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> On Commutators of Fuzzy Multigroups <p>Fuzzy multigroup is an application of fuzzy multiset to group theory. Although, a lots have been done on the theory of fuzzy multigroups, some group's theoretic notions could still be investigated in fuzzy multigroup context. Certainly, the idea of commutator is one of such group's theoretic notions yet to be studied in the environment of fuzzy multigroups. Hence, the aim of this article is to establish the notion of commutator in fuzzy multigroup setting. A number of some related results are obtained and characterized. Among several results that are obtained,&nbsp; it is established that, if $A$ and $B$ are fuzzy submultigroups of a fuzzy multigroup $C$, then&nbsp; $[A, B]\subseteq A\cup B$ holds. Some homomorphic properties of commutator in fuzzy multigroup context are&nbsp;&nbsp; discussed. The notion of admissible fuzzy submultisets $A$ and $B$ of $C\in FMG(X)$&nbsp; under an operator domain $\mathcal{D}$ is explicated,&nbsp; and it is shown that $(A,B)$ and $[A,B]$ are $\mathcal{D}$-admissible.</p> P. A. Ejegwa J. M. Agbetayo Copyright (c) 2020-05-22 2020-05-22 4 2 189 210 10.34198/ejms.4220.189210 Applications of Certain Operators to the Classes of Analytic Functions Related to the Generalized Janowski Functions <p>We introduce certain subclasses of analytic functions related to the class of analytic, convex univalent functions. We discuss some results including inclusion relationships and invariance of the classes under convex convolution in terms of certain linear operators. Applications of these results associated with the generalized Janowski functions and conic domains are considered. Also, several radius problems are investigated.</p> Khalida Inayat Noor Shujaat Ali Shah Copyright (c) 2020-05-24 2020-05-24 4 2 211 225 10.34198/ejms.4220.211225 A Study on Generalized Jacobsthal-Padovan Numbers <p>In this paper, we investigate the generalized Jacobsthal-Padovan sequences and we deal with, in detail, four special cases, namely, Jacobsthal-Padovan, Jacobsthal-Perrin, adjusted Jacobsthal-Padovan and modified Jacobsthal-Padovan sequences. We present Binet’s formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences.</p> Yüksel Soykan Copyright (c) 2020-05-29 2020-05-29 4 2 227 251 10.34198/ejms.4220.227251 Some Fixed Point Theory Results for the Interpolative Berinde Weak Operator <p>Partially inspired by [Erdal Karapinar, Ravi Agarwal and Hassen Aydi, Interpolative Reich-Rus-Ćirić type contractions on partial metric spaces, <em>Mathematics</em> 6 (2018), 256] and [V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, <em>Nonlinear Anal. Forum</em> 9(1) (2004), 43-53], we introduce a concept of interpolative Berinde weak contraction, and obtain some existence theorems for mappings satisfying such a contractive definition, and some of its extensions.</p> Clement Boateng Ampadu Copyright (c) 2020-06-02 2020-06-02 4 2 253 271 10.34198/ejms.4220.253271 Alternative Axial Distances for Spherical Regions of Central Composite Designs <p>Alternatives to the existing axial distances of the Central Composite Design (CCD) in spherical design using three axial distances were studied. The aim of this study is to determine a better alternative to already existing axial distances whose prediction properties are more stable in the spherical design regions. Using the concepts of the three Pythagorean means, the arithmetic, harmonic and geometric axial distances for spherical regions were developed. The performances of the alternative axial distances were compared with the existing ones using the <em>D</em> and <em>G</em> optimality criteria. The study shows that the alternative axial distances are better using the <em>D</em> and <em>G</em> optimality criteria.</p> Linus Ifeanyi Onyishi F. C. Eze Copyright (c) 2020-06-09 2020-06-09 4 2 273 285 10.34198/ejms.4220.273285 Some Topological Measures for Nicotine <p>A topological index is a quantity expressed as a number that help us to catch symmetry of chemical compounds. With the help of quantitative structure property relationship (QSPR), we can guess physical and chemical properties of several chemical compounds. Here, we will compute Shingali &amp; Kanabour, Gourava and hype Gourava indices for the chemical compound Nicotine.</p> Abaid ur Rehman Virk Copyright (c) 2020-06-09 2020-06-09 4 2 287 296 10.34198/ejms.4220.287296 A Study on Generalized Fibonacci Numbers: Sum Formulas $\sum_{k=0}^{n}kx^{k}W_{k}^{3}$ and $\sum_{k=1}^{n}kx^{k}W_{-k}^{3}$ for the Cubes of Terms <p>In this paper, closed forms of the sum formulas $\sum_{k=0}^{n}kx^{k}W_{k}^{3}$ and $\sum_{k=1}^{n}kx^{k}W_{-k}^{3}$ for the&nbsp;cubes of generalized Fibonacci numbers are presented. As special cases, we&nbsp;give sum formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal,&nbsp;Jacobsthal-Lucas numbers.</p> Yüksel Soykan Copyright (c) 2020-06-15 2020-06-15 4 2 297 331 10.34198/ejms.4220.297331 Topological Properties for Harmonic τ-Uniformly Convex Functions of Order ρ Associated with Wanas Differential Operator <p>The purpose of the present paper is to establish some topological properties for a certain family of harmonic τ-uniformly convex functions of order ρ associated with Wanas differential operatordefined in the open unit disk <em>U</em>.</p> Abbas Kareem Wanas Copyright (c) 2020-06-25 2020-06-25 4 2 333 346 10.34198/ejms.4220.333346 Modeling and Forecasting Under-Five Mortality Rate in Nigeria using Auto-Regressive Integrated Moving Average Approach <p>Nigeria’s efforts aimed at reducing avoidable child deaths have been met with gradual and sustained progress. Despite the decline in childhood mortality in Nigeria in the last two decades, its prevalence still remain high in comparison to the global standard of mortality for children under the age of five which stands at 25 deaths per 1000 live births. Knowledge of the chances of Nigeria achieving this goal for childhood mortality will aid proper interventions needed to reduce the occurrence.</p> <p>Therefore, this paper employed the Auto-Regressive Integrated Moving Average (ARIMA) model for time series analysis to make forecast of under-five mortality in Nigeria up to 2030 using data obtained from the United Nation’s Inter Agency Group for Childhood Mortality Estimate (UN-IGME).</p> <p>The ARIMA (2, 1, 1) model predicted a reduction of up to 37.3% by 2030 at 95% confidence interval. Results from the study also showed that a reduction of over 300% in under-five mortality is required for Nigeria to be able to achieve the SDG goal for under-five mortality.</p> Donalben Onome Eke Friday Ewere Copyright (c) 2020-07-01 2020-07-01 4 2 347 360 10.34198/ejms.4220.347360 Complementary Kumaraswamy Weibull Power Series Distribution: Some Properties and Application <p>In this paper, we propose Complementary Kumaraswamy Weibull Power Series (CKWPS) Distributions. The method is obtained by compounding the Kumaraswamy-G distribution and Power Series distribution on a latent complementary distance problem base. The mathematical properties of the proposed class of distribution are studied. The method of Maximum Likelihood Estimation is used for obtaining the estimates of the model parameters. A member of the family is investigated in detail. Finally an application of the proposed class is illustrated using a real data set.</p> Innocent Boyle Eraikhuemen Julian Ibezimako Mbegbu Friday Ewere Copyright (c) 2020-07-04 2020-07-04 4 2 361 398 10.34198/ejms.4220.361398 Enhancing Image Security during Transmission using Residue Number System and k-shuffle <p>This paper proposes an algorithm that enhances the speed of transmission and secure images that are transmitted over internet or a network. The proposed cryptosystem uses a modified k-shuffling technique to scramble pixels of images and further decomposes them using Residue Number System. Simulations are done using two moduli sets with the modified k-shuffle technique. Analyses of results showed that both simulations could secure images without any loss of information and also the time taken for a complete encryption/decryption process is dependent on the moduli set. Among the chosen moduli sets, the even moduli set optimizes and completes execution using less time as compared to the traditional moduli set. The proposed scheme also showed resistance to statistical attacks (histogram, ciphertext, correlation attacks) and a significant reduction in the size of cipher images which enhances the speed of transmission over network.</p> Issah Zabsonre Alhassan Edward Danso Ansong Gaddafi Abdul-Salaam Salamudeen Alhassan Copyright (c) 2020-07-07 2020-07-07 4 2 399 424 10.34198/ejms.4220.399424