Abstract: Servo motors typically utilize Field-Oriented Control (FOC). However, the conventional cascaded PI control framework is inherently constrained by its fixed-parameter design, making it highly susceptible to parameter variations and unmodeled disturbances. While intelligent control strategies—such as model predictive control (MPC)—provide a robust, multi-objective alternative, their intensive stepwise computational demand often degrades transient response. Motivated by the stochastic dynamics of motor operation, we propose a novel physics-informed control paradigm. Specifically, we formulate the FOC-based motor control as an online stochastic optimization problem, wherein the objective function is updated iteratively using stochastic gradient estimates, and the resulting time-varying subproblems are solved efficiently by the MSALM algorithm. Our approach significantly outperforms conventional PI controllers in environmental adaptability and disturbance rejection. Experimental results demonstrate that the proposed method achieves comparable high-precision tracking performance while significantly reducing computational time per iteration, ensuring rapid dynamic response and strict enforcement of physical constraints.

Abstract: China served as the primary source of novel materials and innovations that significantly contributed to the development of medieval Europe. In this study, I employ an unconventional approach grounded in the mathematics of ornamental arts to trace the trajectory of Chinese goods to theWest. Utilizing the concept of the wallpaper group, this research analyzes Chinese ornaments to discern similarities with the artwork of the Arabs and Turkish Seljuks during the 8th to 12th centuries. Furthermore, it elucidates the mechanisms through which Chinese art reached theWest, thereby providing insights into the migration of technology.

Abstract: Spring flood modeling is a major tool used to understand the risks of severe hydrological events in the context of climate change. In Kazakhstan spring of 2024 was a rapid shift from cold to mild temperatures in just a few weeks. While traditional flood forecasting methods have been limited in their ability to consider the interactions of the natural processes that create runoff, this research sets out to address these limitations by modelling the formation of spring floods using a numerical approach. The study discusses the effects of snowmelt and freeze-thaw processes on surface runoff and the flooding that results from it in the northern and western regions of Kazakhstan. A comprehensive model has been developed that considers the heat transfer in soil, infiltration of meltwater, and propagation of runoff. Numerical modelling indicates that in 2024, relative to 2021, there was earlier soil thawing and shallower depths of soil freezing. However, an increase in the intensity of snowmelt leads to the fact that the infiltration capacity of the soil is insufficient, despite the formation of a thawed layer. As a result, a higher surface runoff is formed. Using Saint-Venant’s equations to perform calculations indicates that higher values of current depth and velocity of runoff were observed in 2024 than in 2021, indicating a greater likelihood of flooding. Therefore, it can be concluded that increases in winter temperatures have the potential to create an increased flooding impact due to changes in the proportions of surface runoff and infiltration.

Abstract: The paper proposes a new model of Tuberculosis (TB) dynamics taking into account multi-drug resistant forms, which takes into account the detection of infected people with and without bacterial excretion. The model is described by a system of nine nonlinear ordinary differential equations united by the law of mass action and controlled by 10 epidemiological parameters. The conditions for the stability of the system’s equilibrium states are obtained, and the sensitivity-based identifiability analysis of the model is conducted using the Sobol method. Based on Bayesian optimization, the boundaries of sensitive parameters are specified and posterior distributions of the model parameters are obtained for five regions of the Russian Federation based on statistics from 2009 to 2020. It is shown the heterogeneity of epidemic situation by wide credible intervals of correlated parameters of virus contagiousness, the proportion of infected TB converting to the bacterial excretion form and the rate of detection of TB infected with bacterial excretion. Probabilistic forecasts of the expected number of TB infections to 2025 are constructed and validated to the 2021-2023 data.

Abstract: Fractional quantum calculus provides a flexible mathematical framework for incorporating memory and scaling effects into numerical models. However, classical iterative methods for nonlinear equations often suffer from limited stability, strong dependence on initial guesses, and restricted convergence domains, particularly for highly nonlinear problems. In this work, we introduce a new Caputo fractional--quantum iterative scheme, denoted by MSB$_{\mathfrak{q}:\alpha}$, formulated as a parameterized two-step method based on a Caputo-type fractional quantum derivative. The proposed framework incorporates additional structural parameters that regulate the iterative dynamics and provide enhanced control over convergence behavior and stability properties. To investigate the performance of the proposed scheme, we employ tools from complex dynamical systems, including stability analysis and fractal basin investigations in the complex plane. These analyses illustrate how the fractional and quantum parameters influence the geometry of attraction domains and the global convergence behavior of the method. Numerical experiments on representative nonlinear test problems motivated by engineering and biomedical applications demonstrate improved robustness with respect to initial guesses, reduced residual errors, and competitive computational efficiency compared with classical iterative solvers. Overall, the results indicate that the proposed fractional--quantum framework provides an effective and flexible approach for the numerical solution of challenging nonlinear equations.

Abstract: This work presents a distributed optimal control problem for steady-state heat conduction in a system made up of two solids in thermal contact, with heat flux continuity and a temperature jump at the interface. The control affects the system’s energy source. The existence and uniqueness of optimal control are established, and the corresponding optimality conditions are derived. Additionally, it is shown that optimal control can be considered a fixed point of a well-defined operator. Moreover, an iterative algorithm is introduced to approximate the solution to the optimal control problem, which converges regardless of the initial data. Finally, an explicit solution related to one-dimensional case in Cartesian coordinates is given.

Abstract: Energy consumption demand forecasting plays a critical role in the planning and development of the nation’s energy security, which underpins the 8-year Power Development Plan (PDP8) and Vietnam’s ambitious Net-Zero 2050 commitment. However, this task becomes more difficult while challenges the big data environment is filled with a lot of noise and high fluctuation data. In order to deal with the problem, this paper using four distinct models which are Linear Regression, Holt’s (Additive), PSO-GM (1,1), and Support Vector Regression (SVR) to conduct a rigorous comparative analysis to identify the most accurate forecasting model. The performance evaluated by MAE, RMSE, MAPE indexes based on the Vietnam’s total primary energy demand data from 1986 to 2024. To check the accuracy of forecasting model, this study slits the length of data was into two period time, first time for the training data (1986- 2016) and next time for the testing data set (2017-2024). The results decisively identified that the Holt’s model achieving significantly outperforming all counterparts with the lowest error metrics (MAE = 89.33, RMSE = 99.50, and a MAPE of 7.19%). This model is strongly suggested to forecast the Vietnam’s energy demand in the period time 2025 to 2030. Based on this model, the 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.

Abstract: In this comprehensive study, we meticulously investigated multidimensional data analysis techniques, particularly focusing on Tucker decomposition methods, spanning the period from 2000 to 2025. Our primary objective was to discern trends, advancements, and applications of these techniques across various domains of knowledge and how they have evolved over time. An extensive corpus of 288 scientific articles related to tensor decompositions, Tucker models and applications was previously reviewed. Multivariate methods such as text mining using IraMuteq software and MANOVA-Biplot were employed to visualize identified data patterns, and the analytical capability of ChatGPT artificial intelligence was assessed to provide contextual insights and add another layer of information to the research. Our conclusions underscore the importance of blending traditional statistical approaches with natural language processing prowess to achieve a profound understanding of the data. This analysis offers a comprehensive perspective on the evolution and application of multidimensional data analysis techniques, with a special emphasis on the enduring relevance of Tucker techniques in this new millennium.

Abstract: Quantitative analytics has assumed a growing role in Philippine policy research as government and sectoral databases have become increasingly central to planning, monitoring, and resource allocation. This review synthesizes recent work in education, energy, agriculture, health, and finance to examine how forecasting, statistical forensics, and predictive modeling have been applied to Philippine policy problems. Across these sectors, the literature shows a clear methodological progression from descriptive diagnostics and classical time-series models toward comparative machine learning, deep learning, explainable artificial intelligence, nonlinear embedding, and Benford-based anomaly detection. Several recurring strengths emerge, particularly the consistent use of official Philippine datasets, transparent model benchmarking, and close alignment with practical policy concerns such as dropout reduction, electricity and crop planning, disease surveillance, and financial forecasting. At the same time, important limitations remain, including limited multivariate and spatial modeling, uneven validation practices, and relatively little attention to uncertainty quantification and operational deployment. In comparison with the broader international literature, the strongest contributions are those that position analytics as a support tool for planning and monitoring, while the main gaps lie in external validation, richer explanatory structures, and decision-oriented system integration. The evidence suggests that the next phase of Philippine policy analytics should move beyond isolated single-series applications toward integrated frameworks that combine forecasting, data-quality assessment, explainable modeling, and sector-specific decision thresholds for routine governance.

Abstract: Let f (z) = ∑_n≥0 a_nzⁿ be analytic at the origin, and assume that no Taylor coefficient vanishes. We study the normalized Taylor tails T^f_n (w) := ∑_k≥0 a_n+k/a_nw^k, not as isolated remainders but as a discrete renormalization orbit on the space of normalized analytic germs. The governing map is the nonlinear operator S(F)(w) := F(w)−1 wF′ (0) , which acts as a coefficient shift followed by canonical normalization. The exact identity T^f_n+1 = S(T^f_n) turns the Taylor coefficients of f into a dynamical system. We develop a self-contained theory of this dynamics. First, we prove that the nonlinearity of S is exactly linearized in ratio coordinates: the map F→ (Sⁿ F)′(0)
_n≥0 conjugates S to the one-sided shift on an explicit space of admissible ratio sequences. This yields complete reconstruction of the orbit and a realization theorem for all admissible orbits. Second, we classify the rigid orbit types: fixed points are exactly geometric series, periodic points are exactly rational functions with denominator 1 − Λw^m, and eventual periodicity is equivalent to a polynomial plus a rational tail. Third, we exhibit genuinely rich internal dynamics by constructing compact invariant subsystems on which S is conjugate to full shifts on finite alphabets. Fourth, on the asymptotic side, ratio limits force universal geometric profiles, while first- and second-order corrections to the coefficient ratios produce universal corrections to the tail orbit. In particular, dominant algebraic singularities leave a precise first asymptotic fingerprint on the renormalized tails. We also prove exact transport laws under differentiation and Hadamard products. The basic normalized tail object overlaps, up to an index shift, with the normalized remainders recently studied in the special-functions literature. The present contribution is different in focus: it isolates the renormalization operator itself, proves exact shift linearization and orbit realization, identifies symbolic invariant subsystems, and develops rigidity and asymptotic classification results for the resulting dynamical flow.

Abstract: Distributed heterogeneous hybrid flow shop scheduling with job deadlines and priorities (DHHFSP-JDP) is a combination of scheduling problem and distributionary environment. Addressing complex work sequences and energy consumption in distributed manufacturing with heterogeneous plants is a major challenge. It is necessary for optimizing total weighted delay (TWD) and total energy consumption (TEC) in distributed heterogeneous green hybrid flowshops. A model using mixed integer linear programming is applied to describe DHGHFSP-JDP and a decomposition-based coevolutionary algorithm (DBCEA) is considered to be the solution in this article. In this approach, (1) a decomposition-based heuristic initialization is proposed, in which an initialization strategy with a randomly sized population is adopted to establish effective initial schedules. (2) elite selection strategy based on the integration of an external archive and an elite archive. (3) four problem-based operator selection strategies embedded in a cooperative local search framework, and an Upper Confidence Bound (UCB) mechanism to design a strategy for selecting local search operators. In the end, The superiority of DBCEA is validated through comparative experiments against several advanced algorithms across 20 benchmarks, with results showing it often provides the best Pareto solution set.

Abstract: Lyapunov stability is addressed here, which expands new knowledge of identifying continuous trajectories of fractional order systems that develops the ultimate goal to reach near or converge to its equilibria whenever one convincingly chooses the right Lyapunov functions. The notions of asymptotic stability, stability, and multi-order Mittag-Leffler stability were discussed for complicated nonlinear fractional order systems whenever associated different orders that may lie in $(0,1]$ and begin with the initial position posed at a random initial time take values on the real number line. The overview of this work is to give readers an enlightening insight into the so-called fractional Lyapunov direct method, which asserts how amazingly one can think of scalar Lyapunov functions to reasonably predict stability dynamics in large time, especially when time $t$ tends to $\infty$. We also establish some new sufficient conditions for stability and introduce a new notion of attractiveness of any bounded fixed solution or solution pairs that can be visualized in many such systems. The consequences of some results were adequate in exemplary models.

Abstract: This study investigates the regularity of the three-dimensional (3D) incompressible Navier-Stokes equations (NSE) for plane Couette flow, a canonical shear-driven flow model with a well-defined laminar-turbulent transition threshold. Employing Sobolev space theory and the Poincaré inequality, we rigorously prove that no global smooth solutions exist as the Reynolds number exceeds the critical value \( Re_{cr} \). Prior studies have revealed that a zero velocity gradient on the velocity profile is the necessary and sufficient condition for turbulence generation in 3D plane Couette flow, yet they lack mathematical theoretical proof from the perspective of partial differential equation framework. This study fills this gap via velocity decomposition and singularity analysis. We show that nonlinear disturbance amplification induces local cancellation of mean and disturbance velocity gradients, triggering finite-time singularity formation in flow field, which leads to the breakdown of regularity of the 3D NSE and thus the non-existence of global smooth solutions. It is emphasized that the non-existence of smooth solutions is due to the local regularity breakdown of solutions instead of the velocity blow-up. Further, it is important that the critical condition for regularity breakdown obtained through Sobolev space analysis accords with the critical condition for turbulence onset obtained through experiments and simulations.

Abstract: Non-injective maps on finite structures—maps where distinct inputs can share an output—contract their image under iteration. We introduce the observation scale σc, the resolution at which a non-injective map’s contraction geometry is opti- mally visible, defined via a susceptibility peak in a resolution-dependent observable. We prove that σc exists for every non-injective map on a finite structure and show that the scale has been detected across five physical domains spanning twelve or- ders of magnitude, with statistically significant peaks (p < 0.02) in each case. As a secondary contribution, we propose a four-type classification of mathematical op- erations by injectivity structure: contraction (Type D), oversaturation (Type O), symmetry constraint (Type S), and preservation (Type R). The companion paper [1] develops the core theory for Type D; here we develop σc, identify physical instances of contraction, and apply the classification to illustrative examples including Gold- bach’s conjecture (Type O) and the Riemann hypothesis (Type S), without claiming resolution of either.

Abstract: Forecasting research in the Philippines has evolved from classical time-series analysis toward comparative machine learning and selected hybrid nonlinear models. Across energy, agriculture, health, and finance, this progression reflects changing data complexity, forecasting goals, and temporal behavior rather than simple replacement of older methods. Early studies on electricity consumption, provincial demand, and coal production relied on ARIMA-type models because the series were aggregate, limited, and well suited to interpretable linear frameworks. Later work on crop production, monthly peak demand, and disease incidence adopted comparative designs that evaluated seasonal statistical models alongside neural and machine-learning approaches, showing added value when seasonality was less stable and nonlinear dependence was more evident. The progression culminated in chaos-enhanced LSTM modeling for the Philippine stock exchange index, where nonlinear state reconstruction became methodologically defensible. Overall, ARIMA remains sufficient for largely linear seasonal signals, whereas machine learning and hybrid methods are justified for more complex dynamics.

Abstract: This paper investigates a tracking control problem for a class of strict-feedback nonlinear systems with time delays, asymmetric output constraints, and deception attacks on the controller. First, by introducing a novel error transformation techniques, any non-zero and bounded initial state is converted into zero. Second, a barrier function with the asymmetric output constraints is designed, which convert the problem of satisfying the tracking control problem of nonlinear systems under output constraints boils down to ensuring the boundedness. In additional, the radial basis function neural networks (RBFNNs) are utilized to handle both unknown uncertain term and deception attacks simultaneously. By utilizing the new asymmetric delayed barrier function error together with a RBFNNs technique, the tracking controller is designed to achieve asymptotic tracking, regardless of presence or absence of output constraints. Finally, the effectiveness of the proposed strategy is verified through its simulation on the unmanned aerial vehicle’s (UAVs) systems.

Abstract: We introduce Symbolic Structures of Differences (SSD), a method for quantifying the complexity of time series data based on the local geometry of second-order differences. Unlike global entropy measures, SSD captures the diversity of local sequential patterns by analyzing the signs of first and second-order differences within overlapping triplets, mapping them to a space of 27 unique symbols. We provide a theoretical analysis of SSD, proving its invariance under affine transformations and establishing its relationship to permutation entropy. The method's statistical properties, including robustness to noise and finite-size effects, are examined through Monte Carlo simulations. We validate SSD on a benchmark of synthetic and real-world physiological time series, comparing its performance against four established complexity measures (permutation entropy, sample entropy, Lempel-Ziv complexity, and spectral entropy) in the context of detecting epileptic seizures from EEG data. The results demonstrate that SSD offers a competitive and computationally efficient framework for characterizing dynamical regimes and identifying phase transitions, with unique sensitivity to local geometrical structures.

Abstract: Modern financial markets are increasingly shaped by algorithmic trading systems and artificial intelligence techniques that process large volumes of financial data in real time. However, machine learning–based trading systems often suffer from signal instability and excessive sensitivity to market noise, which may lead to overtrading and increased financial risk. In highly volatile environments such as cryptocurrency markets, the re-liability of trading signals becomes a critical issue for both portfolio allocation and risk management. This study proposes an entropy-filtered machine learning framework designed to en-hance the stability and risk-awareness of algorithmic trading strategies. The proposed approach integrates entropy-based filtering techniques with machine learning classifiers in order to reduce noise in market signals improving the risk-adjusted stability of algo-rithmic trading strategies. Entropy measures are employed as a filtering mechanism that evaluates the informational content of market signals and suppresses unreliable predic-tions generated by the learning model. The empirical analysis is conducted using cryp-tocurrency market data, where the entropy-filtered machine learning framework is ap-plied to trading signal generation and portfolio decision making. The results indicate that the proposed approach improves the stability of trading signals and reduces the occur-rence of false signals compared to conventional machine learning trading models. Moreover, the integration of entropy filtering contributes to a more balanced risk–return profile and enhances the overall robustness of algorithmic trading strategies.The findings suggest that combining information-theoretic measures with machine learning tech-niques represents a promising direction for developing more reliable and risk-aware financial decision systems. The results suggest that entropy-based filtering can substan-tially improve the robustness and risk-awareness of machine learning trading systems, providing a promising direction for future AI-driven financial decision frameworks.

Abstract: Existence of global smooth solutions to the three-dimensional (3D) Navier-Stokes equations is disproved for pressure-driven flows with no-slip boundary conditions. This study is rigorously grounded in Sobolev space analysis. We show that the solution breakdown arises from regularity degeneration instead of velocity blowup. For disturbed laminar plane Poiseuille flow, the instantaneous velocity field is decomposed into a time-averaged flow and a disturbance flow, both characterized by their regularity in Sobolev spaces. When the Reynolds number is larger than the critical Reynolds number, the nonlinear interaction modifies the mean flow profile, and the disturbance amplitude grows exponentially. This amplification leads to a local cancellation between viscous terms of the mean flow and the disturbance flow, resulting in the total viscous term (i.e., the Laplacian term) vanishing locally at the critical point $(\boldsymbol{x}^*, t^*)$. The local vanishing viscous term leads to zero velocity by the elliptic operator estimate, which contradicts the non-vanishing incoming velocity, leading to formation of a singularity. This singularity induces a velocity discontinuity, which causes the $L^\infty$ -norm of the velocity gradient to diverge, violating the definition of a global smooth solution in Sobolev spaces. The analysis is strictly grounded in partial differential equations (PDE) theory, with all key steps validated by Sobolev space properties and a priori estimates.

Abstract: Efficient calibration is essential for the practical application of option pricing models. The Fractional Stochastic Volatility Jump Diffusion (FVSJ) model proposed by Zhang and Yong [1] can reproduce several stylized features observed in option markets, including the volatility smile, volatility clustering, and long-memory effects. However, its multiple stochastic components make conventional calibration computationally expensive. This paper proposes a two-step calibration framework that combines a neural network with a differential evolution (DE) algorithm. In the first step, we construct a Physics-Informed Kolmogorov-Arnold Network (PCKAN) to approximate the FVSJ pricing map. Specifically, we replace the B-spline basis in KAN with second-kind Chebyshev polynomials and incorporate a Black-Scholes PDE residual as an additional penalty term in the training objective, aiming to improve global approximation and enhance numerical stability and interpretability. In the second step, the trained PCKAN is used as a fast surrogate pricer within the DE algorithm to accelerate parameter estimation. Empirical results show that the proposed method achieves calibration accuracy comparable to direct pricing while substantially reducing computational time.