Earthline Journal of Mathematical Sciences <p style="text-align: justify;">The Earthline Journal of Mathematical Sciences (e-ISSN: 2581-8147) is a peer-reviewed international journal devoted to publishing original research papers containing substantial contributions in any direction of Pure and Applied Mathematics, Theoretical and Applied Statistics, Theoretical Computer Science, Mathematical Physics, Mathematical Chemistry, Mathematical Modelling, Mathematical Biology. Applications of Mathematics in Finance and Economics are also welcome.</p> Earthline Publishers, Madanambedu, Chittoor, Andhra Pradesh, India en-US Earthline Journal of Mathematical Sciences 2581-8147 <p><img src=""><br>This work is licensed under a&nbsp;<a href="" rel="license">Creative Commons Attribution 4.0 International License</a>.</p> Coefficient Estimates for Certain Subclasses of m-Fold Symmetric Bi-univalent Functions Associated with Pseudo-Starlike Functions <p>In the present investigation, we introduce the subclasses $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\phi)$ and $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\delta)$ of \textit{m}-fold symmetric bi-univalent function class $\Sigma_m$, which are associated with the pseudo-starlike functions and defined in the open unit disk $\mathbb{U}$. Moreover, we obtain estimates on the initial coefficients $|b_{m+1}|$ and $|b_{2m+1}|$ for the functions belong to these subclasses and identified correlations with some of the earlier known classes.</p> Timilehin G. Shaba Amol B. Patil Copyright (c) 2021-03-07 2021-03-07 6 2 209 223 10.34198/ejms.6221.209223 Special Subfamilies of Holomorphic and Bi-univalent Functions related to Quasi-subordination <p>In the current work, special subfamilies of holomorphic bi-univalent functions based on quasi-subordination are introduced. Initial coefficient estimates for functions belonging to these subfamilies are established. Several consequences of our results and connections to known families are indicated.</p> S. R. Swamy Y. Sailaja Copyright (c) 2021-03-11 2021-03-11 6 2 225 237 10.34198/ejms.6221.225237 Coupled Anti Q-Fuzzy Subgroups using t-Conorms <p>In this paper we study coupled anti <em>Q</em>-fuzzy subgroups of <em>G</em> with respect to <em>t</em>-conorm <em>C</em>. We also discuss the union, normal and direct product of them. Moreover, the homomorphic image and pre-image of them is investigated under group homomorphisms and anti homomorphisms.</p> Clement Boateng Ampadu Copyright (c) 2021-03-13 2021-03-13 6 2 239 251 10.34198/ejms.6221.239251 On the Recurrence Properties of Generalized Tribonacci Sequence <p>In this paper, we investigate the recurrence properties of the generalized Tribonacci sequence and present how the generalized Tribonacci sequence at negative indices can be expressed by the sequence itself at positive indices.</p> Yüksel Soykan Copyright (c) 2021-03-17 2021-03-17 6 2 253 269 10.34198/ejms.6221.253269 Applications of Beta Negative Binomial Distribution Series on Holomorphic Functions <p>The purpose of this article is to derive the necessary and sufficient conditions for the power series 〖P℘〗_(ℷ,γ)^μ (t)&nbsp;whose coefficients are probabilities of the beta negative binomial distribution to be in the family F(σ,τ,ϵ,η,μ,ℷ,γ) of holomorphic functions which are defined in the open unit disk. We establish a number of important geometric properties, such as, coefficient estimates, extreme points, neighborhood property, integral representation, radii of starlikeness and convexity and Hadamard product properties for functions belongs to this family. Also we determinate some differential subordination properties of the power series 〖P℘〗_(ℷ,γ)^μ (t).</p> Abbas Kareem Wanas Najah Ali Jiben Al-Ziadi Copyright (c) 2021-03-23 2021-03-23 6 2 271 292 10.34198/ejms.6221.271292 Third Hankel Determinant Problem for Certain Subclasses of Analytic Functions Associated with Nephroid Domain <p>In this research article we consider two well known subclasses of starlike and bounded turning functions associated with nephroid domain. Our aims to find third Hankel determinant for these classes.</p> Muhammad Ghaffar Khan Bakhtiar Ahmad Wali Khan Mashwani Timilehin Gideon Shaba Muhammad Arif Copyright (c) 2021-04-09 2021-04-09 6 2 293 308 10.34198/ejms.6221.293308 Numerical Solutions of Mixed Integro-Differential Equations by Least-Squares Method and Laguerre Polynomial <p>The main objective of this article is to present a new technique for solving integro-differential equations (IDEs) subject to mixed conditions, based on the least-squares method (LSM) and Laguerre polynomial. To explain the effect of the proposed procedure will be discussed three examples of the first, second and three-order linear mixed IDEs. The numerical results used to demonstrate the validity and applicability of comparisons of this method with the exact solution shown that the competence and accuracy of the present method.</p> Hameeda Oda Al-Humedi Ahsan Fayez Shoushan Copyright (c) 2021-04-24 2021-04-24 6 2 309 323 10.34198/ejms.6221.309323 The Transmuted Kumaraswamy Pareto Distribution <p>The generalization of probability distributions in view of improving their flexibility in capturing the shape and tail behavior of disparate data sets has become one of the most active aspects of statistical research. We developed a new Pareto distribution by using Kumaraswamy method which gave rise to a new distribution called Kumaraswamy Pareto distribution. This method is called transmutation. The mathematical properties of the new generalized distribution was presented using quartiles, moments, entropy, order statistics mean deviation and maximum likelihood method of parameter estimation. The new generalized distribution was applied to a real life data on the exceedances of flood peaks (in m<sup>3</sup>/s)&nbsp; where it was observed to be superior to its sub models in terms of some goodness-of-fit test such as log likelihood criterion, Akaike Information Criterion (AIC) and Kolmogorov-Smirnov (K-S) measures.</p> K. U. Urama S. I. Onyeagu F. C. Eze Copyright (c) 2021-04-26 2021-04-26 6 2 325 358 10.34198/ejms.6221.325358 Modeling of Extreme Crude Oil Price using the Generalized Pareto Distribution: Brent and West Texas Benchmark Price <p><strong>Background and objective:</strong> Crude oil is an essential commodity in many countries of the world. This work studies the risk involved in the extreme crude oil price, using the daily crude oil price of the Brent and the West Texas benchmark from year 1990 to 2019.</p> <p><strong>Materials and methods:</strong> The Peak Over Threshold (POT) approach of the Generalized Pareto Distribution (GPD) was used to model the extreme crude oil price while the value at risk and the expected shortfall was used to quantify the risk involved in extreme price of crude oil. The GPD, using the Q-Q plot was found to be a good model for the extreme values of the crude oil price.</p> <p><strong>Results:</strong> The Value at Risk (VaR) and the Expected Shortfall (ES) calculated at 90%, 95% and 99% with the Maximum Likelihood estimators of GPD parameters and the threshold values were found to decrease with increase in quantile for both benchmark. This shows that risk involved in extreme crude oil price will be borne only by the investors and public.</p> <p><strong>Conclusion:</strong> It was also found that the VaR and ES of the Brent are higher than that of West Texas. This implies that it is safer to invest in West Texas crude oil.</p> Ngozi J. Amachukwu Happiness O. Obiora-Ilouno Edwin I. Obisue Copyright (c) 2021-04-28 2021-04-28 6 2 359 374 10.34198/ejms.6221.359374 Mathematical Analysis of the Effect of Control on the Dynamics of Diabetes Mellitus and Its Complications <p>Diabetes is a disorder in which the body becomes unable to control the amount of sugar in the blood. The pancreas (beta-cells) is not functioning normally, resulting in a partial or total lack of insulin which is the key to the mechanism converting sugar to energy. In this study, mathematical model for the dynamics of diabetes mellitus and its complications incorporating control is developed and analyzed. Positive lifestyle, which includes abstinence from alcohol, smoking and glutoning, and effective management of diabetes condition are incorporated as controls. The analytical solution of the model equations is obtained using Homotopy Perturbation Method. Numerical simulation of the model solution was done using Maple 18 Mathematical software. The parameters are varied and their effects on the model dynamics are presented graphically. The results showed that the two control measures can effectively be used to reduce the evolution of incidence of diabetes and occurrence of complications of diabetes thereby reducing the rate of morbidity and mortality due to diabetes complications.</p> Patrick Olabanji Aye Copyright (c) 2021-05-08 2021-05-08 6 2 375 395 10.34198/ejms.6221.375395