AppliedMath, Volume 6, Issue 4 (April 2026) – 12 articles

Asymptotic solutions are derived to model the development of atmospheric internal gravity waves generated by latent heating in a two-dimensional configuration involving a vertically-sheared background flow. The mathematical model comprises nonlinear partial differential equations derived from the conservation laws of fluid dynamics under the anelastic approximation where the background density and temperature vary with altitude. The latent heating is represented by a horizontally-periodic but vertically-localized nonhomogeneous forcing term in the energy conservation equation. This generates gravity waves that are considered as perturbations to the background flow and are expressed as perturbation series, with the leading-order contributions being the solutions of linearized equations. Taking into account the nonlinear terms at the next order gives expressions for the effects of the waves on the background mean flow. Due to the vertical shear, there is a critical level where momentum and energy are transferred from the wave modes to the mean flow. The asymptotic solutions show that the wave–mean-flow interaction is nonlocal and occurs over the range of altitudes from the thermal forcing level up the critical level. This is in contrast to what occurs in the case of waves forced by an oscillatory lower boundary, where the interaction is typically localized around the critical level. It is found that the wave drag is negative above the thermal forcing level, making the mean flow velocity more negative, but it becomes positive as the waves approach the critical level, indicating wave absorption in this region. There is wave transmission through the critical level, as well as absorption, and the extent of transmission depends on the depth of the latent heating profile. The mean potential temperature is reduced above the thermal forcing level and enhanced at the critical level, a situation that could ultimately lead to the development of convective instabilities. Full article

Harmonic distortion in power systems, primarily caused by nonlinear loads, leads to significant power quality issues such as increased losses, reduced power factor, and equipment malfunctions. To mitigate these effects, passive power filters (PPFs) are widely employed due to their cost-effectiveness and simplicity. This paper presents an optimized design of a single-tuned passive filter (STPF) using the Firefly Algorithm (FFA) and its multi-objective extension, the Multi-Objective Firefly Algorithm (MOFA). The optimization aims to minimize both voltage total harmonic distortion (VTHD) and power loss and to maximize the power factor (PF) while complying with IEEE 519-2014 standards. The study evaluates the proposed method under two different industrial case studies with varying system parameters and harmonic profiles. Simulation results demonstrate that the proposed FFA-based optimization outperforms the Mixed Integer Distributed Ant Colony Optimization (MIDACO) method, achieving superior VTHD reduction, power loss minimization, and power factor enhancement. The MOFA approach provides a Pareto-optimal front, offering trade-offs among competing objectives. Comparative analysis confirms the efficiency, robustness, and faster convergence of FFA-based optimization, making it a promising approach for optimal filter design in power systems. Full article

We develop a categorical framework for modeling recursive uncertainty over preferences in decision theory. Classical models of ambiguity allow for uncertainty over outcomes or beliefs but usually rely on finite or exogenously truncated representations when agents face uncertainty about their own evaluative criteria. Given that such recursive preference formation generates an infinite hierarchy that may not stabilize at any finite level, we introduce a contractive von Neumann–Morgenstern utility functor on a category of compact metric spaces enriched over complete metric spaces, and establish the existence and uniqueness of its canonical fixed point. This fixed point is interpreted as a universal preference space that contains all levels of recursive ambiguity in a consistent and metrically stable form. We further extend the construction to multi-utility representations and discuss its relation to existing models of ambiguity and universal choice spaces. This framework offers a minimal unified representation of recursive preference structures. Full article

A novel flexible single-parameter polynomial distribution is presented in this study. The forms of hazard rate and density functions are examined. Additionally, exact formulas for a number of numerical characteristics of distributions are obtained. Stochastic ordering, the moment technique, the maximum likelihood, and a Bayesian analysis of this novel distribution based on type II censored data are used to derive the extreme order statistics. We construct Bayes estimators and the associated posterior risks using a variety of loss functions, such as the generalized quadratic, entropy, and Linex functions. Since tractable analytical formulations of these estimators are unattainable, we suggest using a simulation technique based on Markov chain Monte-Carlo (MCMC) to examine their performance. Furthermore, we construct maximum likelihood estimators given initial values for the model’s parameters. Additionally, we use integrated mean square error and Pitman’s proximity criteria to compare their performance with that of the Bayesian estimators. Lastly, we apply the new family to many real-world datasets to show its versatility, and we model cancer survival data using this new distribution to explain our methodology. Full article

Substance abuse addictions and hepatitis B infections are two major public health problems facing humanity globally, especially in areas where the two problems co-exist. A mathematical model was used in this work to study the co-dynamics of substance abuse addictions and hepatitis B infections and investigate their possible control strategies. The mathematical features of the model, such as the disease-free equilibrium, endemic equilibrium, and basic reproduction number, were computed. The stability analysis of the disease-free equilibrium and endemic equilibrium was conducted analytically. The impact of multiple control measures, including public enlightenment, rehabilitation of individuals with substance abuse disorders, treatment of persons infected with hepatitis B, and vaccination of susceptible individuals, was examined numerically. The study reveals how co-existence fundamentally alters system behavior and control effectiveness and offers new insights for designing effective control management strategies. Full article

This study introduces a deterministic fractional-penalty refinement of Vogel’s Approximation Method (VAM) for generating high-quality initial basic feasible solutions (IBFS) in classical transportation problems. Unlike the traditional additive regret measure employed in VAM, the proposed method uses a multiplicative contrast ratio between the two smallest admissible costs in each row and column. This modification preserves the allocation structure of VAM while introducing scale-invariant prioritization that improves sensitivity to relative cost differences.The method was evaluated on thirty-four benchmark transportation problems drawn from the literature and self-constructed large-scale instances (up to $10\times 20$). Performance was assessed using percentage optimality gaps relative to optimal solutions obtained via the Stepping–Stone and MODI procedures. Across all instances, the proposed approach achieved a mean optimality gap of $2.78\%$, compared to $5.22\%$ for classical VAM, $14.97\%$ for the Least Cost Method (LCM), and $45.78\%$ for the Northwest Corner Method (NWCM). Dispersion of deviations was also reduced, indicating improved robustness across heterogeneous cost structures Statistical validation confirms the improvement over VAM: the paired t-test yielded $t=-3.17$ ($p=0.00163$, one-sided), and the Wilcoxon signed-rank test produced $p=6.10\times {10}^{-5}$. Computational experiments further show that the refinement does not increase runtime relative to classical IBFS procedures.The proposed method therefore constitutes a structured enhancement of VAM that improves initial solution quality while maintaining computational simplicity. Full article

Crypto-asset markets have been rapidly evolving during the past years, being under the spotlight of a diverse set of actors in the financial ecosystem, including investors, financial institutions, regulators and academics. Their potential interconnections with the traditional financial markets are important, and identifying them can provide useful insight in a diversity of areas such as risk contagion and mitigation, price formation, portfolio management and regulatory framework design. In order to identify such interconnections, various lines of research are followed. Specifically, the correlation between prominent stock market indices and crypto-assets from 2018 to 2025 is examined, while their volatility is also evaluated. Furthermore, the relevant effect of news, events and announcements is explored. The results are based on both daily and high-frequency datasets, with the use of the latter focusing on intra-day variation. The analysis of the results identifies existing interconnections between 2020 and 2025, as well as the important respective impact of news and announcements. An additional generic outcome is the usefulness of high-frequency datasets in the crypto-asset context. The conclusions are useful for all actors in the financial ecosystem. Future work can focus on the extension of the research to additional markets or crypto-assets. Full article

The exact perimeter of an ellipse involves the complete elliptic integral of the second kind, which lacks a closed-form expression in elementary functions. As a result, analytical approximations have been proposed for applications requiring fast and accurate evaluation of elliptical geometries. In this study, we present a new ultra-accurate and compact closed-form approximation for the ellipse perimeter based on an exponential correction applied to Ramanujan’s second formula. The proposed expression preserves simplicity—using only three exponential functions and six constants—while achieving a maximum relative error of approximately 0.57 ppm observed over the tested grids covering the full eccentricity range. This represents a significant accuracy improvement over classical and modern approximations while maintaining a single-line analytical form with low computational cost. Due to its robustness, quasi-exact behavior at both circular and highly eccentric limits, and its suitability for numerical algorithms and embedded implementations, the proposed approximation is particularly useful in engineering computations involving elliptical boundaries. Full article

Sectional warping requires selecting a final operating length when only a small sample of residual cone masses can be measured. This paper proposes a Bayesian chance-constrained planning rule that combines a conjugate log-space model with fast posterior predictive simulation of the population minimum to recommend a risk-limited band length. The method provides a transparent risk parameter, efficient computation, and direct comparison with heuristic, bootstrap, distribution-free, and tail-model baselines. In an industrial-like synthetic study, the Bayesian policy reduced the mean remainder relative to a tuned sample-minimum rule while maintaining controlled shortage risk, and the results clarify why fully distribution-free guarantees are impractical under typical sampling budgets. Full article

We develop a fast numerical method for solving nonlinear diffusion equations with memory phenomena, a class of problems arising within viscoelastic materials, anomalous transport, and hereditary systems. The primary computational problem is the nonlocal temporal dependence captured by Volterra-type memory operators, which makes direct evaluation scale quadratically with the number of time steps ($O\left(N_t^2\right)$), rendering prolonged simulations prohibitively expensive. To address this bottleneck, we develop a novel synthesis that combines a high-order spectral method for spatial discretization with a fast memory algorithm based on a sum-of-exponentials approximation. The spectral method obtains exponential spatial convergence for smooth solutions. At the same time, the fast memory algorithm reduces memory usage and computational complexity to $O\left(N_t\right)$, yielding computational speedups exceeding 414x for prolonged simulations. We rigorously prove that the proposed scheme preserves the discrete energy dissipation law of the continuous system under mild assumptions on the memory kernel, thereby ensuring unconditional stability. Error analysis verifies spectral accuracy in space and first-order temporal convergence. Extensive numerical experiments using exponentially decaying and weakly singular kernels validate the theoretical results and illustrate the method’s effectiveness for modeling viscoelastic transport phenomena and irregular diffusion in complex systems. Full article

This paper studies subsidy allocation in interconnected industrial systems using the spectral theory of positive matrices. The allocation is characterized by the Perron eigenvector of a cost matrix describing inter-factory interactions. We show that convergence to equilibrium is exponential and governed by the spectral ratio. A systemic resilience index based on spectral separation is introduced to quantify both stability and robustness under perturbations. The results demonstrate that stability and fairness arise from the spectral structure of the system. Full article

The main object of this work is to study the generalized B-curvature tensor in an n-dimensional Lorentzian para-Kenmotsu (briefly, ${\left(LPK\right)}_n$) manifold along a semi-symmetric metric connection $\overline{\nabla }$. First, in an ${\left(LPK\right)}_n$-manifold, we explore certain flatness conditions, namely, $\overline{B}(Y,Z)X=0$, $\overline{B}(Y,Z)\zeta =0$, $g(\overline{B}(\phi Y,\phi Z)\phi X,\phi W)=0$, and $\overline{B}(Y,Z)·\phi =0$ conditions, which all result in an $\eta$-Einstein manifold. Furthermore, in an ${\left(LPK\right)}_n$-manifold, we study the curvature conditions $\overline{B}.Q=0$ and $\overline{B}.\overline{Q}$ = 0, which provide the scalar curvature. The generalized B-curvature tensor blends the features of different curvature tensors, allowing researchers to study conditions like semi-symmetry, pseudo-symmetry in a unified framework. Conditions like B-semi-symmetry correspond to conservation laws or stability properties in physical systems. Full article