# Archive

## THE FIVE PARAMETER LOGISTIC (5PL) FUNCTION AND COVID-19 EPIDEMIC IN ICELAND

#### Authors:

Pinaki Pal, Asish Mitra

#### DOI NO:

https://doi.org/10.26782/jmcms.2021.06.00001

#### Abstract:

Right now, investigations are rigorously carried out on modeling the dynamic progress of (Covid-19) pandemic around the globe. Here we introduce a simple mathematical model for analyzing the dynamics of the Covid-19, considering only the number of cumulative cases. In the present work, the 5PL function is applied to study the Covid-19 spread in Iceland. The cumulative number of infected persons C(t) has been accurately fitted with the 5PL equation, giving rise to different epidemiological parameters. The result of the current examination reveals the effectiveness and efficacy of the 5PL function for exploring the Covid 19 dynamics in Iceland. The mathematical model is simple enough such that practitioners knowing algebra and non-linear regression analysis can employ it to examining the pandemic situation in different countries.

#### Keywords:

5PL Function,Covid-19 Pandemic,Daily Growth Rate,Iceland,Simulation,Tipping Point,

#### Refference:

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## AN ITERATIVE, BRACKETING & DERIVATIVE-FREE METHOD FOR NUMERICAL SOLUTION OF NON-LINEAR EQUATIONS USING STIRLING INTERPOLATION TECHNIQUE

#### Authors:

Sanaullah Jamali, Zubair Ahmed Kalhoro, Abdul Wasim Shaikh, Muhammad Saleem Chandio

#### DOI NO:

https://doi.org/10.26782/jmcms.2021.06.00002

#### Abstract:

In this article, an iterative, bracketing and derivative-free method have been proposed with the second-order of convergence for the solution of non-linear equations. The proposed method derives from the Stirling interpolation technique, Stirling interpolation technique is the process of using points with known values or sample points to estimate values at unknown points or polynomials. All types of problems (taken from literature) have been tested by the proposed method and compared with existing methods (regula falsi method, secant method and newton raphson method) and it’s noted that the proposed method is more rapidly converges as compared to all other existing methods. All problems were solved by using MATLAB Version: 8.3.0.532 (R2014a) on my personal computer with specification Intel(R) Core (TM) i3-4010U CPU @ 1.70GHz with RAM 4.00GB and Operating System: Microsoft Windows 10 Enterprise Version 10.0, 64-Bit Server, x64-based processor.

#### Keywords:

Non-linear equation,Stirling Interpolation Technique,convergence,number of iterations,Accuracy,

#### Refference:

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## STRESS AND FATIGUE LIFE PREDICTION OF THE H-TYPE DARRIEUS VERTICAL AXIS TURBINE FOR MICRO-HYDROPOWER APPLICATIONS

#### Authors:

Intizar Ali, Shadi Khan Baloch, Saifullah Samo, Tanweer Hussain

#### DOI NO:

https://doi.org/10.26782/jmcms.2021.06.00003

#### Abstract:

The present study aims to analyze the structural behavior of the Darrieus Hydro-kinetic turbine at different upstream velocity values and rotational rates. For that purpose, one-way fluid-structure interaction is performed to predict stresses, deformation and fatigue life of the turbine. To determine real-time fluid loads three-dimensional fluid flow simulations were performed, the obtained fluid loads were transferred to the structural finite element analysis model. CFD simulation results were validated with experimental results from literature where the close agreement was noticed. Structural analysis results revealed that the highest stresses are produced in the struts and at the joint where the shaft is connected with struts. Moreover, it was also found that the stress produced in the turbine is highly non-linear against Tip Speed Ratio (TSR) i.e inflow water velocity. Finite Element Analysis (FEA) results showed that maximum values of stresses were found in the turbine strut having a value 131.99MPa, which lower than the yield strength of the material, the fatigue life of 117520 cycles and factor of safety 1.89. The study also found that increased inflow velocity results increase in stress and deformation produced in the turbine. Additionally, the study assumed Aluminum Alloy as turbine blade material, further; it was found that the blade which confronts flow, experience higher stresses. Moreover, the study concluded that strut, blade-strut joint and strut-shaft joint are the critical parts of the turbine, require careful design consideration. Furthermore, the study also suggests that the turbine blade may be kept hollow to reduce turbine weight; hence inertia and turbine struts and shaft should be made of steel or the material having higher stiffness and strength.

#### Keywords:

Structural loading,Hydrokinetic turbine,Turbine stress analysis,deflection,fatigue life,Factor of safety,

#### Refference:

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## NUMERICAL SOLUTION OF THE PARTIAL DIFFERENTIAL EQUATION USING RANDOMLY GENERATED FINITE GRIDS AND TWO-DIMENSIONAL FRACTIONAL-ORDER LEGENDRE FUNCTION

#### Authors:

Sanaullah Mastoi, Wan Ainun Mior othman, Umair Ali, Umair Ahmed Rajput, Ghulam Fizza

#### DOI NO:

https://doi.org/10.26782/jmcms.2021.06.00004

#### Abstract:

There are various methods to solve the physical life problem involving engineering, scientific and biological systems. It is found that numerical methods are approximate solutions. In this way, randomly generated finite difference grids achieve an approximation with fewer iterations. The idea of randomly generated grids in cartesian coordinates and polar form are compared with the exact, iterative method, uniform grids, and approximate solutions in a generalized expansion form of two-dimensional fractional-order Legendre functions. The most ideal and benchmarking method is the finite difference method over randomly generated grids on Cartesian coordinates, polar coordinates used for numerical solutions. This concept motivates the investigation of the effects of the randomly generated meshes. The two-dimensional equation is solved over randomly generated meshes to test randomly generated grids and the implementation. The feasibility of the numerical solution is analyzed by comparing simulation profiles.

#### Keywords:

Partial differential equation,Finite difference method,Polar coordinates,Randomly generated grids,Uniform meshes,fractional-order Legendre functions,

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## A NOVEL FUZZY ENTROPY MEASURE AND ITS APPLICATION IN COVID-19 WITH FUZZY TOPSIS

#### Authors:

Razia Sharif, Zahid Hussain, Shahid Hussain, Sahar Abbas, Iftikhar Hussain

#### DOI NO:

https://doi.org/10.26782/jmcms.2021.06.00005

#### Abstract:

Fuzzy sets (FSs) are an important tool to model uncertainty and vagueness. Entropy is being used to measure the fuzziness within a fuzzy set (FS). These entropies are used to find multicriteria decision-making. For measuring uncertainty with TOPSIS techniques an axiomatic definition of entropy measure for fuzzy sets is also given in this paper. The proposed entropy is provided to satisfy all the axioms. Several numerical examples are presented to compare the proposed entropy measure with existing entropies. The corresponding results show that the newly proposed entropy can be computed easily and give reliable results. Finally, the decision-making algorithm TOPSIS (Techniques of ordered preference similarity to ideal solution) is utilized to solve multicriteria decision-making problems (MCDM) related to daily life.  In the current situation, COVID-19 has no proper medical treatment. We use TOPSIS technique to suggest an effective medicine for this pandemic. Numerical results and practical examples show the effectiveness and practical applicability of the proposed entropy.

#### Keywords:

Fuzzy entropy,TOPSIS,Uncertainty,Multicriteria Decision Making,

#### Refference:

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## SIMILARITY MEASURES OF PYTHAGOREAN FUZZY SETS WITH APPLICATIONS TO PATTERN RECOGNITION AND MULTICRITERIA DECISION MAKING WITH PYTHAGOREAN TOPSIS

#### Authors:

Zahid Hussain, Sahar Abbas , Shahid Hussain, Zaigham Ali, Gul Jabeen

#### DOI NO:

https://doi.org/10.26782/jmcms.2021.06.00006

#### Abstract:

The construction of divergence measures between two Pythagorean fuzzy sets (PFSs) is significant as it has a variety of applications in different areas such as multicriteria decision making, pattern recognition and image processing. The main purpose of this study to introduce an information-theoretic divergence so-called Pythagorean fuzzy Jensen-Rényi divergence (PFJRD) between two PFSs. The strength and characterization of the proposed Jensen-Rényi divergence between Pythagorean fuzzy sets lie in its practical applications which are very closed to real life. The proposed divergence measure is utilized to induce some useful similarity measures between PFSs. We apply them in pattern recognition, characterization of the similarity between linguistic variables and in multiple criteria decision making. To demonstrate the practical utility and applicability, we present some numerical examples related to daily life with the construction of Pythagorean fuzzy TOPSIS (Techniques of preference similar to ideal solution). Which is utilized to rank the Belt and Road initiative (BRI) projects. Our numerical simulation results show that the suggested measures are well suitable in pattern recognition, characterization of linguistic variables and multi-criteria decision-making environment.

#### Keywords:

Divergence measure,Intuitionistic fuzzy set (IFS),Pythagorean fuzzy set (PFS),Pattern recognition,similarity measure,multicriteria decision making,

#### Refference:

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## OPTIMIZATION OF DISSIMILAR FRICTION STIR WELDED ALUMINUM PATES (2024 T3 AND 7075T6) BY USING DIFFERENT METHODS

#### Authors:

Rasha M. Hussien, Mohsin Abdullah Al-Shammari

#### DOI NO:

https://doi.org/10.26782/jmcms.2021.06.00007

#### Abstract:

Friction stir welding (FSW) has many advantages when compared with another fusion welding. The experimental analysis and optimization of friction stir welding (FSW) were done to obtain desired mechanical properties of dissimilar aluminum welded plates (2024T3 and 7075T6). The friction stir welding process was done on aluminum plates (2024T3 and 7075T6) for different three rotating speeds (710, 1120 and 1800), three welding speeds (25, 50 and 77), three different steel tools (Square, cylindrical and Hexagonal) and 2° title angle. The different tests of welding were done according to the orthogonal matrix of experimental design analysis, then a tensile test was done to calculate the ultimate stress to get the welding efficiency. The optimum welding environment led to the maximum efficiency was obtained by these methods (Taguchi, Particle Swarm Optimization and new modified Particle Swarm Optimization).  Particle swarm optimization (and its new modification) used an artificial neural network to find the relation between the input and output parameters. The results showed that when the rotating speed is increased and welding speed is decreased (but this conclusion depends on tool shape) the welding efficiency is increased. The present study showed that the modified PSO is the best method to find the optimum welding environment as compared with experimental results.

#### Keywords:

dissimilar aluminum plates,Particle Swarm Optimization,Taguchi,

#### Refference:

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## NUMERICAL ITERATIVE METHOD OF OPEN METHODS WITH CONVERGE CUBICALLY FOR ESTIMATING NONLINEAR APPLICATION EQUATIONS

#### Authors:

Umair Khalid Qureshi, Prem kumar, Feroz Shah, Kamran Nazir Memon

#### DOI NO:

https://doi.org/10.26782/jmcms.2021.06.00008

#### Abstract:

Finding the single root of nonlinear equations is a classical problem that arises in a practical application in Engineering, Physics, Chemistry, Biosciences, etc. For this purpose, this study traces the development of a novel numerical iterative method of an open method for solving nonlinear algebraic and transcendental application equations. The proposed numerical technique has been founded from Secant Method and Newton Raphson Method, and the proposed method is compared with the Modified Newton Method and Variant Newton Method. From the results, it is pragmatic that the developed numerical iterative method is improving iteration number and accuracy with the assessment of the existing cubic method for estimating a single root nonlinear application equation.

#### Keywords:

applications equations,cubic methods,open methods,convergence,results,

#### Refference:

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