Earthline Journal of Mathematical Sciences

Some New Classes of General Harmonic-like Variational Inequalities

Muhammad Aslam Noor, Khalida Inayat Noor — Mon, 08 Sep 2025 14:55:51 +0000

Several new classes of general harmonic-like variational inequalities involving two arbitrary operators are introduced and considered in this paper. Some important cases are discussed, which can be obtained by choosing suitable and appropriate choice of the operators. Projection technique is applied to establish the equivalence between the general harmonic-like variational inequalities and fixed point problems. This alternative formulation is used to discuss the uniqueness of the solution as well as to propose a wide class of proximal point algorithms. Convergence criteria of the proposed methods is considered. Asymptotic stability of the solution is studied using the first order dynamical system associated with variational inequalities. Second order dynamical systems associated with general quasi variational inequalities are applied to suggest some inertial type methods. Some special cases are discussed as applications of the main results. We also show that the change of variable can be used to show that the harmonic-like variational inequalities. Several open problems are indicated for future research work.

Stochastic Dynamics of Dual-Prey–Predator Interactions under Harvesting Pressure: Insights from the California Current Ecosystem

Chandrima Talapatra — Tue, 09 Sep 2025 16:27:04 +0000

This study presents a stochastic predator-prey model involving two harvested prey species—sardines and anchovies—and a common predator, the blacktip shark, under the influence of environmental noise. The model incorporates Holling type-II functional responses, harvesting efforts, and white noise perturbations representing environmental variability. Analytical investigations determine the boundedness and stability conditions of equilibria. Numerical simulations reveal that the predator population is highly sensitive to stochastic perturbations, particularly the noise intensity associated with predator mortality. Notably, a sufficiently large noise intensity in anchovy dynamics ($\alpha_2 > 72.06$) can stabilize the coexistence equilibrium, where higher values of $\alpha_1$ and $\alpha_2$ tend to destabilize the system. Phase portraits and bifurcation analyses illustrate the effects of harvesting rates and noise intensities on species persistence and extinction. These findings highlight critical thresholds for sustainable harvesting and noise tolerance, offering ecological insights into species coexistence within the California Current ecosystem.

Threshold Selection for Peak Over Threshold Models Using Logistic Regression

Temitope Comfort Iroko, Iliyasu Tukur, Victor Adeyanju — Thu, 11 Sep 2025 16:27:43 +0000

Threshold selection remains a critical challenge in the application of Extreme Value Theory (EVT), particularly in actuarial science, where accurate modeling of extreme insurance claims is vital for solvency, capital adequacy, and reinsurance pricing. Traditional graphical tools, such as the mean residual life (MRL) plot, are highly dependent on visual interpretation and expert judgment, which limits reproducibility and consistency between practitioners. This paper proposes a machine learning approach using logistic regression to assign extremeness probabilities to insurance claims. The model is trained on labels generated from an initial quantile-based rule, classifying claims above the 90th percentile as extreme. The optimal threshold is determined as the smallest amount of claim with predicted probability exceeding a predefined cut-off (e.g., $90\%$). This probability-based rule provides an objective alternative to visual diagnostics and aligns well with classical EVT tools such as the MRL plot. After identifying exceedances above the selected threshold, a Generalized Pareto Distribution (GPD) is fitted using maximum likelihood estimation. Tail-based risk measures, including Value at Risk (VaR) and Expected Shortfall (ES), are then computed at the $99\%$ confidence interval to quantify the severity of potential extreme losses. The proposed framework is interpretable, reproducible, and readily applicable in actuarial workflows, offering a more consistent and automated solution for tail risk modeling.

Common Fixed Point Theorem for Berinde Weak Type Contraction Via Interpolation

Clement Boateng Ampadu — Sun, 14 Sep 2025 00:00:00 +0000

In this paper, we introduce the notion of an interpolative Berinde weak pair contraction, and obtain a common fixed point theorem in the setting of metric spaces. We illustrate the main result of the paper with an example.

Examining New Convex Integral Inequalities

Christophe Chesneau — Sun, 14 Sep 2025 16:20:52 +0000

In this article, we introduce new convex integral inequalities based on a contemporary and adaptable analytical framework. These inequalities can handle composed functions, integral expressions, and ratio-type functionals, which make them applicable to a wide range of analysis problems. Our main result, in particular, complements a recent theorem from the literature by providing a valuable and non-trivial lower bound. The proofs are presented in full detail to ensure mathematical rigor, clarity, and reproducibility.

Properties of Generalized Strongly Close-to-convex Functions

Khalida Inayat Noor, Imtiaz Waheed — Mon, 15 Sep 2025 00:00:00 +0000

This paper defines certain subclasses of analytic functions and various properties including necessary conditions, distortion result, inclusion properties are investigated. In addition radius problems are discussed. Several known consequences of our investigations are also pointed out.

Single and Multivalued Extended Interpolative Berinde Weak Type F-Contraction Mapping Theorem

Clement Boateng Ampadu — Mon, 15 Sep 2025 00:00:00 +0000

In this paper we introduce the notion of an extended interpolative single and multivalued Berinde weak type F-contraction, and obtain some fixed point theorems for such mappings. An example is given to illustrate the main result.

On New General Beesack-Opial-type Integral Inequalities

Christophe Chesneau — Mon, 22 Sep 2025 16:03:43 +0000

This article presents new Beesack-Opial-type integral inequalities incorporating three functions. The upper bounds are defined using some derivatives and primitives of these functions. Detailed proofs are provided. These are accompanied by illustrative examples, including applications involving the Laplace transform.

On a New Integral Inequality Derived from the Hardy-Hilbert Integral Inequality

Christophe Chesneau — Mon, 22 Sep 2025 16:15:59 +0000

This article is devoted to a new integral inequality expressed in terms of elementary integrals. The proof is notable for its use of the classical Hardy-Hilbert integral inequality, which provides an elegant and concise argument. As an illustration of its utility, we also present an application to the gamma function.

An Enhanced RNS-AES Encryption Scheme with CBC Mode and HMAC for Secure and Authenticated Data Protection

Sun, 05 Oct 2025 16:33:34 +0000

Modern cryptographic systems in cloud and IoT environments must balance strong security with real-time performance, yet existing methods often require trade-offs that sacrifice speed for security or introduce latency through conservative designs. This paper presents RNS-AES-CBC-HMAC, a hybrid framework that integrates Residue Number System (RNS) arithmetic with AES-256 and HMAC-SHA256 to deliver both performance and robust security. Using a balanced modulus set $\{2^n - 1,\, 2^n,\, 2^n + 1\}$ for constant-time, carry-free arithmetic mitigates side-channel risks, while AES-256 in Cipher Block Chaining (CBC) mode ensures confidentiality and HMAC-SHA256 provides message integrity with minimal overhead. Implemented in Python 3.10 with PyCryptodome 3.18.0 and tested on an AMD Ryzen~5~2500U, the framework achieved encryption/decryption latencies of $55$--$593\,\mu\text{s}$ for 4--15 character payloads, representing 99\% improvement over previous RNS-based hybrids. It scales linearly in time and memory $\mathcal{O}(n)$, consumes only $21\,\text{KB}$, and produces ciphertext entropy of $7.999\,\text{bits/byte}$, surpassing NIST SP~800-22 standards. This dual-layer architecture effectively counters both passive and active threats, making it suitable for low-latency IoT edge devices and high-throughput cloud systems, merging theoretical number systems with practical cryptography for real-world deployment.

Intuitionistic Fuzzy Riemann-Liouville and Hadamard Fractional ⊕⊗Integrals

Enes Yavuz — Mon, 06 Oct 2025 15:38:39 +0000

In this study, we introduce intuitionistic fuzzy Riemann-Liouville and Hadamard fractional ^⊕⊗integrals of intuitionistic fuzzy valued functions and obtain some of their basic properties. We also give some examples to illustrate the obtained results.

A Collection of Trigonometric Inequalities via Functional Estimates

Alexandros Kyriakis, Marios Kyriakis — Mon, 13 Oct 2025 16:11:25 +0000

In this article, a stream of inequalities involving trigonometric functions is presented. All inequalities are rigorously proved and derived via a specific collection of functional estimates. Most of the results that are presented in the literature rely on monotonicity properties or power series expansions to derive inequalities, but in this work the authors heavily rely on functional estimates involving Lebesgue norms. The inequalities derived are non-trivial and they enrich the current works in the mathematical literature.

A Subclass of Harmonic Multivalent Functions Associated with Differential Operator

Kirti Pal, A. L. Pathak — Wed, 22 Oct 2025 00:00:00 +0000

In the present paper, we propose and study a new subclass of harmonic multivalent functions in the open unit disc $ U=\{z:z\in \mathbb{C},|z|<1\},$ which is characterized by its association with a special differential operator. This investigation focuses on establishing several fundamental properties of the introduced subclass including coefficient bounds, convex combination criteria, convolution conditions and the characterization of its extreme points.

A New T-X Family of Distributions: Structural Properties and Applications

Sunday A. Osagie, Toritsesan B. Batubo — Tue, 04 Nov 2025 00:00:00 +0000

This study introduces a new class of probability distributions within the transformed-transformer (T - X) family framework, using the paralogistic distribution as the baseline generator. The proposed Paralogistic-X family provides a flexible model capable of capturing various distributional shapes such as skewness and heavy tails. General expressions for its structural properties including the density, distribution, quantile function, moments, and entropy measures are developed in terms of the baseline distribution. A special submodel, the Paralogistic--Burr III (PBIII) distribution, is examined in detail. Maximum likelihood estimation is used for parameter inference, and a simulation study is conducted to evaluate the estimators' performance under varying sample sizes. The results confirm the consistency and efficiency of the estimators across different settings. To assess its practical utility, the PBIII distribution is applied to real-world datasets and compared with four established competing distributions. The comparison, based on both graphical tools and model selection criteria such as AIC, BIC, and log-likelihood, shows that the proposed model offers superior fitting capabilities in the two cases. The findings highlight the versatility and robustness of the Paralogistic-X family for statistical modeling.

Semi-Analytical Solution of a Two-Dimensional Time-Fractional Fisher’s Equation via the Homotopy Analysis Method

Ogugua N. Onyejekwe — Mon, 10 Nov 2025 17:24:28 +0000

This paper presents a semi-analytical solution to the two-dimensional time-fractional Fisher’s equation using the Homotopy Analysis Method (HAM). The governing equation models reaction–diffusion processes with memory effects, incorporating the Caputo fractional derivative to account for anomalous temporal behavior. The HAM framework is constructed by first selecting an appropriate initial guess that satisfies both the initial and boundary conditions, followed by the recursive generation of higher-order approximations. The convergence of the series solution is controlled through the auxiliary parameter $\hbar$, whose optimal value is determined at each time level by enforcing consistency with boundary conditions. The analytical results are validated against numerical simulations, demonstrating excellent agreement. This study highlights the flexibility and efficiency of HAM in handling high-dimensional nonlinear fractional partial differential equations and provides a foundation for extending the method to more complex biological or ecological models.

Predicting the Dynamics of Nigeria's External Reserves Using the Buys-Ballot Method

P. O. Aye, D. Jayeola, O. J. Felemu, K. A. Adeyemo — Wed, 12 Nov 2025 00:00:00 +0000

This study presents a model to predict the dynamics of External Reserves of Nigeria. The choice of suitable time series model, trend estimation and seasonal effect assessment was done using Buy-Ballot method. The result of the analysis showed that an additive model is most suitable for modelling External Reserves of Nigeria between the times considered in the study. The four different trend curves considered for this study which include linear, quadratic, exponential and S-curve were subjected to three test of accuracy such as Mean Absolute Percentage Error (MAPE), Mean Absolute Deviation (MAD) and Mean Squared Deviation (MSD) to determine the one with the least error estimate and it was found that the quadratic trend curve had the least error estimates when compared with other trend curves, hence the quadratic trend curve was adopted and fitted to the External Reserves of Nigeria. There was a downward trend as revealed by trend-cycle component which shows that between the periods under study, the External Reserves of Nigeria has been on the decline. The Dot also revealed the influence of seasonal effect on External Reserve of Nigeria. The model equation obtained was used to predict the External Reserve of Nigeria for a period of eight years. The study recommended that the Nigerian government should concentrates more on growing the External Reserves so as to build global community confidence and trust in the nation's fiscal policies and creditworthiness.