AppliedMath

A reduced analytical formulation for the linear elastic behavior of axisymmetric shells subjected to axisymmetric load distributions is presented. The mechanical response of the shell is interpreted through the interaction between two families of one–dimensional structural elements, namely meridian fibers and circumferential fibers, whose kinematic coupling emerges naturally from the compatibility relations of the classical Reissner–Mindlin shell theory. By exploiting a geometric reinterpretation of the shell kinematics in terms of auxiliary curvature radii, a simplified mechanical model is derived by neglecting the kinematic contributions associated with one of these radii, which become negligible for shells sufficiently far from the degenerative planar membrane/plate configuration. The resulting formulation leads to a reduced set of compatibility, equilibrium, and constitutive equations that preserve the essential mechanical features of the shell response while significantly simplifying the mathematical structure of the problem. Two internally constrained variants of the reduced model are introduced, corresponding, respectively, to shear–indeformable and inextensible meridian fibers. Within this framework, the governing equations reduce to ordinary differential equations that, for specific shell geometries such as spherical and conical shells, admit closed-form analytical solutions. Based on these reduced models, two approximate solution strategies are developed. The first relies directly on the reduced shear–indeformable shell formulation to describe the overall structural behavior, whereas the second combines membrane solutions with the more internally constrained shell model to capture boundary effects through a superposition procedure. The effectiveness of the proposed approaches is assessed through comparison with numerical solutions obtained from the classical Reissner–Mindlin axisymmetric shell model. The results show that the proposed formulations provide an accurate approximation of both displacements and stress resultants for a sufficiently large range of spherical and conical shell configurations under distributed loads. Full article

An analytical solution is presented for transient heat conduction in a two-layer composite cylinder subjected to outer-surface convection with a general time-dependent ambient temperature. Using Duhamel’s principle, closed-form series expressions are derived and then specialized to harmonic ambient fluctuations, recovering the classical constant-ambient solution in the zero-frequency limit. A parametric study shows that the ratio of the inner layer conductivity to the conductivity of the outer layer strongly shapes interfacial gradients and mean-temperature evolution, with sensitivity concentrated at small ratios and diminishing when the ratio is larger than 0.1. Increasing Biot number accelerates the heat transfer and approaches the isothermal-surface limit as it becomes extremely large. The geometric aspect ratio is most influential when the inner layer is resistive, and becomes weak for large conductivity ratio, supporting thin-coating approximations. Under harmonic ambient fluctuations, the response rapidly reaches a periodic steady state; higher frequency decreases amplitude and increases phase lag, while larger Biot numbers amplify oscillations and reduce delay. The coupled effects of the aspect ratio and the conductivity ratio govern penetration and phase behavior. Full article

Adversarial perturbations measured by ${\mathsf{\ell }}_p$ norms do not reflect key structural constraints in tabular security data, including anisotropic geometry, feature dependence, and distributional plausibility. We introduce a composite attacker cost functional $C_{\mathrm{atk}}(\mathit{x},{\mathit{x}}^{\prime })=\tau max\{0,m\left({\mathit{x}}^{\prime }\right)\}+{\lambda }_1{\mathit{\delta }}^{\top }{\mathit{G}}_{\perp }^{\left(\gamma \right)}\left(\mathit{x}\right)\mathit{\delta }+\lambda {\displaystyle \sum _j}{\omega }_j|{\delta }_j|+{\lambda }_2{\mathit{\delta }}^{\top }{\mathit{L}}_H\mathit{\delta }+{\lambda }_3\left[log{\widehat{f}}_1^{\left(ϵ\right)}\left(\mathit{x}\right)-log{\widehat{f}}_1^{\left(ϵ\right)}\left({\mathit{x}}^{\prime }\right)\right]+{\displaystyle \sum _{j\in supp\left(\mathit{\delta }\right)}}{c}_j+\beta {\left|\mathcal{M}(supp\left(\mathit{\delta }\right))\right|}^{\nu },$ which integrates a spectrally truncated geometric term, a graph-based coherence penalty, a smooth copula density barrier, and a superlinear module-spread term. Under spectral degeneracy of the legitimate-class covariance, we establish nonnegativity under density dominance, exact zero self-cost, lower semicontinuity, and ${\lambda }_3{\kappa }_K$-weak convexity of the continuous component on compact convex sets, for both affine and ${\rho }_m$-weakly convex scoring functions. These properties yield existence of constrained minimizers. The continuous component is locally Lipschitz, whereas the full functional is not due to the support-counting term. A component feasibility result shows that each term eliminates a distinct class of degenerate perturbations. Limiting regimes and refined evasion cost bounds are derived. An empirical instantiation on PHIUSIIL indicates that perturbations with identical ${\mathsf{\ell }}_2$ norm can incur costs differing by an order of magnitude. Full article

Bazilevič mappings are considered very important in the theory of geometric mappings because they provide a way to generalize and study the properties of important classes of univalent mappings. Their importance is not only in the deepening of the theory, but also in the practical means of modeling phenomena in applied science and engineering, physics, and differential equations. This paper, in this sense, provides a new subclass of bi-Bazilevič mappings with the use of advanced analytical methods, Chebyshev polynomials on one side, and a Miller–Ross-type Poisson distribution on the other side. The Poisson distribution is considered one of the most important models of probability distributions with a large scope of application in the various sciences. The main components of this study are the definition and the study of this new class of functions, in which the initial Taylor–Maclaurin coefficients, in particular, $q_2$ and $q_3$, are determined and estimated for mappings in this subclass. Also, the classical Fekete–Szegö problem is solved and the first-order limits of this important functional are obtained with respect to the newly introduced bi-Bazilevič mappings. The outcomes contribute to expanding both the theoretical and practical aspects of this type of mapping. Full article

A warrant is a financial derivative that grants the holder the right to purchase company shares at a predetermined price within a specified period. Generally, upon exercise, the total number of outstanding shares increases because of the issuance of new shares, reducing the stock price. In this study, an analytical formula for warrant valuation is developed without relying on the restrictive assumptions of log-normal asset return distributions or constant volatility. The model incorporates key financial variables, including the current asset price, the strike price, the risk-free interest rate, the time to maturity, and the dilution factor. To capture dynamic market conditions, asset return volatility is estimated using GARCH-type models. The performance of this analytical approach is evaluated by comparing its numerical results with those obtained using alternative methods, such as Monte Carlo simulations and the conventional warrant valuation framework. An empirical analysis based on data from the Stock Exchange of Thailand indicates that the proposed method yields improved pricing accuracy with lower estimation errors than existing benchmarks. Full article

Energy consumption demand forecasting plays a critical role in the planning and development of national energy security, which underpins the Vietnam’s Eighth National Power Development Plan (PDP VIII) and Vietnam’s ambitious Net-Zero 2050 commitment. However, this task becomes more difficult because the big data environment is filled with a lot of noise and highly fluctuating data. In order to deal with the problem, this paper evaluates five models: Linear Regression, Holt’s Exponential Smoothing, PSO-GM (1,1), Support Vector Regression (SVR), and Random Forest as a benchmark to conduct a rigorous comparative analysis to identify the most accurate forecasting model. The performance was evaluated by MAE, RMSE, and MAPE indexes based on Vietnam’s total primary energy demand data from 1986 to 2024. To check the accuracy of the forecasting model, this study split the data into two periods: first time for the training data (1986–2016), and second for the testing data set (2017–2024). Furthermore, a five-fold rolling-window time-series cross-validation method and Diebold–Mariano tests were employed to ensure the statistical robustness of the findings on the small-sample datasets (n = 39). The results decisively identified that the Holt’s model as the superior framework, maintaining high stability and achieving a testing MAPE of 7.19% (training MAPE of 5.52%), while the complex machine learning benchmark shows severe over-fitting. Applying this model, Vietnam’s energy demand will reach 1528.08 TWh and 1882.55 TWh in 2025 and 2030, respectively. Furthermore, this study provides empirical evidence that simpler, well-chosen statistical models can surpass complex alternatives in small-sample scenarios, offering a reliable quantitative baseline for policymakers to navigate infrastructure development and decarbonization challenges. Full article

In this paper, we introduce and systematically study the class of interpolative Geraghty-type contractive mappings within the framework of complete bicomplex-valued metric spaces (bi-CVMS). We prove seven new results: (i) a fixed point theorem for a single interpolative Geraghty contraction; (ii) a common fixed point theorem for a pair of such mappings; (iii) a fixed point theorem for interpolative Reich–Rus–Ćirić type contractions in bi-CVMS; (iv) a coincidence point and common fixed point theorem for weakly compatible maps; (v) a fixed point theorem for Jaggi-type hybrid contractions in bi-CVMS; (vi) a stability result for the Picard iteration associated with the main contraction; and (vii) an application theorem establishing the existence and uniqueness of solutions to a boundary value problem governed by a Caputo fractional differential equation. All results are furnished with complete proofs and non-trivial illustrative examples. Several well-known theorems—including those of Banach, Kannan, Reich, Geraghty, and their complex-valued analogues—follow as special cases. The paper significantly advances the fixed point theory in bicomplex-valued metric spaces. Full article

This paper presents a proposed architecture for an artificial intelligence-driven unmanned aerial vehicle (UAV) system intended for tactical intelligence, surveillance, and reconnaissance (ISR) missions. The architecture brings together electro-optical imaging, long-wave infrared sensing, two-dimensional light detection and ranging (LiDAR), inertial navigation support, onboard edge computing, and resilient communication links within a unified system-level framework. Unlike many existing approaches that treat perception, autonomy, communication, and safety as loosely coupled functions, the proposed architecture combines multi-modal sensing, operator-supervised autonomy, and a safety-oriented decision validation layer intended for future integration with Ansys SCADE. The system is structured around operational and sensor-performance requirements used to justify the selection and interaction of the main onboard subsystems. At the architectural level, the proposed framework is intended to support target detection, tracking, environment awareness, and mission-level decision support under degraded visibility, constrained communication, and contested operating conditions. The paper therefore contributes a requirement-driven and safety-aware ISR UAV architecture that provides a scalable basis for future implementation, validation, and multi-UAV extension. Full article

This paper presents a hybrid two-stage implicit scheme for the numerical solution of fractional initial value problems involving Caputo derivatives. The proposed formulation incorporates the nonlinear source term directly into the time-stepping procedure, leading to improved stability and accuracy compared with classical fractional implicit schemes. The resulting nonlinear systems are solved using a parallel iterative strategy based on the Weierstrass-type method, combined with OpenMP-style parallelization to ensure efficient workload distribution and accelerated convergence. In addition, a data-driven module is introduced to generate high-quality initial guesses, thereby enhancing the robustness and efficiency of the nonlinear solver. The main contributions include the development of a unified fractional-parallel-data-driven framework, improved stability properties with enlarged real-axis stability regions, and reduced computational cost through parallel implementation and informed initialization. A theoretical analysis establishes consistency, boundedness, and convergence under standard Lipschitz assumptions. Numerical experiments on representative fractional models demonstrate that the proposed schemes achieve higher accuracy and improved efficiency compared with classical implicit methods, with significant reductions in error and iteration counts. The ANN-enhanced variant further attains near machine-precision accuracy for a range of fractional orders. Overall, the proposed approach provides a robust and scalable computational framework for the efficient solution of nonlinear fractional dynamical systems. Full article

This research presents a fractional-order formulation and mathematical analysis of the Rössler chaotic attractor. By utilizing the Nabla discrete Atangana–Baleanu fractional difference derivative in the Caputo sense, the classical integer-order attractor is extended into the fractional domain. The existence and uniqueness of solutions for the resulting fractional system are established via the fixed-point theorem, thereby ensuring that the recommended attractor is well-posed. Furthermore, the Ulam–Hyers stability is investigated within the Nabla discrete Atangana–Baleanu fractional difference derivative in the Caputo sense framework. For numerical investigations, an Euler numerical scheme adapted to the fractional difference derivative is developed and implemented, yielding high-quality phase portraits of a chaotic attractor. The results highlight the effectiveness of fractional-order modeling and numerical methods in capturing the dynamics and stability of the Rössler chaotic system. Full article

The problem that this study is concerned with is the ontogenetic growth of humans and animals. The aim of this research is to analyze a model of the ontogenetic growth of animals. The target of the analyses is to show a link between growth and longevity. This model has implications for modelling the growth of humans as well. In this study, pigs were considered model animals for humans. Humans and pigs have a number of comparable physiological features as well as a few analogous aspects of growth. The resemblance of the biological functions leads us to think that by modelling the growth of pigs, one can gain a better look into the growth of humans. In this research, we model growth, which is operationalized as weight gain; weight loss was not considered. In this study, a discussion of the translation of the results to the growth and longevity of humans was provided. The lifespan or longevity of animals was not modelled explicitly; predictions were made in accordance with the results of the growth model. The main result of the model is that growth promotes, if not causes, longevity. Full article

Crime forecasting in heterogeneous urban contexts remains challenging due to the combined effects of territorial heterogeneity and complex temporal dynamics. However, a large portion of the existing literature tends to address territorial segmentation and predictive modeling separately, or to combine them within unified workflows that may obscure their distinct analytical roles. This study presents a modular spatial–temporal analytical approach that treats territorial segmentation and short-term crime prediction as complementary but methodologically independent components. Unsupervised segmentation captures territorial heterogeneity, while a supervised ensemble model estimates short-term crime occurrence. A chronological expanding-window validation scheme is implemented, reserving the most recent period as a blind test set to prevent temporal leakage. Across municipalities, recall values in 2022 range from 0.36 to 0.77, with corresponding F1-scores ranging from 0.174 to 0.696, while blind-test recall ranges from 0.184 to 0.856, with F1-scores ranging from 0.000 to 0.784, and AUC values up to 0.88, indicating that predictive performance is context-dependent rather than uniform. The proposed approach provides a replicable and context-aware analytical approach for spatially differentiated crime risk estimation under strict forward-looking evaluation. Full article

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