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AppliedMath
Scopus
ISSN 2673-9909 · MDPI AG · 506 articles in the index
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Recovering Einstein’s Mature View of Gravitation: A Dynamical Reconstruction Grounded in the Equivalence Principle
The historical and conceptual foundations of General Relativity are revisited, putting the main focus on the physical meaning of the invariant ds2, the Equivalence Principle, and the precise interpretation of spacetime geometry. It is argued that Albert Einstein initially sought a dynamical…
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Uncertainty-Aware Multimodal Fusion and Bayesian Decision-Making for DSS
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 multimodal data fusion and Bayesian decision-making…
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Assessing Cost Efficiency Thresholds in Fragmented Agriculture: A Gamma-Based Model of the Trade-Off Between Unit and Total Parcel Costs
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 integrate actual parcel size distributions into cost…
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Examining the Nature and Dimensions of Artificial Intelligence Incidents: A Machine Learning Text Analytics Approach
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 computational analysis of AI incident discourse…
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A Maple Implementation for Deterministically Certifying Isolated Simple Zeros of Over-Determined Polynomial Systems with Interval Arithmetic and Its Applications
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 higher numerical accuracy. The implementation…
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Spatial Prediction of Forest Fire Risk in Guangdong Province Using Multi-Source Geospatial Data and Sparrow Search Algorithm-Optimized XGBoost
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. Utilizing Moderate-resolution Imaging…
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A Note on Tutz’s Pairwise Separation Estimator
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 estimation approaches in the Rasch model exploit this…
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Dynamical System Stability Criteria Based on the Frobenius Norm
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 just to see their position is computationally…
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Enhanced Moving Object Detection in Dynamic Video Environments Using a Truncated Mean and Stationary Wavelet Transform
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 techniques. This method aims to significantly enhance…
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On Families of Elliptic Curves Ep,q:y2=x3−pqx That Intersect the Same Line La,b:y=abx of Rational Slope
We investigate a special family of elliptic curves, namely Ep,q:y2=x3−pqx, where p
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Online Hyperparameter Tuning in Bayesian Optimization for Material Parameter Identification: An Application in Strain-Hardening Plasticity for Automotive Structural Steel
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-process surrogate, which are often kept fixed. In this…
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Foundations and Clinical Applications of Fractal Dimension in Neuroscience: Concepts and Perspectives
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 Euclidean metrics. In neuroscience, FD serves as…
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Conceptual Proposal for a Computational Platform to Assist in the Learning and Cognitive Development Process of Children with Autism Spectrum Disorder: A Solution Based on a Multicriteria Structure
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 learning limitations and reduced attention span…
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Advanced Computational Insights into Coronary Artery Disease Drugs: A Machine Learning and Topological Analysis
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 interactions are predicted, drug candidates are…
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Generalized Interval-Valued Convexity in Fractal Geometry
The main goal of this study is to explain the idea of generalized interval-valued (I.V) convexity on a fractal set. We first define the basic operations for a generalized interval of Rs with 0
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Mind the Gap: A Solution to the Robustness Problem of Turing Patterns Through Patterning Mode Isolation
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 small initial perturbations. In this paper, we introduce a…
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Dynamic Behavior of a Delayed Model with One Core Enterprise and Four Satellite Enterprises
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 original solution after a change of variables corresponds to…
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A Sixth-Order Vieta–Lucas Polynomial-Based Block Method with Optimal Stability for Solving Practical First-Order ODE Models
This paper addresses the numerical integration of first-order ordinary differential equations by developing a continuous linear multistep block method. The method is constructed through the approximation of the exact solution using a linear combination of shifted Vieta–Lucas polynomials defined on…
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Hadamard Products of Projective Varieties with Errors and Erasures
In Algebraic Statistics, M.A. Cueto, J. Morton and B. Sturmfels introduced a statistical model, the Restricted Boltzmann Machine, which introduced the Hadamard product of two or more vectors of an affine or projective space, i.e., the componentwise product of their entries, forcing Algebraic…
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Exploring Artificial Intelligence and Machine Learning Approaches to Legal Reasoning
Modeling legal reasoning with artificial intelligence and machine learning presents formidable challenges. Legal decisions emerge from a complex interplay of factual circumstances, statutory interpretation, case precedent, jurisdictional variation, and human judgment—including the behavioral…