field, thermal circulation, and meditation is described. Moreover, the flow field behavior due to the Wall friction, local Nusselt, and Sherwood numbers are examined. This study is significant as this transformation determined the shooting technique’s numerical result and ensured the physical parameters’ behavior graphically. The results show that the velocity field diminishes by escalating the Weissenberg (We) figure and power-law index (n), while thermal and concentration fields remain to detect elevating at similar parameters. Furthermore, the computed result is compared with existing literature and gets accuracy

Solution of Time-Fractional Third-Order Partial Differential Equations of One and Higher Dimensions

The purpose of this study is to develop the third order time fractional partial differential equations (PDEs) in one and higher dimensions, by taking Laplace Adomian decomposition method (LADM) and q-homotopy analysis transform method (q-HATM). To define fractional derivative, the Caputo operator is used for both fractional and integer orders. The solutions are obtained in the form of series. To understand the procedure of the suggested procedure, three numerical examples are taken. The graphs are plotted for the proposed solution at different values of fractional order ???? which is 0< ???? ≤ 1. Both proposed methods are implemented by using (LADM) and (q-HATM) showing that the proposed technique is found to be better and accurate instrument for solving linear and non-linear time fractional PDEs. The Novelty of the proposed study is that the provided solution for fractional order partial differential equations has never been attempted for third order, this means that the provided solution can solve the third order and could be generalized for the higher order also

Neural minimization methods (NMM) for solving variable order fractional delay differential equations (FDDEs) with simulated annealing (SA).

To enrich any model and its dynamics introduction of delay is useful, that models a precise description of real-life phenomena. Differential equations in which current time derivatives count on the solution and its derivatives at a prior time are known as delay differential equations (DDEs). In this study, we are introducing new techniques for finding the numerical solution of fractional delay differential equations (FDDEs) based on the application of neural minimization (NM) by utilizing Chebyshev simulated annealing neural network (ChSANN) and Legendre simulated annealing neural network (LSANN). The main purpose of using Chebyshev and Legendre polynomials, along with simulated annealing (SA), is to reduce mean square error (MSE) that leads to more accurate numerical approximations. This study provides the application of ChSANN and LSANN for solving DDEs and FDDEs. Proposed schemes can be effortlessly executed by using Mathematica or MATLAB software to get explicit solutions. Computational outcomes are depicted, for various numerical experiments, numerically and graphically with error analysis to demonstrate the accuracy and efficiency of the methods