Modelling to Engineering Data Using a New Class of Continuous Models

In this paper, a new flexible generator of continuous lifespan models referred to as the Topp-Leone Weibull G (TLWG) family is developed and studied. Several mathematical characteristics have been investigated. The new hazard rate of the new model can be “monotonically increasing,” “monotonically decreasing,” “bathtub,” and “J shape.” The Farlie Gumbel Morgenstern (FGM) and the modified FGM (MFGM) families and Clayton Copula (CCO) are used to describe and display simple type Copula. We discuss the estimation of the model parameters by the maximum likelihood (MLL) estimations. Simulations are carried out to show the consistency and efficiency of parameter estimates, and finally, real data sets are used to demonstrate the flexibility and potential usefulness of the proposed family of algorithms by using the TLW exponential model as example of the new suggested family.

On Beta Exponentiated Moment Exponential Distribution with Mathematical Characteristics and Application to Engineering Sectors

A new BEME distribution known as beta Exponentiated moment exponential (BEME) distribution is proposed. We provide here some shape properties, moments in the form of special functions, mean deviations of BEME distribution. We derive mathematical properties of the BEME distribution including the reliability measures, the Bonferroni and the Lorenz curves, rth order statistics, measures of uncertainty: the Shannon entropy measure and the s-entropy measure. The parameters of the BEME distribution are estimated by the method of maximum likelihood estimation and estimated non-linear equations for these estimates are presented. The application of BEME distribution is explored in three different fields of engineering.

On the Characteristics and Application of Inverse Power Pranav Distribution

In this article, we study the mathematical characteristics of the inverse power Pranav distribution. The proposed distribution has three special cases namely Pranav, inverse Pranav and inverse power Pranav distributions. In addition with the basic properties of the distribution, the maximum likelihood method was employed in computing the parameters of the distribution. The 95% confidence interval was estimated for each of the parameters and finally, the distribution was applied to 128 bladder cancer patients to illustrate its applicability, and compared to Pranav distribution, inverse power Lindley distribution and inverse Ishita distribution. However, the inverse power Pranav distribution proved superiority over the competing models.

Modeling Sustainable Economic Development Using Production Functions

The most popular two-factor production functions used in the process of modeling sustainable economic development are examined. Economic and mathematical characteristics of Cobb-Douglas production functions, CES-function, linear function, Leontief and Allen functions are considered, in particular, type of dependence of labour productivity in relation to capital-labour ratio of commodity production system within mentioned production functions. Their most important economic and mathematical characteristics are presented: factors average and marginal return, demand for production resources, factor substitution, factors marginal rate of technical substitution, output elasticity by factors, elasticity of factors technical substitution, optimal capital-labour ratio according to the criterion of maximum output. Comparative analysis is given to Cobb-Douglas and CES-functions, which are two production functions mostly required in practice.

Convex combination of alternating projection and Douglas–Rachford operators for phase retrieval

We present the convergence analysis of convex combination of the alternating projection and Douglas–Rachford operators for solving the phase retrieval problem. New convergence criteria for iterations generated by the algorithm are established by applying various schemes of numerical analysis and exploring both physical and mathematical characteristics of the phase retrieval problem. Numerical results demonstrate the advantages of the algorithm over the other widely known projection methods in practically relevant simulations.

Intersection Sight Distance Characteristics of Turbo Roundabouts

A turbo roundabout uses spiral circulatory roads for effectively counteracting the problems faced in modern multilane roundabouts. First developed in 1996, the turbo roundabout has an advantage over the conventional roundabout regarding capacity and safety. Turbo roundabouts are still in the developing phase in North America, but even in the European subcontinent where they exist in large numbers, reliable analytical studies on the critical parameters of roundabout visibility are lacking. Visibility (sight distance) helps to shape the geometry of the intersection and aids in safety. This paper presents the mathematical characteristics of the intersection geometry and intersection sight distance (ISD) of the turbo roundabout. Mathematical formulas are presented for the sight distance from the approaching vehicle to the conflicting-entering and circulating vehicles. The maximum lateral clearances to the conflicting vehicles are derived using mathematical optimization. The developed analytical method is verified graphically using AutoCAD. To assist in practical applications, design aids for the maximum lateral clearance are presented. The presented method and design aids should aid in promoting safety at turbo roundabouts.

A Further Study on Multiperiod Health Diagnostics Methodology under a Single-Valued Neutrosophic Set

Employing the concept and function of tangency with similarity measures and counterpart distances for reliable medical consultations has been extensively studied in the past decades and results in lots of isomorphic measures for application. We compared the majority of such isomorphic measures proposed by various researchers and classified them into (a) maximum norm and (b) one-norm categories. Moreover, we found that previous researchers used monotonic functions to transform an identity function and resulted in complicated expressions. In this study, we provide a theoretical foundation to explain the isomorphic nature of a newer measure proposed by the following research paper against its studied existing one in deriving the same pattern recognition results. Specifically, this study initially proposes two similarity measures using maximum norm, arithmetic mean, and aggregation operators and followed by a detailed discussion on their mathematical characteristics. Subsequently, a simplified version of such measures is presented for easy application. This study completely covers two previous methods to point out that the complex approaches used were unnecessary. The findings will help physicians, patients, and their family members to obtain a proper medical diagnosis during multiple examinations.