Science & Technology Asia

A New Family of Distribution with Application on Two Real Datasets on Survival Problem

Kanak Modi, Devendra Kumar, Yudhveer Singh — Thu, 26 Mar 2020 13:28:56 +0700

In this paper we introduce a new Modi family of continuous probability distributions with application on patients suffering from disease and their survival times. The proposed distribution possesses a density function with three parameters and an inverted J-shape hazard rate function. We studied the nature of proposed distribution with the help of its mathematical and statistical properties. The probability density function of order statistics for this distribution is also obtained. We perform classical estimation of parameters by using the technique of maximum likelihood estimate. We apply it to two real datasets and show that it provides better fit than other well known distributions.

Influences of Polarization on Two Equal Semi-permeable Cracks in a Piezoelectric Media

Kamlesh Jangid, Devendra Kumar, Jagdev Singh — Thu, 26 Mar 2020 13:37:19 +0700

In this paper, the influence of arbitrary poling direction on a cracked piezoelectric medium is studied. For this purpose, an infinite piezoelectric plate cut along to equal semipermeable collinear cracks is considered. Stroh’s formalism and complex variable technique are used to formulate the problem. The closed-form analytical expressions are derived for the various fracture parameters viz. crack opening displacement, crack opening potential drop, intensity factors, and energy release rate. Moreover, the quadratic equation is derived to find the electric displacement inside the crack gap media. For a poled PZT-5H ceramic plate, an illustrative numerical investigation is implemented to demonstrate the effect of arbitrary polarization on the various fracture parameters.

MHD Fluid Flow with Cross-Diffusion Effects through Channel Using Optimal Homotopy Analysis Method

Khushbu Bhaskar, Kalpna Sharma, Sumit Gupta, Ruchika Mehta — Thu, 26 Mar 2020 13:50:20 +0700

The intention of the present study is to investigate the cross-diffusion effect on MHD fluid flow passing through a vertical channel. Navier slip boundary conditions are applied by assuming that the channel is filled with a porous medium. The effect of considered parameters is also studied on heat as well as on mass transfer. With the help of an optimal homotopic procedure, the transformed governing equations are evaluated. The quantitative estimates are contributed through graphs and physical quantities are presented through a table.

Statistical Deferred Euler Summability Mean and Associated Korovokin-type Approximation Theorem

Madhusudan Patro, Susanta Kumar Paikray, Hemen Dutta — Thu, 26 Mar 2020 13:59:49 +0700

Statistical convergence has recently attracted the wide-spread attention of researchers due mainly to the fact that it is more general than the classical convergence. As far as the recent research on the theory and applications of summability is concerned, two basic concepts, namely statistical convergence and Korovokin-type approximation theorems play a very vital role. In the present paper, we introduce the notions of deferred Euler statistical convergence as well as statistical deferred Euler summability means and establish some inclusion relations between them. Furthermore, we prove a Korovokin-type approximation theorem based on our proposed mean, and we also show that our theorem is stronger than the classical versions of Korovokin-type approximation theorem.

Certain New Integral Properties of a Product of Generalized Special Functions Associated with Feynman Integrals

Sapna Tyagi, Monika Jain, Jagdev Singh — Thu, 26 Mar 2020 14:08:25 +0700

In the present study we deal with certain integral properties pertaining to a general class of polynomials, Aleph function, H-function, and the generalized M-Series. The main outcomes presented here are nature wise basic and unified and are possibly useful in many fields particularly statistical mechanics, probability theory, electrical networks, etc. The integrals involved here include several types of Feynman integrals, the precise division of Gaussian models in statistical mechanics, and many other special case functions. These results provide numerous corresponding remarkable results, such as simpler special functions and polynomials, which are special cases of expressions.

Statistical Analyses of Impressions Related to the Customer’s Experience while Attending Restaurants Located in Vlore, Albania

Orgeta Gjermëni, Elenica Pjero — Thu, 26 Mar 2020 14:14:50 +0700

Studies on customer’s experience are important to better understand what is offered and to define what should be improved. The purpose of this study is to measure and observe customer’s satisfaction from the quality of services received from restaurants located in Vlore, Albania. Data is gathered through an online survey which was filled 700 times. Descriptive analysis, Cronbach’s alpha, chi-square test, Cramer’s measure of association, Spearman’s rho correlation coefficient, and generalized linear model are used throughout the analysis. Findings showed that the overall level of customer’s satisfaction was neutral with 37:6 5% followed by satisfied ones with 27:9 5%. There was statistical evidence of a frail relationship at the 1% level of significance between the overall level of satisfaction and gender, employment, monthly income, bill accuracy, fairness of the prices, speed in service, the patience to bring the bill, clear communication, and politeness of the host staff. Further, there was evidence of a negative relationship at the 5% level between the overall level of satisfaction and employment, monthly income and fairness of the price. 66:18% of the variation of the overall level of satisfaction was explained by age, gender, employment, monthly income, patience to bring the bill, bill accuracy, and variety in menu, warm and fresh served foods. The best model predicts 62:25% of the overall satisfaction. These results help restaurant businesses, and whoever wants to invest in this sector, to better understand customer’s satisfaction about service quality and to pinpoint aspects that can be improved.

Selection of Inventory Policy under Pythogrean Fuzzy Environment

Prabjot Kaur, Anjali Priya — Thu, 26 Mar 2020 14:19:14 +0700

This paper is an application of inventory policy selection using Grey Relational Analysis (GRA) under Pythagorean Fuzzy Environment. Ranking of inventory policy is a complex multiple criteria decision making (MCDM) problem. The multi-criteria problem comprises qualitative and quantitative factors that are uncertain and contradictory. These factors are not always crisp and are some of the times subjected to vagueness because of the unreliable nature of the data collected. Hence, they are considered in the Pythagorean fuzzy environment which removes this vagueness by assigning membership and non-membership functions to these factors. A comparison of GRA method is made with VIKOR for determining the rank of the best inventory policy. A numerical example is depicted to outline the application of these two algorithms. The first rank of one of the inventory policies is the same by both these methods. Spearman Rank Correlation is utilized to compare the results of both the methods; a high correlation value illustrates the validity of the methods used for comparison of the results.

Geometric Properties for an Unified Class of Functions Characterized Using Fractional Ruscheweyh-Goyal Derivative Operator

Ritu Agarwal, Gauri Shankar Paliwal, Sunil Dutt Purohit — Thu, 26 Mar 2020 14:27:52 +0700

By means of the principle of subordination, we commence with a unified subclass of analytic functions involving the fractional Ruscheweyh-Goyal derivative operator introduced by Goyal and Goyal (2005). The properties like inclusion relationships, coefficient inequalities and distortion theorems for the above mentioned class have been analyzed. For analytic functions defined in open disk of unit radius, we have incorporated the differential sandwich theorem.

An Efficient Computation Approach for Abel’s Integral Equations of the Second Kind

Rajendra K. Bairwa, Ajay Kumar, Devendra Kumar — Thu, 26 Mar 2020 14:32:58 +0700

This paper presents the application of a new powerful method named as q-homotopy analysis transform method (q-HATM). The q-HATM is a combination of the q-homotopy analysis scheme and the Laplace transform approach and more general than other existing techniques. Abel’s integral equation of the second kind has been solved by using this method. We solve some examples and plot the graphs. The numerical solutions are shown in the form of graphs.

An Approach to Identify Significant Parameters in Blood Flow Through Human Arteries

Karthik Alasakani, Sai Lakshmi Radhika Tantravahi, Praveen Kumar — Thu, 26 Mar 2020 14:45:18 +0700

In this work, we attempt to identify parameters that are significant in blood flow through human arteries. For this, we developed a mathematical model and carried out simulations using data on human arteries and then performed a statistical analysis of the data generated. The mathematical model considers blood as a Newtonian fluid with its constitutive equation comprising two parameters termed as fluid parameters, namely the density and viscosity. Arteries are modelled as tapered and elastic circular pipes wherein the radius of the artery is in terms of the material parameters, termed taper fraction, expanding/contracting parameter and aspect ratio (=radius of the artery/length of the artery). Blood flow is described as pulsatile with the frequency of oscillations as the flow parameter monitored. The resulting system of partial differential equations is solved using the Homotopy Analysis Method (HAM). Data on human arteries (healthy) has been taken from literature, and we worked on different age groups ranging from 15 years to 65 years, both on male and female populations. The two physical quantities of interest i.e. the wall shear stress (WSS) and the volumetric flow rate have been computed and analysis has been carried out to identify significant parameters using a multiple linear regression model.

Unsteady Magnetohydrodynamic Flow in the Presence of Permeable Medium through an Upstanding Channel with Persistent Suction and Heat Source

Tripti Mehta, Ruchika Mehta, Devendra Kumar — Thu, 26 Mar 2020 14:59:09 +0700

The present study explores unsteady magnetohydrodynamic, incompressible viscous fluid flow through upstanding equidistant plates in the presence of permeable media, persistent heat flux and heat source. The flow is constrained due to the flow between two equidistant plates, one of which is moving and other is at rest, and the occurrence of free convection because of the stationary wall with persistent temperature while heat flux is persistent on the wall with a uniform upstanding motion in its self plane. The fluid is considered emitting/absorbing but medium is non-scattering, so taking it as grey and to describe the radiative heat flux with persistent suction we used the Rosseland approximation. Numerical results for the velocity and temperature distribution for various physical parameters as well as the local skin friction coefficient and local Nusselt number are discussed numerically and shown through graphs.

Evolution of Modulational Instability in Non-linear Hirota Types Equation

Ram Dayal Pankaj, Arun Kumar, Bhawani Singh — Thu, 26 Mar 2020 15:06:55 +0700

The Time Dependent Variational Approach (TDVA) is applied to estimate the modulational instability (MI) for Non-Linear Hirota type equations. This approach is new to obtain the nonlinear dispersion relation (NDR) for such equations. The classical modulational instability criterion is nascent and it establishes many prospective for the MI domain because of the generalized dispersion relation. Analyzing the Non Linear Partial Differential Equations, we rederive the classical modulational instability criterion.

Embedded Pseudo-Runge-Kutta Methods for First and Second Order Initial Value Problems

Shruti Tiwari, Ram Kishor Pandey, Harendra Singh, Jagdev Singh — Thu, 26 Mar 2020 15:15:34 +0700

In this paper, we have proposed an embedded pseudo-Runge-Kutta method (EPRKM) of order three. We have developed two implicit embedded pseudo Runge-Kutta methods (EPRKM) for the solution of first order initial value problems of which the first one is fully implicit and the other is diagonally implicit. Also, a two-step explicit embedded pseudo- Runge-Kutta method for solving second order initial value problems is also derived. This development is an effort to minimize the computational cost of classical Runge-Kutta (RK) method. A classical s-stage RK method requires s function evaluations (slopes) per step. The present methods require four evaluations in the first step and from the second step onwards
it requires only two evaluations per step. The cost of computation in the form of number of function evaluations (slopes) are compared via Table 1, from which it is evident that our proposed developments are cost-efficient. The proposed methods are tested on two initial value problems (IVPs) and the errors obtained by these methods are compared with the errors by RK third order (RK3), third order implicit Runge-Kutta (IRK3) method and Runge-Kutta- Nyström 3-stage method (RKN3) which are shown in Tables 2 and 3. The convergence and stability properties are established and the governing theorems are also derived. Intervals and regions of absolute stability of the proposed methods are also derived, and regions are depicted in Fig. 1. The proposed methods have wide scope of applicability for the numerical solution of IVPs which are frequently occurred in physics, chemistry, molecular dynamics, fluid dynamics and several branches of engineering.

Charnes and Cooper’s Transformations for Solving Uncertain Multi-Item Fixed Charge Solid Transportation Problem

Vandana Kakran, Jayesh Mohan Dhodiya — Thu, 26 Mar 2020 00:00:00 +0700

This paper focusses on the multi-item fixed charge solid transportation problem (MIFCSTP) with parameters like transportation cost, fixed charge, conveyance capacities, and supply and demand values taken as uncertain variables. The model representing MIFCSTP with uncertain variables is known as an uncertain model which cannot be solved directly by standard techniques. So, to deal with uncertain MIFCSTP, the expected value model (EVM) and dependent chance-constrained model (DCCM) are formulated. Later, using the theory of uncertainty, these two models are converted into their corresponding deterministic forms. This crisp formulation of the EVM is solved directly by LINGO 18.0 software whereas the Charnes and Cooper’s transformation is applied on the deterministic form of the DCCM for converting it into linear form. Then, the optimal solution of the transformed linear form of the DCCM is obtained using LINGO 18.0 software. At the end, the application of the formulated models is demonstrated with the help of a numerical illustration.

On a Paradox in Multi-Objective Linear and Fractional Transportation Problem

Vishwas Deep Joshi, Jagdev Singh, Rachana Saini — Thu, 26 Mar 2020 15:25:49 +0700

In this paper, a more-for-less (MFL) paradox situation is discussed for a multiobjective transportation problem with linear and fractional objective function. By using the MFL paradox in multi-objective programming, we can transfer more goods from source to destination with less or equal compromise optimal solution. In this approach, it is not necessary that a paradox is present in every objective. If a paradox is found in one of the objectives, then we can use this approach. We compare the paradoxical solution with compromise solution using ranking procedure [1] and show the superiority of the proposed paradoxical approach. For proper explanation of theory two examples are discussed.