AppliedMath, Volume 5, Issue 4 (December 2025) – 23 articles

In this paper, we consider a general quadratic problem (P) with linear constraints that are not necessarily linear independent. To resolve this problem, we use a new algorithm based on the Inertia-Controlling method while replacing the condition of the Lagrange multiplier vector μ by resolution of a linear system obtained thanks to the Kuruch–Kuhn–Tuker matrix (KKT-matrix) in order to determine the minimizing direction of (P) and so calculate the steep length in general cases, as follows: indefinite, concave, and convex cases. This paper has an interesting topic and meaningful results. Full article

This study introduces Itô-RMSProp, a novel extension of the RMSProp optimizer inspired by Itô stochastic calculus, which integrates adaptive Gaussian noise into the update rule to enhance exploration and mitigate overfitting during training. We embed this optimizer within Gated Recurrent Unit (GRU) networks for stock price forecasting, leveraging the GRU’s strength in modeling long-range temporal dependencies under nonstationary and noisy conditions. Extensive experiments on real-world financial datasets, including a detailed sensitivity analysis over a wide range of noise scaling parameters ($\epsilon$), reveal that Itô-RMSProp-GRU consistently achieves superior convergence stability and predictive accuracy compared to classical RMSProp. Notably, the optimizer demonstrates remarkable robustness across all tested configurations, maintaining stable performance even under volatile market dynamics. These findings suggest that the synergy between stochastic differential equation frameworks and gated architectures provides a powerful paradigm for financial time series modeling. The paper also presents theoretical justifications and implementation details to facilitate reproducibility and future extensions. Full article

In the present study, we aimed to derive analytical solutions of the homotopy analysis method (HAM) for the time-fractional Navier–Stokes equations in cylindrical coordinates in the form of a rapidly convergent series. In this work, we explore the time-fractional Navier–Stokes equations by replacing the standard time derivative with the Katugampola fractional derivative, expressed in the Caputo form. The homotopy analysis method is then employed to obtain an analytical solution for this time-fractional problem. The convergence of the proposed method to the solution is demonstrated. To validate the method’s accuracy and effectiveness, two examples of time-fractional Navier–Stokes equations modeling fluid flow in a pipe are presented. A comparison with existing results from previous studies is also provided. This method can be used as an alternative to obtain analytic and approximate solutions of different types of fractional differential equations applied in engineering mathematics. Full article

Phenomena from a variety of disciplines, including biology, computer science and sociology, can be modeled by graph dynamics in which nodes are associated with states and the node-state association changes in time. Although general k-state dynamics have been considered, most of the research in this area refers to binary dynamics especially as far as deterministic dynamics are regarded. In this paper 3-state deterministic dynamics are studied from the computational complexity perspective. A tractability result is proved when the third state is a state of neutrality, adopted by any node unable to establish a preference between the two remaining states. Subsequently, two hardness results are proved for two cases where each of the three states represents a semantically distinct state: the case in which a state change occurs in a node only if the most preferred state among the remaining two receives a suitable number of preferences, and the case in which a state change occurs in a node only if its current state lacks sufficient preferences and the most preferred state among the remaining two receives a suitable number of preferences. Finally, the relation of the last two results and a conjecture from the 1980s is discussed and it is shown that the conjecture is contradicted in both cases. Full article

The paper investigates the regularization of solutions to nonlinear Volterra integral equations of the first kind, under the assumption that a solution exists and belongs to the space of continuous functions. The kernel of the equation is a differentiable function and vanishes on the diagonal at an interior point of the integration interval. By applying an appropriate differential operator (with respect to x), the Volterra integral equation of the first kind is reduced to a Volterra integral equation of the third kind, equivalent with respect to solvability. The subdomain method is employed by partitioning the integration interval into two subintervals. Within the imposed constraints, a compatibility condition for the solutions is satisfied at the junction point of the partial subintervals. A Lavrentiev-type regularizing operator is constructed that preserves the Volterra structure of the equation. The uniform convergence of the regularized solution to the exact solution is proved, and conditions ensuring the uniqueness of the solution in Hölder space are established. Full article

The increasing need for high-resolution, real-time radiative transfer (RT) modeling in climate science, remote sensing, and planetary exploration has exposed limitations of traditional solvers such as the Discrete Ordinate Radiative Transfer (DISORT) and Rapid Radiative Transfer Model for General Circulation Models (RRTMG), particularly in handling spectral complexity, non-local thermodynamic equilibrium (non-LTE) conditions, and computational scalability. Quantum-Inspired Neural Radiative Transfer (QINRT) frameworks, combining tensor-network parameterizations and quantum neural operators (QNOs), offer efficient approximation of high-dimensional radiative fields while preserving key physical correlations. This review highlights the advances of QINRT in enhancing spectral fidelity and computational efficiency, enabling energy-efficient, real-time RT inference suitable for satellite constellations and unmanned aerial vehicle (UAV) platforms. By integrating physics-informed modeling with scalable neural architectures, QINRT represents a transformative approach for next-generation Earth-system digital twins and autonomous climate intelligence. Full article

Several studies have reported methods for signal similarity measurement. However, none of the reported methods consider temporal peak-shape features. In this paper, we formalize signal similarity using mathematical concepts and define a new distance function between signals that considers temporal peak-shape characteristics, providing higher precision than current similarity measurements. This distance function addresses latent geometric characteristics in quotient spaces that are not addressed by existing methods. We include an example of using this method on discrete MEG recordings, known for their high spatial and temporal resolution, which were recorded in neighborhoods of extreme points in a cross-area projection of brain activity. Full article

This study introduces a novel hybrid framework that integrates machine learning (ML) with fractional-order differential equations (FDE) to enhance the prediction and clinical management of psoriasis, leveraging real-world data from the UCI Dermatology Dataset. By optimizing ML models, particularly the Voting Ensemble, to inform FDE parameters, and developing a user-friendly graphical user interface (GUI) for real-time diagnostics, the approach bridges computational efficiency with physiological realism, capturing memory-dependent disease progression beyond traditional integer-order models. Key findings reveal that the Voting Ensemble achieves a precision of 0.986 ± 0.007 and an AUC of 0.992 ± 0.005. At the same time, the fractional-order model, with an optimized order of 0.6781 and a mean square error (MSE) of 0.0031, accurately simulates disease trajectories, closely aligning with empirical trends for features such as Age and SawToothRete. The GUI effectively translates these insights into clinical tools, demonstrating probabilities ranging from 0% to 100% based on input features, supporting early detection and personalized planning. The framework’s robustness and potential for broader application to chronic conditions highlight its significance in advancing healthcare. Full article

The geometric foundations of General Relativity are revisited here, with particular attention to its gauge invariance, as a key to understanding the true nature of spacetime. Beyond the common image of spacetime as a deformable “fabric” filling the Universe, curvature is interpreted as the dynamic interplay between matter and interacting fields, a view already emphasized by Einstein and Weyl but sometimes overlooked in the literature. Building on these tools, a Newtonian framework is reconstructed that captures essential aspects of cosmology, showing how classical intuition can coexist with modern geometric insights. This perspective shifts the focus from substance to relationships, offering a fresh magnifying glass through which to reinterpret gravitational dynamics and the large-scale structure of the Universe. The similarities of this approach with other recent, more ambitious ones carried out at the quantum level are quite remarkable. Full article

This paper presents a novel class of conformable integro-differential operators designed to model systems with rapid and ultra-rapid dynamics. This class of local operators enables the design of controllers and observers that induce hyperexponential convergence and provide robustness against bounded disturbances and dynamic uncertainties. The proposed method leverages Nested Exponential Functions (NEFs) and Nested Exponential Factorial Functions (NEFFs) to capture fast dynamics effectively. Additionally, the proposed study examines the Fundamental Theorem of Calculus in the context of Nested Exponential Conformable (NEC) operators, unveiling structural properties, such as stability and robustness, that produce dynamical systems with enhanced hyperexponential convergence and faster dynamics compared to existing approaches. Stability results for NEC systems are established, and some illustrative examples based on numerical simulations are presented to demonstrate the reliability of the proposed approach. Full article

Large multiple datasets were simulated through sampling, and regression modeling results were compared with known parameters—an analysis undertaken here for the first time on such a scale. The study demonstrates that the impact of multicollinearity on the quality of parameter estimates is far stronger than commonly assumed, even at low or moderate correlations between predictors. The standard practice of assessing the significance of regression coefficients using t-statistics is compared with the actual precision of estimates relative to their true values, and the results are critically examined. It is shown that t-statistics for regression parameters can often be misleading. Two novel approaches for selecting the most effective variables are proposed: one based on the so-called reference matrix and the other on efficiency indicators. A combined use of these methods, together with the analysis of each variable’s contribution to determination, is recommended. The practical value of these approaches is confirmed through extensive testing on both simulated homogeneous and heterogeneous datasets, as well as on a real-world example. The results contribute to a more accurate understanding of regression properties, model quality characteristics, and effective strategies for identifying the most reliable predictors. They provide practitioners with better analytical tools. Full article

This paper introduces a digital adaptive control framework for large-scale multivariable systems, integrating matrix linear Diophantine equations with block pole placement. The main innovation lies in adaptively relocating the full eigenstructure using matrix polynomial representations and a recursive identification algorithm for real-time parameter estimation. The proposed method achieves accurate eigenvalue placement, strong disturbance rejection, and fast regulation under model uncertainty. Its effectiveness is demonstrated through simulations on a large-scale winding process, showing precise tracking, low steady-state error, and robust decoupling. Compared with traditional non-adaptive designs, the approach ensures superior performance against parameter variations and noise, highlighting its potential for high-performance industrial applications. Full article

In this paper, we present an effective two-stage numerical algorithm for the simultaneous finding of all roots of meromorphic functions in a region within the complex plane. At the first stage, we construct a polynomial with the same roots as the ones of the considered function; at the next step, we apply some method for the simultaneous approximation of its roots. To show the efficiency and applicability of our algorithm together with its advantages over the classical Newton, Halley and Chebyshev’s iterative methods, we conduct three numerical examples, where we apply it to two test functions and to an important engineering problem. Full article

This study applies psychological network analysis to explore the structure and dynamics of parental stress, offering a novel perspective beyond traditional latent variable approaches. Rather than treating parental stress as a unidimensional construct, network analysis conceptualizes it as a system of interrelated emotional, behavioral, and contextual symptoms. Using cross-sectional data from Latinx parents of children with intellectual and developmental disabilities (IDD), we compared and identified key central and bridge stress symptoms of Latinx parents of children with autism versus other disabilities that hold influential positions within the stress network. These findings suggest that certain stressors may act as hubs, reinforcing other stress components and potentially serving as high-impact targets for intervention. Network analysis also highlights how symptom relationships vary by types of disabilities, offering insight into tailored support strategies. Overall, this approach provides a dynamic and clinically actionable framework for understanding parental stress, with implications for assessment, early intervention, and personalized mental health care for parents. Full article

Using Taylor-type expansions, we obtain identity expressions for functions on three intervals and differences for two pairs of Csiszár $\varphi$-divergence. With some more assumptions in these identities, inequalities for functions on three intervals and Csiszár $\varphi$-divergence can be obtained as special cases. They can also deduce the known generalized trapezoid type inequality. Furthermore, we use the identity to obtain a new extension for Levinson inequality; thus, new refinements and reverses for Ky Fan-type inequalities are established, which can be used to compare or estimate the yields in investments. Special cases of Csiszár $\varphi$-divergence are given, and we obtain new inequalities concerning different pairs of Kullback–Leibler distance, Hellinger distance, $\alpha$-order entropy and ${\chi }^2$-distance. Full article

The Sporulation-Inspired Optimization Algorithm (SIOA) is an innovative metaheuristic optimization method inspired by the biological mechanisms of microbial sporulation and dispersal. SIOA operates on a dynamic population of solutions (“microorganisms”) and alternates between two main phases: sporulation, where new “spores” are generated through adaptive random perturbations combined with guided search towards the global best, and germination, in which these spores are evaluated and may replace the most similar and less effective individuals in the population. A distinctive feature of SIOA is its fully self-adaptive parameter control, where the dispersal radius and the probabilities of sporulation and germination are dynamically adjusted according to the progress of the search (e.g., convergence trends of the average fitness). The algorithm also integrates a special “zero-reset” mechanism, enhancing its ability to detect global optima located near the origin. SIOA further incorporates a stochastic local search phase to refine solutions and accelerate convergence. Experimental results demonstrate that SIOA achieves high-quality solutions with a reduced number of function evaluations, especially in complex, multimodal, or high-dimensional problems. Overall, SIOA provides a robust and flexible optimization framework, suitable for a wide range of challenging optimization tasks. Full article

The proposed study explores the consistency of the geometrical character of surfaces under scaling, rotation and translation. In addition to its mathematical significance, it also exhibits advantages over image processing and economic applications. In this paper, the authors used partition-based principal component analysis similar to two-dimensional Sub-Image Principal Component Analysis (SIMPCA), along with a suitably modified atypical wavelet transform in the classification of 2D images. The proposed framework is further extended to three-dimensional objects using machine learning classifiers. To strengthen fairness, we benchmarked against both Random Forest (RF) and Support Vector Machine (SVM) classifiers using nested cross-validation, showing consistent gains when TIFV is included. In addition, we carried out a robustness analysis by introducing Gaussian noise to the intensity channel, confirming that TIFV degrades much more gracefully compared to traditional descriptors. Experimental results demonstrate that the method achieves improved performance compared to traditional hand-crafted descriptors such as measured values and histogram of oriented gradients. In addition, it is found to be useful that this proposed algorithm is capable of establishing consistency locally, which is never possible without partition. However, a reasonable amount of computational complexity is reduced. We note that comparisons with deep learning baselines are beyond the scope of this study, and our contribution is positioned within the domain of interpretable, affine-invariant descriptors that enhance classical machine learning pipelines. Full article

This study examined the psychometric properties of the Family Empowerment Scale (FES) among Latinx parents of children with intellectual and developmental disabilities (IDDs), a population historically underrepresented in empowerment research. Given the cultural and contextual factors that may shape empowerment experiences, Exploratory Structural Equation Modeling (ESEM) was utilized to assess the scale’s structural validity. ESEM supports a four-factor model that aligns with, but also refines, the original structure of the FES. The lack of loading for several items indicates the need for revisions that better reflect the lived experiences of Latinx parents. ESEM provided a more nuanced view of the scale’s dimensional structure, reinforcing the value of culturally informed psychometric evaluation. These results underscore the importance of validating empowerment measures within diverse populations to inform equitable family-centered practices. Full article

We present a theoretical model to explain how tubulin dimers in neuronal microtubules might achieve collective quantum coherence, resulting in wavefunction collapses that manifest as avalanches within a self-organized criticality (SOC) framework. Using the Orchestrated Objective Reduction (Orch-OR) theory as inspiration, we propose that microtubule subunits (tubulins) become transiently entangled via dipole–dipole couplings, forming coherent domains susceptible to sudden self-collapse. We model a network of tubulin-like nodes with scale-free (Barabási–Albert) connectivity, each evolving via local coupling and stochastic noise. Near criticality, the system exhibits power-law avalanches—abrupt collective state changes that we identify with instantaneous quantum wavefunction collapse events. Using the Diósi–Penrose gravitational self-energy formula, we estimate objective reduction times $T_{\mathrm{OR}}=\hslash /E_g$ for these events in the 10–200 ms range, consistent with the Orch-OR conscious moment timescale. Our results demonstrate that quantum coherence at the tubulin level can be amplified by scale-free critical dynamics, providing a possible bridge between sub-neuronal quantum processes and large-scale neural activity. Full article

Credit card fraud detection remains a major challenge due to severe class imbalance and the constantly evolving nature of fraudulent behaviors. To address these challenges, this paper proposes a hybrid framework that integrates a Variational Autoencoder (VAE) for probabilistic anomaly detection, a Graph Attention Network (GAT) for capturing inter-transaction relationships, and a stacking ensemble with XGBoost for robust prediction. The joint use of VAE anomaly scores and GAT-derived node embeddings enables the model to capture both feature-level irregularities and relational fraud patterns. Experiments on the European Credit Card and IEEE-CIS Fraud Detection datasets show that the proposed approach outperforms baseline models by up to 15% in F1-score, achieving values above 0.980 with AUCs reaching 0.995. These results demonstrate the effectiveness of combining unsupervised anomaly detection with graph-based learning within an ensemble framework for highly imbalanced fraud detection problems. Full article

This paper investigates a unique and stable numerical approximation of the Riemann–Liouville Fractional Derivative. We utilize diagonal norm finite difference-based time integration methods within the summation-by-parts framework. The second-order accurate discretizations developed in this study are proven to possess eigenvalues with strictly positive real parts for non-integer orders of the fractional derivative. These results lead to provably invertible, fully discrete approximations of Riemann–Liouville derivatives. Full article

In this purely analytical analysis, we have investigated the effects of a point-like defect in a continuous medium on a diatomic molecule under the influence of small oscillations arising from the Lennard-Jones potential. In the search for bound-state solutions, we have shown that the allowed values for the lowest energy state of the molecule are influenced by the presence of the defect. Furthermore, another quantum effect was observed: the stability radial point of the diatomic molecule depends on the system’s quantum numbers; it is quantized. Full article

We propose the Clustered Link-Prediction SEIRS model with Temporal Node Activation (CLP-SEIRS-T), a novel epidemiological framework that integrates community structure, link prediction, and temporal activation schedules to simulate malware propagation in urban communication networks. Unlike traditional static or homogeneous models, our approach captures the heterogeneous community structure of the network (modular connectivity), along with evolving connectivity (emergent links) and periodic device-usage patterns (online/offline cycles), providing a more realistic portrayal of how computer viruses spread. Simulation results demonstrate that strong community modularity and intermittent connectivity significantly slow and localize outbreaks. For instance, when devices operate on staggered duty cycles (asynchronous online schedules), malware transmission is fragmented into multiple smaller waves with lower peaks, often confining infections to isolated communities. In contrast, near-continuous and synchronized connectivity produces rapid, widespread contagion akin to classic epidemic models, overcoming community boundaries and infecting the majority of nodes in a single wave. Furthermore, by incorporating a common-neighbor link-prediction mechanism, CLP-SEIRS-T accounts for future connections that can bridge otherwise disconnected clusters. This inclusion significantly increases the reach and persistence of malware spread, suggesting that ignoring evolving network topology may underestimate outbreak risk. Our findings underscore the importance of considering temporal usage patterns and network evolution in malware epidemiology. The proposed model not only elucidates how timing and community structure can flatten or exacerbate infection curves, but also offers practical insights for enhancing the resilience of urban communication networks—such as staggering device online schedules, limiting inter-community links, and anticipating new connections—to better contain fast-spreading cyber threats. Full article