Search Results (1,789)

As a core load-bearing component, the aero-engine rear cooling plate requires its design to simultaneously meet strength requirements and lightweight indicators. The topology optimization method considering stress constraints is the core technical path to achieve this goal, but it suffers from insufficient control precision in key areas, easily leading to material redundancy. To address this issue, a partitioned topology optimization method based on the multi-feature K-means algorithm is proposed. First, by integrating multi-dimensional features including element stress, physical density, and spatial position, an innovative multi-feature K-means algorithm is employed to realize dynamic adaptive partitioning during the optimization process. Secondly, combined with the p-norm method for partitioned stress aggregation, a precise prediction and control method for partitioned stress is adopted to refine stress constraints. Thirdly, a topology optimization model of the rear cooling plate with multi-feature partitioned stress constraints is constructed, and the adjoint method is used to solve the stress sensitivities under centrifugal loads. Finally, the effectiveness of the proposed method is verified using the rear cooling plate model. The rear cooling plate is discretized with 0.5 mm 2D axisymmetric finite elements, the filter radius is 4 mm, and the Method of Moving Asymptotes (MMA) is employed for the solution. The mass fraction of the finally optimized rear cooling plate structure is 0.157, which is 13.7% lower than that obtained by the global stress constraint method and 11.3% lower than that obtained by the topology optimization method considering both the geometric partitioned stress constraints and global stress constraints. The proposed method provides a new approach for the lightweight design of the aero-engine rear cooling plate. Full article

This paper presents a unified analytical and computational framework for the study of typhoid fever transmission dynamics governed by a Caputo fractional-order compartmental model of order $\kappa \in (0,1]$. The population is stratified into five epidemiological classes, namely susceptible $\left(\mathcal{S}\right)$, asymptomatic $\left(\mathcal{A}\right)$, symptomatic $\left(\mathcal{I}\right)$, hospitalised $\left(\mathcal{H}\right)$, and recovered $\left(\mathcal{R}\right)$, and the governing system explicitly incorporates asymptomatic transmission, treatment dynamics, and temporary immunity with waning. The use of the Caputo fractional derivative is motivated by the well-documented existence of chronic asymptomatic Salmonella Typhi carriers, whose heavy-tailed sojourn times in the carrier state are naturally encoded by the Mittag–Leffler waiting-time distribution arising from the fractional operator. A complete qualitative analysis of the fractional system is carried out: the basic reproduction number ${\mathcal{R}}_0$ is derived via the next-generation matrix method; local and global asymptotic stability of both the disease-free equilibrium ${\mathcal{E}}_0$ (when ${\mathcal{R}}_0\le 1$) and the endemic equilibrium ${\mathcal{E}}^{*}$ (when ${\mathcal{R}}_0>1$) are established using fractional Lyapunov theory and the LaSalle invariance principle; and the normalised sensitivity indices of ${\mathcal{R}}_0$ are computed to identify transmission-amplifying and transmission-suppressing parameters. Existence, uniqueness, and Ulam–Hyers stability of solutions are established via Banach and Leray–Schauder fixed-point arguments. To complement the analytical results, a fractional physics-informed neural network ($\mathcal{PINN}$) framework is developed to simultaneously reconstruct compartmental trajectories and identify unknown biological parameters from sparse synthetic observations. $\mathcal{PINN}$ embeds the L1-Caputo discretisation directly into the training residuals and employs a four-stage Adam–L-BFGS optimisation strategy to recover five trainable parameters $\Theta$ = $\{\varphi ,\mu ,\sigma ,\psi ,\beta \}$ across three fractional orders $\kappa \in \{1.0,0.95,0.9\}$. The estimated parameters show strong agreement with the true values at the classical limit $\kappa =1.0$ ($\mathrm{MAPE}=2.27\%$), with the natural mortality rate $\mu$ recovered with $\mathrm{APE}\le 0.51\%$ and the transmission rate $\beta$ with $\mathrm{APE}\le 3.63\%$ across all fractional orders, confirming the structural identifiability of the model. Pairwise correlation analysis of the learned parameters establishes the absence of equifinality, validating that $\beta$ can be reliably included in the trainable set. Noise robustness experiments under Gaussian perturbations of $1\%$, $3\%$, and $5\%$ demonstrate graceful degradation ($\mathrm{MAPE}$: $0.82\%\to 3.10\%\to 7.31\%$), confirming the reliability of the proposed framework under realistic observational conditions. Full article

In the ElastoHydrodynamic Lubrication (EHL) meshing contact model for rough interfaces with convex–concave textured micro-asperities, the geometric morphology of the meshing interface exhibits pronounced multiscale characteristics: the macroscale manifests as the correlation between Interface-Enriched Lubrication (IEL) performance and meshing Anti-Scuffing Load-Bearing Capacity (ASLBC), while the microscale corresponds to the textured morphology of rough interfaces. In numerical simulations of EHL meshing contact, such cross-scale disparities necessitate solving large-scale systems of analytical solution equations. Assuming periodicity or quasi-periodicity at the microscale, various established methods enable decoupling the macroscopic and microscopic scales, such formalized approaches constitute homogenization theory. However, classical asymptotic assumptions may introduce considerable approximation errors. This study proposes a micro-texture-informed homogenized contact model based on multiscale characterization that incorporates the coupled effects of gear interface meshing forces and thermo-elastic deformations, effectively extending the applicability of classical asymptotic homogenization methods. Full article

Minimizing the impacts of coupling, randomness, time variation and uncertain nonlinearity to enhance real-time performance is critical for controlling complex industrial systems. This paper proposes an optimized adaptive filtering method (LAF-MTNF) for time-varying uncertain nonlinear systems with multiple-input multiple-output (MIMO) measurement noise, which integrates the multi-dimensional Taylor network (MTN) with Lyapunov stability theory (LST). Leveraging MTN’s inherent advantages—simple structure, linear parameterization, and low computational complexity—LAF-MTNF achieves efficient real-time filtering while avoiding the exponential computation burden of neural networks. The contributions of this work are threefold: (1) A novel integration of LST and MTN is proposed for MIMO filtering, in which an energy space is constructed with a unique global minimum to eliminate local optimization traps, addressing the stability deficit of traditional MTN filters using LMS/RLS algorithms. (2) Convergence performance is systematically quantified by deriving explicit expressions for the error convergence rate (regulated by a positive constant) and convergence region (a sphere centered at the origin) while modifying adaptive gain to avoid singularity, filling the gap of incomplete performance analysis in existing Lyapunov-based filters. (3) The design is disturbance-independent, relying only on input/output measurements and requiring no prior knowledge of noise statistics, thus enhancing robustness to unknown industrial disturbances. We systematically analyze the Lyapunov stability of LAF-MTNF, and simulations on a complex MIMO system verify that it outperforms existing methods in filtering precision (mean error 0.0227 vs. 0.0674 of RBFNN) and dynamic response speed, while ensuring asymptotic stability and real-time applicability. The proposed LAF-MTNF method achieves significant advantages over traditional adaptive filtering methods in filtering accuracy, convergence speed and anti-cross-coupling capability. This method has broad application prospects in high-precision industrial servo motion control, power system state monitoring and other multi-variable nonlinear industrial scenarios with complex noise environments. Full article

In this paper, we present a mathematical analysis of within-host CHIKV dynamics by developing and studying a novel delay differential equation model that incorporates persistent infected monocytes, discrete time delays, and an antibody-mediated humoral immune response. The model includes five compartments: susceptible monocytes, persistent infected monocytes, actively infected monocytes, CHIKV pathogens, and neutralizing antibodies. To reflect key biological latencies, we introduce four distinct discrete delays accounting for the periods between viral entry and the emergence of infected cell populations, intracellular virion production, and antibody activation. We analyze the model, establishing the positivity, boundedness, and invariance of solutions, and derive the basic reproduction number ${\mathcal{R}}_0$ via the next-generation matrix method. Using Lyapunov functions and LaSalle’s Invariance Principle, we prove a threshold dynamic: the infection-free equilibrium is globally asymptotically stable (GAS) when ${\mathcal{R}}_0\le 1$, while a unique endemic equilibrium is GAS when ${\mathcal{R}}_0>1$. Numerical simulations validate the analytical results and illustrate threshold behavior. A detailed local sensitivity analysis of ${\mathcal{R}}_0$ identifies the most influential parameters, offering theoretical insights into potential intervention strategies. We further investigate the effects of antiviral therapy as a theoretical intervention, deriving a treatment-dependent reproduction number and the critical drug efficacy required for eradication, and explore how the intracellular production delay can itself serve as a critical threshold for infection clearance. The study provides a rigorous theoretical framework that highlights the roles of latency, immune response, and biological delays in CHIKV pathogenesis and offers qualitative insights that may inform future experimental and treatment design studies. Full article

This paper develops a rigorous inferential framework for a class of Gaussian stochastic processes driven by white noise with constant drift, whose temporal evolution is governed by a Caputo fractional derivative of order ${\displaystyle \alpha \in (1/2,1)}$. The model belongs to the family of fractional Volterra processes, where memory is generated by the dynamics themselves rather than by correlated noise. We derive explicit analytical expressions for the mean, variance, and covariance structure of the solution, thereby characterizing in a precise manner how the fractional order ${\displaystyle \alpha }$ governs both variance growth and the strength of temporal dependence. In particular, the process exhibits correlated increments and a power-law variance scaling of order ${\displaystyle t^{2\alpha -1}}$, highlighting the dual role of ${\displaystyle \alpha }$ as a regularity and memory parameter. Building on this structural analysis, we address the statistical problem of estimating the parameter vector ${\displaystyle (\mu ,\sigma ,\alpha )}$ from discrete-time observations. Two complementary procedures are proposed for the estimation of the fractional order: a variance-growth method based on log–log regression of empirical variances, and a wavelet-based estimator exploiting multi-scale scaling properties of the process. For the drift and diffusion parameters ${\displaystyle (\mu ,\sigma )}$, we construct explicit Gaussian pseudo-maximum likelihood estimators derived from the Volterra covariance structure of the increment process. We establish unbiasedness, ${\displaystyle L^2}$-convergence, strong consistency, and asymptotic normality for all estimators. Furthermore, we derive Berry–Esseen type bounds that quantify the rate of convergence toward the Gaussian law, providing sharp distributional approximations in a genuinely fractional and non-Markovian setting. A Monte Carlo study is carried out, using high-resolution Volterra discretizations, large-scale simulation budgets, covariance-structured linear algebra, and multi-scale diagnostic tools. The numerical experiments confirm the theoretical convergence rates, demonstrate the finite-sample reliability of the estimators, and illustrate the sensitivity of the process dynamics to the fractional order ${\displaystyle \alpha }$: smaller values of ${\displaystyle \alpha }$ produce stronger memory effects and higher variability, while values closer to one lead to smoother and more stable trajectories. The proposed methodology unifies statistical inference for long-memory Gaussian processes with fractional differential stochastic dynamics, offering a coherent analytical and computational framework applicable in areas such as quantitative finance, anomalous diffusion in physics, hydrology, and engineering systems with hereditary effects. Full article

This paper is concerned with a chemotaxis-competition system modeling the spatiotemporal evolution of two species that proliferate and compete according to Lotka–Volterra-type kinetics. We study the asymptotic behavior of solutions in the case of strong competition and show that they spatially segregate as the competition rate tends to infinity. Moreover, using a blow-up method, we obtain the uniform Hölder continuity of the solutions. Full article

We investigate whether the geometric parameters of a three-dimensional domain can be recovered from the Dirichlet spectrum of the Laplacian. As a controlled benchmark, we consider rectangular boxes, about which the eigenvalues are explicitly known and the Weyl coefficients can be computed in closed form. Exploiting the short-time asymptotics of the heat trace, we extract the leading Weyl coefficients from finite spectral data and show how they encode volume, surface area, and the third spectral Weyl term. These coefficients uniquely determine the side lengths of the box via an explicit cubic reconstruction formula. Numerical experiments based on several thousand eigenvalues demonstrate that the method is stable, accurate, and robust with respect to spectral truncation. The box setting thus provides a stringent validation of the proposed inverse spectral methodology and serves as a foundation for its extension to smooth curved domains, such as triaxial ellipsoids, where explicit spectral formulas are no longer available. Full article

This article provides a selective review of offline change-point detection methods, with a particular emphasis on weak change-points. The study of such weak changes plays a central role in establishing the asymptotic properties of test statistics designed for detecting fixed (non-vanishing) changes. In addition, it is crucial for analyzing the asymptotic behavior of change-point location estimators. We review the current state of the literature, identify key limitations, and outline promising directions for future research in this challenging setting. Full article

In recent years, fractional HIV models have received increasing attention. This study derives a fractional HIV model using the continuous-time random walk (CTRW) method, endowing the mathematical model with physical significance. Based on the transmission characteristics of HIV, the proposed model considers extrinsic infectivity, intrinsic infectivity, and drug control, specifically as follows: the extrinsic infectivity is a constant independent of the infection time; the intrinsic infectivity is a power-law function that depends on drug efficacy and infection time; the drug efficacy rate follows a Mittag–Leffler distribution with a long-term effect. Based on these considerations, a fractional HIV model with drug control is established in this paper. In addition, the global asymptotic stability of the equilibrium and the sensitivity analysis of the basic reproduction number $R_0$ are studied, and the theoretical results are verified by numerical simulations. The results show that reducing extrinsic infectivity, controlling intrinsic infectivity, and the drug efficacy rate are crucial in controlling the spread of HIV. Full article

This article develops a boundary-adaptive nonparametric methodology for estimating the geometric conditional quantiles of a multivariate response when the conditioning covariate is supported on the simplex—an important case, as it is the natural domain of compositional data. The statistical difficulty addressed here is twofold. First, geometric conditional quantiles for multivariate responses must be defined and estimated through a genuinely directional and convex framework rather than through any scalar ordering. Second, when the covariate is compositional or otherwise simplex-constrained, conventional symmetric kernel procedures suffer from intrinsic support mismatch and severe boundary distortion, thereby compromising both estimation accuracy and inferential validity near faces and edges of the simplex. The method proposed in this paper is designed precisely to overcome this combined obstacle. Our main innovation consists in embedding the spatial quantile formalism of Chaudhuri within a Dirichlet–Kernel smoothing scheme whose shape parameters depend deterministically on the evaluation point. This produces a convex M-estimator that respects the simplex geometry exactly, automatically adapts its local shape to the position of the target point, and removes the need for artificial boundary corrections. To the best of our knowledge, this is the first contribution to provide a complete asymptotic treatment of geometric conditional quantile estimation under simplex-supported covariates with location-adaptive asymmetric kernels. We establish a Bahadur-type linear representation with an explicit negligible remainder, from which we derive refined asymptotic bias and variance expansions. The variance analysis reveals a distinctive geometric phenomenon: each coordinate direction approaching the simplex boundary induces an additional $b^{-1/2}$ inflation factor, so that the variance at a face of codimension $\left|\mathcal{J}\right|$ scales as $n^{-1}{b}^{-(s+|\mathcal{J}\left|\right)/2}$. We further obtain the asymptotic mean squared error, an explicit optimal bandwidth rate, asymptotic normality under the nonstandard normalization $n^{1/2}{b}^{-s/4}$, and consistent plug-in covariance estimators yielding valid confidence ellipsoids. Numerical experiments and a real-data illustration based on the GEMAS data confirm the practical merit of the approach, especially in boundary regions where classical methods are known to deteriorate. Full article

Measles remains a significant public health threat despite widespread vaccination, with recent resurgences driven by vaccine hesitancy and coverage gaps. Existing mathematical models often fail to capture the substantial temporal heterogeneity in incubation periods, vaccine-induced protection, and recovery processes that characterize measles transmission. We develop and analyze an SVEIR epidemic model incorporating four independent distributed time delays with exponential survival factors, capturing the realistic variability in these epidemiological processes. The model features compartment-specific mortality rates, disease-induced mortality, and imperfect vaccination with failure probability $\theta$. Using next-generation matrix methods adapted for delay kernels, we derive the delay-dependent reproduction number ${\mathcal{R}}_0^d$ and prove, via systematic construction of Volterra-type Lyapunov functionals, that it constitutes a sharp threshold: the disease-free equilibrium is globally asymptotically stable when ${\mathcal{R}}_0^d\le 1$, while a unique endemic equilibrium emerges and is globally stable when ${\mathcal{R}}_0^d>1$. Normalized forward sensitivity analysis reveals that the transmission rate $\beta$ and recruitment rate $\Lambda$ exhibit maximal positive elasticity, while the vaccination rate p, vaccine failure probability $\theta$, and incubation delay ${\tau }_3$ possess the largest negative elasticities. Critically, ${\tau }_3$ exerts exponential influence via $e^{-n_3{\tau }_3}$, making interventions that delay infectiousness—such as post-exposure prophylaxis—unusually potent. We derive an explicit expression for the critical delay ${\tau }_3^{\mathrm{cr}}$ at which ${\mathcal{R}}_0^d=1$, demonstrating that prolonging the effective incubation period sufficiently can shift the system from endemic persistence to extinction. Numerical simulations using Dirac delta kernels confirm all theoretical predictions. These findings provide three actionable insights for public health: (1) maintaining high vaccination coverage among new birth cohorts remains paramount; (2) improving vaccine quality (reducing $\theta$) yields substantial returns; and (3) the incubation delay represents a quantifiable, measurable target for evaluating the population-level impact of time-sensitive interventions. The framework is broadly applicable to infectious diseases characterized by significant temporal heterogeneity. Full article

Asymptotic solutions that can describe the incidence and reflection of waves have been used in various situations. They can also be applied to inverse problems and provide useful information in situations where a precise evaluation is required. However, the construction of standard asymptotic solutions requires higher regularity with respect to the boundaries of the observation target. This article proposes a “modified asymptotic solution” to overcome this weakness. To demonstrate its usefulness, it is applied to the analysis of the indicator function in the enclosure method for the inverse problem of the wave equation in a mixed-type medium. Full article

Structural Equation Modeling (SEM) is a key framework for analyzing complex economic relationships involving latent variables, mediation effects, and endogeneity, yet the choice between frequentist and Bayesian estimation remains theoretically and practically contested, especially in settings with non-stationary data and small samples. This study provides a formal comparison of the two approaches by formulating SEM as a probabilistic graphical model and deriving the corresponding estimation procedures, identifiability conditions, and uncertainty measures. We examine asymptotic properties of frequentist estimators and posterior consistency in Bayesian SEM, with particular attention to integrated time-series SEM applications such as shadow economy estimation. The analysis shows that while both approaches converge under large-sample conditions, important differences arise in finite samples. Bayesian methods exhibit more stable point estimates through coherent uncertainty quantification, particularly when prior information regularizes an otherwise ill-conditioned likelihood. Under model misspecification, Bayesian posteriors concentrate around the pseudo-true parameter defined by the Kullback-Leibler projection, providing a probabilistic representation of misspecification uncertainty through posterior spread—an advantage over frequentist inference, which typically conditions on the maintained model as exact. These findings carry direct implications for empirical economic modeling under realistic data constraints. In settings where sample sizes are small, identification is weak, and model uncertainty is substantial, conditions that routinely characterize macroeconomic research, the choice of inferential framework is not a matter of philosophical preference but a determinant of whether policy-relevant conclusions can be credibly defended. Bayesian SEM offers a principled and transparent path forward in precisely these conditions. Full article

This paper proposes an adaptive wavelet neural network nonsingular fast terminal sliding mode control strategy based on a finite-time framework for a space robot system under external disturbances and model uncertainties. Firstly, the dynamic model of space robot is established based on the second Lagrange equation. Unlike sliding mode control, which converges asymptotically, terminal sliding mode control (TSMC) has been proposed to ensure finite-time convergence for a space robot system. Based on the aforementioned TSMC framework, the fast terminal sliding mode control (FTSMC) is proposed to enhance system convergence rate. However, TSMC exhibits a singularity issue attributed to the presence of negative fractional order. To avoid this issue, a nonsingular fast terminal sliding mode controller (NFTSMC) has been proposed. The controller is designed to integrate linear and nonlinear terms into a novel nonsingular fast terminal sliding mode surface. The method achieves fast finite-time convergence concurrently with improved robustness, while effectively avoiding singularities. To compensate for external disturbances and model uncertainties in the space robot system, this paper proposes the combination of wavelet neural network (WNN) for the real-time estimation of lumped uncertainties. Network parameters are dynamically adjusted via an adaptive law to mitigate chattering effectively and enhance trajectory tracking precision. Utilizing Lyapunov stability theory and numerical simulations, the space robot system’s stability is rigorously proven and the controller effectiveness is validated. Compared with the traditional NFTSMC, the proposed control strategy reduces the convergence time by 20.74%. In the case of trajectory tracking comparison, the root mean square error (RMSE) improves by 35.85%, the mean tracking error improves by 63.29%, the integral of absolute error (IAE) improves by 29.37%, and the integral of time-weighted absolute error (ITAE) improves by 93.06%. Additionally, a comparative simulation with RBFNN is included in this paper. Compared with RBFNN, the proposed control strategy reduces input torque energy consumption by 77.36% and improves control smoothness by 87.03%, quantitatively demonstrating the effectiveness of the proposed control strategy. Full article