Search Results (504)

Economically motivated adulteration of olive oil, coffee and fruit juice is a persistent food-fraud problem for which Fourier-transform infrared (FTIR) spectroscopy with chemometrics offers rapid screening. Linear partial least squares (PLS) is interpretable but cannot capture non-linear mixing; neural networks add flexibility at the cost of becoming black boxes. We evaluated a Kolmogorov–Arnold network (KAN), which places learnable univariate functions on its edges and is therefore intrinsically interpretable, against PLS, support-vector regression, random forests, a multilayer perceptron and a one-dimensional convolutional network on three attenuated total reflectance (ATR)–FTIR datasets (olive oil + sunflower oil, coffee + malt flour, orange juice + apple juice; approximately 350, 400 and 400 spectra). All models were compared under identical, leakage-free validation that splits spectra by physical sample. The compact KAN was consistently competitive (cross-validated coefficients of determination (R²) = 0.86, 0.93 and 0.69) and yielded closed-form equations whose variables map to recognised vibrational bands and whose importance ranking agrees with SHapley Additive exPlanations (SHAP; Spearman ρ = 0.86–0.90); symbolic conversion costs no accuracy. We also report the following limits: PLS was strongest where the chemistry was linear (coffee) and the multilayer perceptron was strongest on fruit juice, whose equation is the weakest (R² = 0.47–0.75 across seeds); a parameter-matched perceptron matched the KAN’s accuracy; and leave-one-brand-out validation degraded every model. The KAN is therefore a promising, compact and genuinely transparent alternative under controlled multi-matrix conditions, not a deployment-ready method. Full article

Electromechanical thrust-vector control systems are subject to friction, backlash, and configuration-dependent dynamics that are difficult to model explicitly, motivating controllers that adapt from operational data without requiring an identified plant. This paper proposes a data-driven, disturbance-observer-based controller in actuator space for a dual-axis thrust-vectoring platform. The controller operates on a sliding surface defined over the actuator tracking error and uses an adaptive input matrix gain together with a lumped disturbance observer, both of which are updated from encoder and control data through gradient descent applied to a joint identification loss. The Newton–Euler equations of the mechanical system are projected onto the actuator coordinates through the angular-velocity map, yielding a structurally well-posed actuator-space model, which is used to design the adaptive gain; nonetheless, the dynamic model is never evaluated online. The resulting controller requires only encoder measurements of actuator displacements, a reference trajectory computed from the platform geometry, and bounded normalized commands; the mechanism Jacobian and the inertia and Coriolis matrices are not evaluated online. Boundedness of the adaptive gain and disturbance estimate is established, and uniform ultimate boundedness of the tracking error follows under a mild alignment condition. Simulation results on a coupled nonlinear plant and hardware-in-the-loop experiments on a dual-channel actuator testbed are presented, comparing the proposed controller against PID, super-twisting, unit-vector sliding mode, and MFAC baselines on a circular thrust-vector reference. Full article

This paper presents a numerical method for solving transient one-dimensional heat conduction problems in multilayer slabs with temperature-dependent thermal conductivities. The governing nonlinear partial differential equations are formulated separately in each layer, allowing for distinct material properties. Perfect thermal contact at internal interfaces is enforced through continuity of temperature and heat flux, while general boundary conditions are imposed at the external boundaries, including prescribed temperature, specified heat flux, and convective exchange. A key feature of the proposed approach is to discretize the partial differential equations first in time using the implicit Euler method, thereby reducing the original problem to a sequence of nonlinear two-point boundary value problems with interface (transmission) conditions. A second-order finite difference scheme is employed for spatial discretization, and the resulting system is expressed in global form using a unified indexing strategy. The system is solved at each time step by Newton linearization, yielding a sparse Jacobian matrix that is tridiagonal in the interior and locally extended at the interfaces. Efficient banded solvers lead to O(N) cost per time step, where N is the number of spatial nodes. Numerical experiments confirm the expected accuracy, unconditional stability, and computational complexity of the method. Full article

To overcome the limitations of existing three-degree-of-freedom milling stability models in representing axial cutting conditions, this study develops a stability prediction framework that accounts for both axial segmentation and the axial contact angle. A three-degree-of-freedom dynamic model of the milling system is first formulated by introducing the axial contact angle. The tool axis is then discretized, so that the cutting force coefficients can be evaluated in different axial sections and the non-uniform distribution of cutting forces along the tool can be captured more accurately. After incorporating the regenerative mechanism, the milling dynamics are expressed in the form of a linear time-delay differential equation. To enhance the numerical accuracy of the time-delay system solution, a full-discretization scheme using third-order Lagrange–Hermite interpolation is developed for constructing the state transition matrix. The stability boundary is subsequently determined based on Floquet theory, from which the stability lobe diagram is generated. The proposed model and solution procedure are validated by comparison with existing methods and by time-domain simulation. The results show that, when the spindle speed ranges from 5000 to 10,000 rpm and the axial depth of cut ranges from 0 to 8 mm, the overall variation rate of the predicted stability region is 11.19% after incorporating axial discretization and 59.88% after considering the axial contact angle. The stable and unstable cutting responses obtained from time-domain simulations are consistent with the regions predicted by the stability lobe diagram, which supports the validity of the proposed approach. Further investigation shows that, for the established three-degree-of-freedom milling model and the specified cutting parameters, the axial contact angle exerts a pronounced nonlinear effect on the stability boundary. Specifically, as the axial contact angle $\epsilon$ increases within the range $0^{°}<\epsilon \le {45}^{°}$, the stable region gradually shrinks; when $\epsilon$ increases from 45° to 90°, the stable region expands instead. These observations can provide useful guidance for selecting milling parameters and identifying stable machining conditions. Full article

In this paper, we introduce and study proximal $\mathfrak{Z}$-condensing operators in strictly convex Banach spaces by combining simulation functions with measures of noncompactness. A Darbo-type best proximity point theorem is established, and several consequences corresponding to nonlinear condensing conditions are obtained. As an application, a system of nonlinear ordinary differential equations is embedded into a non-self operator problem on an enlarged product space; in this formulation, best proximity points are shown to be equivalent to classical solutions of the system. We also prove a Krasnoselskii-type best proximity point theorem for the sum of a simulation-function contraction and a compact operator and apply it to a nonlinear matrix-valued integral equation. Finally, a multiplicative best proximity point theorem is obtained in strictly convex Banach algebras and is used to study a nonlinear integral equation. The results provide a unified operator-theoretic framework for additive and multiplicative equations involving non-self mappings. Full article

We develop a tensor-based dynamical framework for monetary flows in multi-sector, multi-agent economies and quantify the information destroyed when the monetary state is reduced to a scalar aggregate. The state is a third-order tensor encoding capital flows across sectors, agent classes, and time; deviations from equilibrium obey a tensor-indexed Langevin (multivariate Ornstein–Uhlenbeck) equation with a coupling operator and channel-specific friction rates. Using standard Lyapunov theory, we assemble a stability and convergence framework for the induced vectorized system, with a bound stated so as to remain valid for the non-normal system matrices generated by asymmetric economic coupling, and characterize the stochastically forced case in the mean-square sense. Shannon entropy, Kullback–Leibler divergence, and sector–agent mutual information measure the structural information discarded by scalar aggregation. We then study a stylized, heuristically calibrated $3\times 3$ economy subject to a shock inspired by the 2007–2009 crisis; we emphasize at the outset that the figures reported below are properties of that calibration and are not empirical estimates. In this scenario Finance absorbs an 18.9% peak capital loss while Manufacturing and Services suffer 5.8% and 3.9% secondary drops, against an aggregate contraction of only 8.6%; the Kullback–Leibler divergence of the sector–agent flow distribution recovers systematically later than the aggregate signal, a lag that is positive in 96.6% of a 1000-draw Monte Carlo ensemble, although its magnitude is calibration-dependent. Under a symmetric exit rule, a deficit-targeted stimulus restores equilibrium substantially faster than a share-weighted uniform stimulus in 100% of the ensemble while spending strictly less—its realized expenditure saturates below the uniform budget because it self-terminates as deficits close—and attains integrated disequilibrium within 18% of the exact linear-quadratic optimum at equal control effort while requiring no knowledge of the system matrix. The ordinal conclusions—aggregation masks the epicenter, structure lags the aggregate, and deficit targeting dominates uniformity—are robust across a wide neighborhood of the calibration, and identify the disaggregated state as the object that stabilization policy needs and that scalar aggregation destroys. Full article

Nonlocal circumstances in genetic engineering are crucial as they pertain to the understanding of genetic material. When these conditions are associated with differential integral equations, particularly concerning the time variable, they yield comprehensive insights into the material’s temporal memory, which can be advantageous for understanding all material properties (including chronic conditions or behavioral characteristics), thereby assisting specialists in managing its future evolution. The novelty of this manuscript resides in the exploration of fractional nonlinear mixed integro-differential equations (FrN-MIo-DE) under nonlocal conditions, employing the Toeplitz matrix method with a genetic application. This issue has previously been examined via the Nyström technique and solely under local conditions. A category of mathematical problems prevalent in many domains, including physics, engineering, and biological systems, is fractional calculus. Fractional calculus, which generalizes classical differentiation and integration to non-integer orders, offers a robust foundation for modeling memory and hereditary characteristics in complex systems. We examine the existence and uniqueness of solutions to FrNMIo-DE under nonlocal restrictions, using a discontinuous kernel dependent on location and time-space $L_2[-\mathrm{1,1}]\times C[0,T]$, where T < 1, via analytical methods. According to the features of fractional integrals, FrNMIo-DE adheres to the second-kind Volterra–Hammerstein integral equation (V-HIE), characterized by a discontinuous kernel in position for the Hammerstein integral term and a continuous kernel in time for the Volterra integral (VI) term. Subsequently, we use a separation approach technique to produce HIE with time-dependent physical coefficients. Following an analysis of the system’s convergence, a nonlinear algebraic system (NAS) is constructed using the Toeplitz matrix technique (TMT) and related methodologies. The numerical data and associated errors are shown via the Maple 2022 software. Full article

This paper presents the mathematical modeling, numerical implementation, and experimental validation of a decoupling control algorithm for a five-port multiport modular active bridge (MMAB) converter in DC microgrid applications. Based on an analytically derived generalized state-space framework of the MMAB topology, a matrix-based method for suppressing non-linear mutual cross-couplings among individual ports is proposed. The study addresses parametric uncertainties within the system matrix caused by parasitic bus inductances; by formulating a linear system of equations solved via the numerical least-squares method, the equivalent parameter identification error was reduced from over 18% to a valid threshold. The decoupling performance and dynamic responsiveness of the closed-loop system were experimentally verified on a dual-core TMS320F28379D digital signal processor. The experimental results demonstrate that the proposed algorithm effectively isolates transient step-load perturbations, maintaining voltage stability on adjacent undisturbed ports within a strict deviation of less than $+0.51\%$ and achieving a recovery time below 5 ms. Furthermore, the real-time execution of the online Jacobian matrix inversion via the Newton–Raphson method confirms the computational feasibility and convergence of the iterative approach under tight sampling periods. The obtained results provide a robust, experimentally validated foundation for advanced algebraic and numerical control strategies in high-stability multiport power conversion systems. Full article

The long-term productivity of hydraulically fractured deep coalbed methane (CBM) wells is jointly governed by desorption-driven gas supply from the coal matrix, the effective-stress response and time-dependent creep of natural cleats, and the progressive degradation of hydraulic-fracture conductivity. To address the difficulty of conventional models in consistently describing the time-dependent transport capacities of natural cleats and hydraulic fractures, this study develops a productivity-prediction model for hydraulically fractured deep CBM wells that couples gas storage in the coal matrix, dynamic natural-cleat permeability, and dynamic hydraulic-fracture conductivity. Based on mass conservation, the model accounts for free- and adsorbed-gas storage, single-phase gas flow, matrix-fracture mass transfer, and wellbore production. The evolution of natural-cleat permeability incorporates effective-stress-induced closure, Langmuir desorption shrinkage, and fractional-order creep, whereas the evolution of hydraulic-fracture conductivity considers fracture compaction, elastic deformation and embedment of proppants, and creep-induced closure of the coal rock. The nonlinear coupled equations are solved using a fully implicit finite-difference scheme. The field dataset comprises daily production records from six deep CBM wells and is used only to constrain physically reasonable ranges of field parameters and provide reference production characteristics. The results indicate that effective stress primarily controls the rapid closure of flow pathways during the early production stage, while the relative contribution of coal creep increases with production time. Neglecting either coal creep or stress sensitivity leads to an overestimation of cumulative gas production over the medium and long term. The proposed model provides a physically constrained analytical framework for evaluating the long-term productivity of hydraulically fractured deep CBM wells and comparing alternative production strategies. Full article

Traditional frameworks of innovation diffusion, such as epidemic and Lotka–Volterra–Gause models, treat technological substitution primarily as a population-driven or social communication process, frequently overlooking the critical constraints imposed by external factor scarcities. To address this fundamental economic gap, this study performs a qualitative analysis of exploitative competition between two distinct technologies sharing two complementary resources, modeled via a non-linear system of chemostat-type consumer–resource ordinary differential equations. Technologies are represented as homogeneous populations of elemental firms, where individual output is governed by a ratio-dependent, fixed-proportions Leontief production function integrated with a hyperbolic clearing response. Operating within an open industrial system, the model accounts for resource supply rates and firm exit dynamics. We analytically derive the coordinates of both boundary and interior fixed points within the non-negative orthant of the phase space. By investigating the eigenvalues of the associated Jacobian matrix, we establish necessary and sufficient conditions for local asymptotic stability, competitive exclusion, and technological coexistence, demonstrating that efficiency is determined by a break-even resource availability threshold. Our results reveal that structural reconfigurations of the industry supply plane trigger bifurcations between local dominance and multistability. The latter manifests as a path-dependent, Quastlerian selection of initial conditions rather than inherent technological superiority. Finally, we establish the geometric boundaries of the stable assemblage niche, proving that technological diversity is regulated by resource supply rates. By explicitly incorporating resource scarcity into a dynamical predator–prey framework, the proposed model offers a more robust economic and mathematical foundation for innovation diffusion, providing policymakers with structural insights into the resource allocation strategy and the long-term management of industrial diversity. Full article

This paper introduces and investigates a novel inhomogeneous variable-coefficient discrete Hirota equation which is a combination of discrete nonlinear Schrödinger equation and discrete complex modified Korteweg–de Vries equations. Through spectral analysis, the related compatibility conditions and Lax pairs are explicitly derived, on which basis we successfully construct a generalized $(n,N-n)$-fold discrete Darboux transformation. Leveraging this newly established gauge matrix framework, we obtain and graphically characterize several families of exact localized solutions, including non-trivial solitons and breathers. Our visual simulations reveal that the dynamic trajectories and structural profiles of these localized patterns are strongly governed by the external potential functions. Furthermore, by employing the algebraic infrastructure of the Tu scheme, we derive a novel integrable discrete Hirota hierarchy associated with the given spectral problem, subsequently establishing its rigid Hamiltonian formulation alongside an infinite set of conservation laws. Full article

Thermomechanical coupling effects significantly influence the dynamic response of flexible multibody systems operating in thermal environments. Accurate simulation using conventional projection-based reduced-order models remains challenging due to strong nonlinearity and the time-varying nature of thermal fields. This work proposes a projection-free sparse-solving framework for thermomechanical coupling dynamics. The elastic and thermal fields are represented using sparse POD coefficients, and the governing equations are directly sampled online without Galerkin projection. The sparse coefficients are recovered via l₁ norm optimization at each time step. To ensure stable recovery under thermal-mechanical coupling, a unit-norm tight frame-based preconditioner is introduced to reduce the coherence of the underdetermined system matrix. The proposed method is validated through three numerical examples. Results show that the method maintains stable accuracy over long-time simulations, reduces computational time by over 40%, and exhibits improved robustness compared with the discrete empirical interpolation method in thermomechanical coupling problems. The adaptive basis selection capability and the necessity of unit norm tight frame preconditioning are confirmed. The method offers an efficient and reliable alternative for thermomechanical multibody dynamics simulation. Full article

Strong consistency and asymptotic error distribution for a new class of nonlinear recursive parameter estimation algorithms of an approximate Newton–Raphson type are established. The system model is given in the discrete-time domain by a linear difference equation with constant parameters. The parameter estimator design is based on martingale theory and the Cramér–Rao (CR) theorem, providing a maximum likelihood (ML)-type optimal recursive parameter identification algorithm, whose minimum asymptotic estimation error covariance matrix achieves the CR bound under the worst-case pdf within a specified class; this worst-case pdf simultaneously yields the maximum asymptotic error covariance matrix within the class. However, the worst-case pdf does not generally exist, making the min–max optimal design indeterminable. Therefore, an approximate ML (AML)-type optimal on a class design, based on a suboptimal worst-case pdf, minimizing the scalar Fisher information within the specified class, has also been developed. The proposed design minimizes the conditional estimation error covariance under the specified suboptimal worst-case pdf. Such an approach results in Huber’s M-robustified version of the AML-based optimal design on the class of contaminated Gaussian pdfs. The practical performance of the proposed approach is analyzed through statistical validation, based on the relative asymptotic estimation efficiency measure and Monte Carlo simulations. Full article

This work presents an exact microcanonical combinatorial analysis of the one-dimensional antiferromagnetic Ising model. At the primary ground-state level crossing $B/J=2$, degeneracies follow the Fibonacci and Lucas sequences for open chains and periodic rings, respectively. We extend this framework to the complete excitation spectrum, demonstrating that the density of states is constructed from topological defects governed by linear Diophantine equations and p-fold Fibonacci convolutions. Open boundaries act as fractional defects, densifying the chain spectrum into energy steps of $2J$, whereas the closed ring remains quantized in units of $4J$. Notably, this exact topological counting exposes non-trivial spectral gaps near the fully polarized limit, strictly forbidding the penultimate macroscopic energy levels in both topologies. Using the transfer-matrix formalism, we derive exact closed-form expressions for the critical degeneracies at all energy levels. These results provide a rigorous analytical foundation for extracting exact residual entropies and exposing the intrinsic number-theoretic architecture of quantum critical manifolds. Full article

This study presents the analysis of global dynamics and stability (e.g., coexisting attractors, Hopf bifurcation boundary) for a nonlinear rotor system with an automatic ball balancer (ABB). The presence of nonlinearity, anisotropy and non-ideal dynamics makes this system not fully understood. The Lagrangian is written explicitly in terms of the displacement of the rotor centre and the angular positions of the balls $(x,y,\psi ,{\phi }_j)$. The kinetic energy separates into structural, unbalance coupling, and ball coupling blocks, and the Rayleigh dissipation function covers both support damping and race drag. The three families of equations of motion (translational, spin, ball) are compacted into the matrix form and solved numerically. Non-dimensionalisation introduces the seven groups $(\Omega ,{\mu }_{\mathrm{un}},{\mu }_b,\epsilon ,\widehat{\beta },\widehat{D},\Delta )$ with $\Delta$ being the anisotropy parameter. The results document bistability between the clustered and balanced ball configurations depending solely on ball initial conditions rather than rotor displacement, together with a basin of attraction analysis in which the balanced basin occupies only approximately $20\%$ of ball initial-condition space. A three-dimensional stability map reveals a previously unreported phenomenon: narrow islands of stability at very low race damping, suggesting that effective balancing may not always require dissipation, alongside a two-lobe Hopf bifurcation boundary with a disconnected instability pocket. Anisotropy study uncovers that the rotor’s response is dominated by quasi-periodic torus attractor across almost the entire ($93.5\%$) parameter space rather than the simple periodic balancing usually assumed, with a clean analytical rule identifying exactly when support asymmetry will resonantly amplify vibration. Together these findings point to design principles on ball seeding, damping selection, and permissible anisotropy. Full article