AppliedMath, Volume 6, Issue 1

The historical and conceptual foundations of General Relativity are revisited, putting the main focus on the physical meaning of the invariant $d{s}^2$, the Equivalence Principle, and the precise interpretation of spacetime geometry. It is argued that Alb...

Parcel size strongly influences agricultural production costs, and combining spatial and economic information within a mathematical setting helps to clarify this relationship. In this study, we introduce a Gamma-based stochastic framework to integrat...

Uncertainty-aware decision-making increasingly relies on multimodal sensing pipelines that must fuse correlated measurements, propagate uncertainty, and trigger reliable control actions. This study develops a unified mathematical framework for multim...

This paper presents a Maple implementation of an interval verification method for identifying isolated simple zeros in square polynomial systems. Compared to the known MATLAB (R2019b) implementation, the Maple-based approach achieves significantly hi...

We investigate a special family of elliptic curves, namely $E_{p,q}:y^2=x^3-pqx$, where $p<q$ are odd primes. We study sufficient conditions for p and q so that the corresponding elliptic curve has non-trivial rational points. The number of sufficien...

The Rasch model has the desirable property that item parameter estimation can be separated from person parameter estimation. This implies that no assumptions about the ability distribution are required when estimating item difficulties. Pairwise esti...

In this paper, we present a novel method for background estimation and updating in video sequences, utilizing an innovative approach that combines an intelligent truncated mean, the stationary wavelet transform (SWT), and advanced thresholding techni...

As artificial intelligence systems proliferate across critical societal domains, understanding the nature, patterns, and evolution of AI-related harms has become essential for effective governance. Despite growing incident repositories, systematic co...

Forest fires pose escalating threats to ecological security and public safety in Guangdong Province. This study presents a novel machine learning framework for fire occurrence prediction by synergistically integrating multi-source geospatial data. Ut...

It is well known that the position of the Jacobian matrix spectrum in the left-half complex plane provides the local asymptotic stability of a nonlinear dynamical system, but it is also well known that for large matrices, computing its eigenvalues ju...

This study proposes a structured multicriteria approach to assist professionals in the selection of appropriate computing platforms for children diagnosed with Autism Spectrum Disorder, particularly those between 4 and 6 years of age. Recognizing the...

Fractal geometry offers a mathematical framework to quantify the complexity of brain structure and function. The fractal dimension (FD) captures self-similarity and irregularity across spatial and temporal scales, surpassing the limits of traditional...

Effective identification of strain-hardening parameters is essential for predictive plasticity models used in automotive applications. However, the performance of Bayesian optimization depends strongly on kernel hyperparameters in the Gaussian-proces...

The main goal of this study is to explain the idea of generalized interval-valued ($\mathbb{I}.\mathbb{V}$) convexity on a fractal set. We first define the basic operations for a generalized interval of ${\mathbb{R}}^s$ with $0<s\le 1$. Then, we expand the idea of ($\mathbb{I}.\mathbb{V}$) Riemann inte...

Machine learning (ML) is a powerful tool in drug design, enabling the rapid analysis of large and complex molecular graphs that represent the structural and chemical properties of medications. It enhances the precision and speed with which molecular...

Turing patterns, characterised by spatial self-organisation in reaction–diffusion systems, exhibit sensitivity to initial conditions. This sensitivity, known as the robustness problem, results in different final patterns emerging even from smal...

In this paper, an economic competition–cooperation model is examined, which has one core enterprise and four satellite enterprises. This extends previous smaller models in the literature mathematically. The unique positive solution to the origi...

Fractional transforms have emerged as powerful analytical tools that bridge the time, frequency, and scale domains by introducing a fractional-order parameter into the kernel of classical transforms. This survey provides an overview of the mathematic...