Earthline Journal of Mathematical Sciences

A Note on Summability of Infinite Series

2024-04-07T10:25:39+00:00

The purpose of the present paper is to get the necessary and sufficient conditions for absolute matrix summability of infinite series.

$K^{th}$-order Differential Subordination Results of Analytic Functions in the Complex Plane

2024-04-07T16:17:12+00:00

In recent years, there have been many interesting usages for differential subordinations of analytic functions in Geometric Function Theory of Complex Analysis. The concept of the first and second-order differential subordination have been pioneered by Miller and Mocanu. In 2011, the third-order differential subordination were defined to give a new generalization to the concept of differential subordination. While the fourth-order differential subordination has been introduced in 2020. In the present article, we introduce new concept that is the K^th-order differential subordination of analytic functions in the open unit disk U.

Fixed Point Theorems in Extended Convex Quasi s-metric Spaces

2024-04-08T17:33:21+00:00

In this work, through the convex structure, we introduce the concept of the extended convex quasi s-metric spaces. In addition, through Mann's iterative technique, we theorize the existence of a unique fixed point for two types of contraction mapping in extended convex quasi s-metric spaces.

A Mathematical Logistic Model Describes Both Global CO2 Emissions and its Accumulation in the Atmosphere

2024-04-11T16:48:55+00:00

A single kinetic model, of a logistic nature, is able to describe two different phenomena: the global emission of CO₂ due to the combustion of fossil fuels and the observed accumulation of CO₂ in the atmosphere. Unexpectedly, the analysis of the experimental data clearly shows that the two rates of emission and accumulation are almost exactly in phase and differ by a constant factor. The fraction of CO₂ that accumulates in the atmosphere is constantly equal to 65% of the emissions. The same percentage also applies to the rate of change of the two phenomena, i.e., the accelerations.

Improving Security on Election Results Data Transmission via Cloud Using Hybrid Homomorphic Encryption

2024-04-29T17:06:01+00:00

Elections in recent years have become topical issues and characterized by violence and conflicts leading to loss of lives and properties. The integrity and confidentiality of the declared collated results have been questioned by individuals and organisations with keen interest in the outcomes of every election. Different countries have adopted different Election Results Management Systems (RMS) to help present a credible, fair and transparent election results. These systems adopted are not without criticisms and suspicions. This research paper has presented various factors that need to be considered when selecting a Results Management System (RMS) for elections. A cloud-based using a Hybrid homomorphic encryption approach is proposed in managing the election results data security and transmission. The proposed scheme has demonstrated effectiveness in handling data integrity, data confidentiality, data privacy and access control. The proposed scheme presented has enhanced the security of election results data against Chosen Ciphetext Attacks (CCA) and Denial of Service (DoS) as well as other cyber related attacks. The time required for the entire election data encryption, transmission, decryption, upload time and download time has been greatly enhanced with the proposed system. The proposed system workflow algorithm, key generation algorithm, encryption algorithm and decryption have been presented in this research paper. The outcome of the research work indicates that only 0.00078 seconds is required to generate keys for about 100 users. About 0.705 seconds and 0.863 seconds is required for the encryption and decryption of a 500MB election results data. It was observed that the overall election results data transmission time is about 51.779 seconds which is less than one minute (60 seconds) for about 500MB data size of the election results data. This paper makes a case for the adoption and implementation of the proposed system since it performs better in terms of securing the election results data and transmission time in the cloud environment.

Causes of Backward Bifurcation in a Tuberculosis-Schistosomiasis Co-infection Dynamics

2024-05-01T17:30:33+00:00

To obtain a thorough understanding of the influence of schistosomiasis infections on the transmission dynamics of tuberculosis, a deterministic mathematical model for the transmission dynamics of tuberculosis (TB) co-infection with schistosomiasis is created and examined. The aim of the research is to examine the reasons behind the backward bifurcation in the co-infection dynamics of tuberculosis and schistosomiasis. The backward bifurcation phenomena can be caused by the following parameters, according to the model's analysis (when the associated reproduction number is less than one), other than the well established route of exogeneous re-infection of latently infected TB individuals, the relative rates at which humans with latent schistosomiasis ($\eta_1$) and active schistosomiasis ($\eta_2$) are infected with TB, respectively, the lowered rate of reinfection with schistosomiasis ($\psi$), the fraction of individuals who experience fast progression to active TB ($p$), the adjustment parameter which accounts for the increased probability of infectiousness of humans with active TB and latent schistosomiasis ($\Pi_1$), the treatment rate of people infected with active TB exposed to schistosomiasis ($\zeta_{T1}$) and the rate of progression to active TB and exposed to schistosomiasis to active TB and active schistosomiasis ($\sigma$).

An Improvement on Likert Scale via Fuzzy Relation

2024-05-20T15:34:11+00:00

Relation is a mathematical concept that is often used in modeling relationships in physical and social sciences and the likes. The advent of fuzzy sets which model imprecision and uncertainties that occur in social animals necessitates the introduction of fuzzy relations. Besides, events and situations possess properties which are often contradictory such as good and bad, positive and negative, profit and loss and so on. We dug several literatures, particularly the analysis and hypothesis testing of several results from questionnaires, compared one of them with our newly proposed Likert scale which has fuzzy influence. The results of the two cases was analysed and presented with a bar chart, and it was clear that unlike the usual Likert scale that could be restricted from outliers, the one with fuzzy influence took care of uncertainties.

Polytropic Dynamical Systems with Time Singularity

2024-05-20T16:51:59+00:00

In this paper we consider a class of second order singular homogeneous differential equations called the Lane-Emden-type with time singularity in the drift coefficient. Lane-Emden equations are singular initial value problems that model phenomena in astrophysics such as stellar structure and are governed by polytropics with applications in isothermal gas spheres. A hybrid method that combines two simple methods; Euler's method and shooting method, is proposed to approximate the solution of this type of dynamic equations. We adopt the shooting method to reduce the boundary value problem, then we apply Euler's algorithm to the resulted initial value problem to get approximations for the solution of the Lane-Emden equation. Finally, numerical examples and simulation are provided to show the validity and efficiency of the proposed technique, as well as the convergence and error estimation are analyzed.