182 results
Showing 1–20 · 0.12 seconds · RSS
Foundations
ISSN 2673-9321 · MDPI AG · 182 articles in the index
-
Journal Article Full text
Extremal Classification for Pairwise Linear Combinations of Third-Order Zernike Polynomials
We study the extremal behavior of real two-term linear combinations of third-order Zernike modes on the closed unit disk D2. Our primary focus is the classification of interior local extrema; absolute extrema on the boundary circle are treated only where they admit a concise description or as a…
-
Journal Article Full text
Equilibrium in a Failed Cartel: Set-Valued Reactions and Sources of Market Asymmetry
We study a three-firm market following the breakdown of an initially complete cartel, taking both the breakdown and the identity of the departing firm as exogenously given. In the baseline model, the former cartel members no longer coordinate: all three firms choose quantities simultaneously and…
-
Journal Article Full text
Influence of Silver Content on the Structural Characteristics and Antibacterial Activity of ZnO–Ag Nanoparticles Against Escherichia coli and Salmonella typhimurium
Antimicrobial nanomaterials have attracted increasing attention as potential alternatives for controlling pathogenic microorganisms. In this study, pure ZnO and Ag-modified ZnO nanoparticles prepared using nominal Ag contents of 1 and 5 wt.% were synthesized using a reflux-assisted polyol method…
-
Journal Article Full text
Fitting Accumulated Stock Returns with Tempered Skew t-Distribution
We analyze the distributions of historic S&P500 multi-day returns for the number of days of accumulation from 20 to 120. With the increase in the number of days of accumulation, we observe clear tempering of power-law tails toward a seemingly finite value. To explain this phenomenon, we employ a…
-
Journal Article Full text
State-Dependent Coefficients in Electrical-Engineering Pedagogy: A Comparative Metrological and Coupling-Theory Audit with a Reserved Paraformer Test Section
Introductory and intermediate electrical-engineering education commonly models fundamental circuit and device parameters, including inductance, capacitance, resistance, permeability, permittivity, conductivity, characteristic impedance, transformer turns ratio, machine constants, amplifier gain…
-
Journal Article Full text
On the Axiom of the Second Law of Thermodynamics and the Modelling of Flexoelectricity
The present paper addresses models of non-local materials and, in particular, flexoelectric materials as dielectrics with higher-order gradients. While the literature develops the subject through variational formulations, here the modelling is developed within a thermodynamic framework with a…
-
Journal Article Full text
Reconstruction of Quantum Field Equations from Multi-Branch Hamilton–Jacobi Structures
We develop a framework in which quantum field equations are reconstructed from a multi-branch Hamilton–Jacobi structure supplemented by density functionals on configuration space. Each branch is defined by a solution of a functional Hamilton–Jacobi equation, while the associated density encodes…
-
Journal Article Full text
Uniting Psychometric Modelling and Poisson Distributions: A Metrological Study of Elementary Counting
A study of elementary counting (of simple clouds of dots by the Munduruku indigenous people of Brazil) is reanalysed in order to compare and contrast three kinds of probability mass functions (PMFs): (i) quantitative response to a discrete range of counts; (ii) the classic Poisson distribution of…
-
Journal Article Full text
Membrane Potential as a Manifestation of the Boltzmann Distribution: A Free-Energy Derivation Within the Association-Induction Hypothesis
This paper presents a comprehensive theoretical derivation of a membrane potential formula based on the Association-Induction Hypothesis (AIH), challenging traditional membrane theory and the Goldman–Hodgkin–Katz equation (GHK equation). The study demonstrates that membrane potential is not…
-
Journal Article Full text
The Perceptual Game-Theoretic Transform (PGTT): Axiomatizing Signal Compression via the Fourier–Shapley Isomorphism
The mathematical representation of discrete signals is classically governed by linear basis transforms, such as the Discrete Fourier Transform (DFT), which treat spectral projection as a rigid, deterministic geometric operation. Under this paradigm, signal compression and thresholding rely on…
-
Journal Article Full text
Exact Confidence Intervals in Distributions with One Parameter
The Clopper–Pearson method of constructing a confidence interval for the probability of success in a binary population that follows a Bernoulli distribution is well known. This paper pedagogically justifies the Clopper–Pearson method and extends the method to all distributions with one parameter…
-
Journal Article Full text
The Evolution of Mathematization: From Classical Science to Computationally Emergent Structures
The mathematization of science is undergoing a structural transformation driven by the rise of computation and data-intensive methods. While classical mathematization relied largely on explicitly formulated laws and formal structures, contemporary scientific practice increasingly encounters…
-
Journal Article Full text
Broken Symmetry, “Conservation Law”, and Scaling in Accumulated Stock Returns: A Modified Jones–Faddy Skew t-Distribution Perspective
We analyze historic S&P500 multi-day returns: from daily returns to those accumulated over up to ten days. Despite symmetry breaking between gains and losses in the distribution of returns, resulting in its positive mean and negative skew, realized variance (volatility squared) exhibits remarkably…
-
Journal Article Full text
A New Arithmetic Structure Matrix Related to the Hardy–Littlewood F-Conjecture
This study introduces a novel matrix defined over the nonzero natural numbers, whose entries are governed by a rigorous closed-form expression. The matrix architecture replicates the topological properties of the Ulam spiral, mapping the integer sequence onto a structured lattice with a…
-
Journal Article Full text
Backstepping Control for Systems with Fast Time-Varying Reference Signals—An Autonomous Landing Application
A nonlinear backstepping control framework is developed for autonomous landing of a quadrotor on a wave-excited marine platform. This study addresses the underactuated nature of the aerial vehicle and the strong coupling between translational and rotational dynamics, ensuring stable trajectory…
-
Journal Article Full text
Parallel Balanced Grey Wolf Optimizer: A Cooperative Parallel Approach for Large-Scale Optimization Problems
In recent years, large-scale optimization problems have become increasingly common in various fields, such as machine learning and data analysis, generating increased references to both computational cost and accurate solutions. The Grey Wolf Optimizer (GWO) is an efficient collective intelligence…
-
Journal Article Full text
Learning and Teaching Differential and Integral Calculus: A Case Study in Portugal
Students entering engineering programs often exhibit insufficient mathematics knowledge and considerable variability in prior training, which can create learning gaps and challenges for higher education integration. This study aims to characterize students’ mathematics proficiency at the Coimbra…
-
Journal Article Full text
Coherent Comparison as Information Cost: Axiomatic Foundations for Discrete Ledger Dynamics
We develop an information-theoretic, cost-first framework for discrete dynamics in which the primitive operation is ratio-based comparison. Given two quantities compared via their ratio x=a/b, we assign a cost F(x) measuring deviation from equilibrium (x=1). Adopting a reciprocal d’Alembert…
-
Journal Article Full text
Efficient and Structure-Preserving Numerical Methods for Time–Space Fractional Diffusion in Heterogeneous Biological Tissues
Time–space fractional diffusion equations are widely used to model anomalous transport in heterogeneous biological tissues, where memory effects, spatial nonlocality, and coefficient variability are intrinsically coupled. However, existing numerical approaches typically treat these aspects in…
-
Journal Article Full text
On Least Squares Approximations of Shapley Values and Applications to Interpretable Machine Learning
The Shapley value is the predominant point-valued solution concept in cooperative game theory and has recently become a foundational method in interpretable machine learning. In this domain, a prevailing strategy for circumventing the computational intractability of exact Shapley values is to…