Earthline Journal of Mathematical Sciences

New One-parameter Integral Formulas and Inequalities of the Logarithmic Type

2025-06-02T15:13:25+00:00

This article deals with two fundamental topics in mathematical analysis: the formulation of integral expressions and the derivation of integral inequalities. In particular, it introduces new one-parameter integral formulas and inequalities of the logarithmic type, where the integrands involve the logarithmic function in one way or another. Among the results are weighted Hölder-type integral inequalities and two different forms of Hardy-Hilbert-type integral inequalities. These results are illustrated by various examples and accompanied by rigorous proofs.

Wardowski Type Characterization of the Interpolative Kannan Fixed Point Theorem

2025-06-03T17:06:03+00:00

In [1], Wardowski introduced the F-contraction, and used it to prove the Banach contraction mapping theorem. In this paper, we introduce a concept of F-interpolative Kannan contraction, and use it prove the interpolative Kannan contraction mapping theorem of [2].

Mathematical Model and Analysis of Toxicant Effect on Human Health in Fuzzy Environment

2025-06-16T14:21:08+00:00

A nonlinear mathematical model is proposed and analyzed to examine the impact of a toxicant effect on human health in fuzzy environment, specifically its detrimental effects on the reproductive health of a subclass within the species. By applying stability theory, it is demonstrated that the overall species population stabilizes at an equilibrium level. Additionally, findings indicate that as the toxicant emission rate increases, the population density of the subclass severely affected by the toxicant—rendered incapable of reproduction—also rises.

F-Alternate Interpolative Ciric-Reich-Rus Contraction Mapping Theorem

2025-06-16T14:48:58+00:00

In [1], the authors introduced the interpolative Ciric-Reich-Rus operator in Branciari metric space and obtained some fixed point theorems. In [2], an alternate characterization of the interpolative Ciric-Reich-Rus operator was given, and some fixed point theorems were obtained. In the present paper, we consider the alternate interpolative Ciric-Reich-Rus operator is an F-contraction [3], and obtain a fixed point theorem.

Exploring the Statistical Treatments, Different Methods of Parameter Estimation, and Practical Applications of a New Probability Model

2025-06-23T14:04:09+00:00

This paper proposes a new three-parameter generalized Fréchet distribution using the MTI transformation scheme. We refer to the proposed model as MTI-Fréchet (MTIF) distribution. Several statistical treatments of the MTIF distribution, including survival, hazard rate, and quantile functions, moments, incomplete moments, moment-generating function, probability-weighted moment, and Renyi entropy, are derived. The study adopts four methods of parameter estimation to estimate the parameters of the MTIF distribution, followed by a simulation experiment to investigate the performance of the parameter estimates based on the four methods. The simulation results suggest that the MPS is the most appropriate estimation method for estimating the parameters of the MTIF distribution. The flexibility of the proposed MTIF distribution in practical data fitting is illustrated using two data sets. The results obtained from some model selection criteria and goodness-of-fit test statistics revealed that the MTIF distribution offered a better fit for the data sets compared to the classical Fréchet distribution and other generalized Fréchet distributions.

A Novel Cryptographic Approach for Enhanced Data Security in Cloud Computing Environments Using Residue Number System and Advanced Encryption Standard

2025-06-27T17:25:26+00:00

The rapid growth of cloud computing has made it an important area of study in computer science. While cloud computing offers many benefits, it also faces many challenges, including information security. To address this challenge, this paper proposes and tests a new double-layered encryption method to improve data security in the cloud. The method combines the residue number system (RNS) and the advanced encryption standard (AES) to reduce hardware complexity and improve encryption efficiency. This help address the changing landscape of security threats and computational needs that are part of cloud computing. The results show that the proposed method has the features needed to make an effective encryption algorithm for cloud computing. It combines security and speed and works better than other hybrid AES cryptographic techniques. The proposed technique was comprehensively evaluated and tested using Python Programming Language version 3.9.7, executed on a 1.4 GHz Quad-Core Intel Core ™i5 macOS processor laptop.

Non-ergodicity of the Earth’s Annual Temperature in a Precession Cycle of the Equinoxes

2025-06-29T17:07:43+00:00

A three-parameter paleoclimate model has revealed the non-ergodicity of the Earth’s annual temperature during a precession cycle. This result comes from the inverse problem of free parameter identification when the experimental input data are the mean winter and summer solstice temperatures for the period 1950-1975. The inverse problem is underdetermined and admits infinite solutions. However, it is possible to order these solutions in symmetric pairs according to the increasing level of entropy possessed by the annual half-cycle between the two solstices, up to the maximum value at which the two solutions collapse into one. Therefore, the parameter identification process admits uniqueness if, as a third constraint, one searches for the solution of the annual temperature profile that has the maximum entropy, i.e. the highest probability. The existence of a unique solution with the highest probability among the infinite other possible solutions implies the non-ergodic character of the annual temperature.