Search Results (9,746)

To investigate the underlying mechanisms of talent mobility in higher-education institutions influenced by factors such as the development environment, macroeconomic policies, and evaluation mechanisms, this paper proposes a nonlinear stochastic differential equation (SDE) dynamical model that incorporates time delays and multiplicative noise. We analyze the dynamic processes of talent mobility under varying conditions regarding the number of nodes, policy implementation cycles, and noise intensity. First, we employ central manifold theory and stochastic averaging methods to reduce the system to a one-dimensional averaged $It\widehat{o}$ equation. Subsequently, with $\tau$ as a parameter, we conduct an in-depth study of the system’s stochastic bifurcation behavior using the corresponding Fok–Planck–Kolmogorov equations. Finally, we validate the theoretical conclusions through numerical simulations. The results indicate that the number of nodes, policy delay, and noise intensity all have significant effects on system stability; an increasing delay induces random P-bifurcation in the system, and when $N\le 3$ and $N>3$, the system exhibits distinctly different steady-state behaviors. We also found that excessively high noise intensity disrupts system stability, whereas moderate noise intensity has a positive effect on stability. This study not only provides theoretical insights into the dynamic evolution mechanisms of talent mobility in regional universities but also offers valuable guidance for universities in formulating talent recruitment and evaluation policies. The methodology employed in this study opens up a promising avenue for analyzing complex dynamic problems in the field of sociology. Full article

We perform stochastic simulations of the Hodgkin–Huxley and Morris–Lecar models with different numbers of ion channels in order to describe the effects of periodic electrical driving on spike rates and the regularity of spiking in a single neuron. For stochastic modeling, we use an efficient method that reduces the piecewise-deterministic Markov process of the membrane potential evolution to an ordinary differential equation between random opening and closing events. To characterize a regular component in the resulting voltage time series, we adopt a Wiener order parameter based on the autocorrelation function. We show that the effect of ion channel stochasticity on the spike rate is stronger at lower external force frequencies. The regular component of neural activity exhibits resonant-like behavior as a function of the driving frequency, with a maximum in the beta range. Full article

This paper advances a comprehensive controllability framework for Prabhakar fractional differential systems ($\mathcal{PFDS}$s) of order $\eta \in (1,2)$ with nonlocal initial conditions, where the second-order setting requires the joint specification of both an initial state and an initial velocity. Explicit solution representations for four structurally distinct classes of second-order Prabhakar systems are derived via the Laplace transform method and Neumann series expansions, revealing that the placement of the forcing term directly in the system or under the Prabhakar fractional integral operator produces fundamentally different convolution kernels. For linear integro-differential systems, necessary and sufficient controllability conditions are established through a Gramian rank criterion with an explicit norm-bounded control law, while for nonlinear systems, sufficient conditions are obtained via the Schauder fixed-point theorem under an asymptotic growth condition. Three numerical examples validate the theory: a three-dimensional linear system and a two-dimensional nonlinear integro-differential system achieve terminal errors of order ${10}^{-12}$ and ${10}^{-7}$, respectively, and a Prabhakar fractional mass–spring–damper system with viscoelastic hereditary damping demonstrates direct physical relevance, with all theoretical conditions verified and a terminal error of $7.42\times {10}^{-5}$ confirming precise rest-position steering by the Gramian-based control law. Full article

This work studies a finite-time mean-field type control problem arising from optimal investment under uncertainty with risk management. The problem leads to a nonlinearly coupled system of parabolic equations with temporal and nonlocal interactions. An explicit characterization of the solution to the system is obtained, and a generalized finite difference method (GFDM) combined with an iterative scheme is developed to ensure global temporal consistency of the mean-field feedback during backward computation. Numerical experiments illustrate the accuracy and effectiveness of the proposed approach.In addition, sensitivity studies with respect to the volatility and risk-aversion parameters demonstrate the robustness of the proposed numerical framework under parameter perturbations. Full article

This work addresses the boundary disturbance attenuation problem for a flexible beam governed by a fourth-order partial differential equation. A boundary disturbance observer based on a radial basis function neural network is proposed to achieve high-accuracy online estimation of disturbances without prior knowledge of the disturbance dynamics. In addition, a boundary feedback controller acting only at the fixed end is designed. The control objectives are to ensure accurate tracking of the desired angular position, suppress elastic vibrations, and attenuate the influence of unknown time-varying boundary disturbances. By constructing a Lyapunov functional, the stability of the closed-loop system is established. Numerical simulations demonstrate the effectiveness of the proposed observer and control law. Full article

A comprehensive numerical method was developed to ensure energy-efficient operating modes of a linear motion module powered by an induction motor. The proposed approach is based on minimizing inertial torque, accounting for the inertial properties of the drive components and the load carriage, followed by structural-parametric optimization and dynamic modeling. For the optimization of the drive system, comprising an intermediate gear stage and a primary ball screw mechanism, a normalization-based method combined with numerical parameter sweep was employed. The optimization process yielded optimal values of the screw lead and the number of gear teeth, which were further validated in terms of Pareto optimality. The carriage design was optimized with respect to mass, strength constraints, and dynamic stiffness using the finite element method. For the developed linear motion module, dynamic behavior was simulated by means of a system of nonlinear differential equations, taking into account the electromagnetic characteristics of the induction motor and the nonlinearities of the gear mesh. As a result of the comprehensive approach, the kinematic, force, and energy characteristics of the linear motion module, which was optimized at the design stage, were determined. Full article

Eight Lie algebras of point-symmetric groups and corresponding generators are admitted by the equation of motion, which is obtained from a general time-dependent quadratic Hamiltonian. We show that invariant quantities obtained by eight algebraic generators are the Wronskian constant, three conserved quantities, which are time-dependent quadratic forms in position and momentum, and trivial, 0. All obtained invariant quantities are represented by auxiliary conditions, which are two linearly independent solutions of a homogeneous differential equation of the equations of motion. Invariant variables associated with an invariant consisting of the linearity of x and p are defined. It shows that, if the motion of the system is oscillatory, the Poisson bracket of the two invariant variables is obtained as i, and in the case of monotonic motion, it is obtained as 1. Full article

The new projective solutions methods (PSMs) for solving the Stokes, Oseen, and Brinkman flow problems are presented in this paper. They automatically satisfy the governing equations and are therefore Trefftz-type methods. Utilizing the third-order formulation and three-dimensional analytic functions, we derive a meshless Trefftz-type method to solve three-dimensional Stokes flow problems. The Oseen and Brinkman equations are transformed into four coupled third-order/first-order partial differential equations. The projective-type particular solution (PTPS) is obtained via a projective function in terms of the projective variable; the third-order ordinary differential equations (ODEs) with constant coefficients are derived to determine the projective functions. The Trefftz-type PSM is extremely accurate, because the governing equations (including the incompressibility condition) are implemented automatically. For the Brinkman equations, the general solutions of velocity and pressure are presented by using the Helmholtz function and a harmonic function, whose corresponding Trefftz-type numerical method is developed. Upon comparison with the method of fundamental solutions (MFS), the new methods exhibit some advantages, including lower condition numbers, faster convergence, and better accuracy. We also apply the Trefftz-type PSM to solve the exterior problem of the Stokes equations, where the velocity tends to zero at infinity. Full article

After more than a century of unremitting efforts by scholars, nonlinear analysis has found widespread and important applications in many fields that are at the core of many branches of pure and applied mathematics, including functional analysis, fixed point theory, nonlinear ordinary and partial differential equations, variational analysis, dynamical system theory, control theory, convex analysis, nonsmooth analysis, critical point theory, nonlinear optimization, fractional calculus and its applications, probability and statistics, mathematical economics, data mining, signal processing, biological engineering, electronic networks, electromagnetic theory, and so forth [...] Full article

In this article, we investigate the existence of solutions for a class of fractional integro-differential equations (FIDE’s) involving the $\psi$-Caputo fractional derivative ($\psi$-CFD) subject to $\psi$-Caputo boundary conditions. The analysis is carried out in an appropriate Banach space setting using the Mönch fixed-point theorem. Furthermore, sufficient conditions ensuring the existence and uniqueness of solutions are derived by employing tools from nonlinear functional analysis. In addition, the obtained results contribute to the current literature by extending existing works on fractional differential equations (FDE’s) involving generalized Caputo-type operators. The novelty of this study lies in the incorporation of $\psi$-CFD’s together with $\psi$-Caputo boundary conditions under the framework of Mönch fixed-point theory. An illustrative example is provided to verify the applicability and effectiveness of the theoretical findings. Full article

Rural e-commerce is treated as a lever for common prosperity, but its welfare effect turns non-monotonic across digital-development gradients, raising concerns about the widening urban–rural gap in sustainable regional development. We built a county-year panel of 2725 Chinese counties from 2014 to 2022, with Taobao village density as the treatment, land-based agricultural value conversion efficiency as the county-level mediator, and the Peking University digital financial inclusion digitization sub-index as the moderator. The estimations combine two-way fixed-effect regressions, continuous-interaction moderation, Hansen panel-threshold regression, Callaway–Sant’Anna difference-in-differences, Bartik shift-share instrumentation with Rotemberg-weight diagnostics, and multiple imputation by chained equations supplemented by propensity-score sensitivity checks. Taobao village density linearly depresses rural per-capita disposable income and produces a significant U-shape in the nightlight Gini with an in-sample turning point. The marginal effect on Sen welfare moves from approximately $+0.99$ log-units at low digitization to approximately $-0.95$ at high digitization, with the sign-reversal becoming statistically significant only above the 55th percentile of the moderator (Hansen threshold at the 85th percentile), so the trap is a tail regime rather than a generalized reversal; over the panel window, however, 80.5% of counties cross into the trap zone in at least one year. Approximately 28 percent of the welfare squeeze passes through the land-based ecological efficiency channel, with parallel mediators delivering 19–90 percent. The deepest squeeze appears in cash-crop counties that platform theory predicted to benefit most, where the welfare effect at high digitization is roughly $3.1$ times the staple-grain effect. We label this pattern the Digital Saturation Trap and argue that sustainable urban–rural policy should shift from uniform platform access toward differentiated platform governance in counties beyond the saturation threshold. Full article

Accurate estimation of the internal spatial-temporal temperature distribution is crucial for the safety and performance management of lithium-ion batteries. However, traditional lumped parameter models overlook spatial gradients, while numerical methods for partial differential equations (PDEs) incur high computational costs. This paper proposes a hard constraint physics-informed neural network (HCPINN) framework for the real-time reconstruction of the axial temperature field in 18,650 cylindrical batteries. By restructuring the neural network’s solution space through distance functions, the Robin boundary conditions are strictly embedded as hard constraints, ensuring exact satisfaction of the prescribed Robin boundary conditions within the mathematical model and eliminating boundary loss terms. An electro-thermal coupled model considering the Arrhenius effect and state-of-charge (SOC) dependent internal resistance is integrated into the loss function to capture the nonlinear heat generation dynamics. Experimental validation across discharge rates from 1C to 4C demonstrates that the HCPINN achieves high estimation accuracy with a mean absolute error (MAE) below 0.34 °C. Furthermore, by leveraging the continuous differentiability of the model, this study quantifies the evolution of spatial temperature gradients and reveals the ideal heat transfer coefficients required for thermal equilibrium are inverted, providing a quantitative basis for the design of advanced battery thermal management systems (BTMS). Full article

Fisheye lenses can capture surrounding spatial information at once, making them widely applied in various fields. However, the imaging principle of fisheye lenses does not satisfy the collinearity equation, so the theory of orthorectification using traditional differential orthorectification is no longer applicable for a fisheye image in practice. Therefore, this paper develops a single-spherical-geometry-transformation model for fisheye image orthorectification. This model directly establishes the relationship between spatial ground points and image plane coordinates through spherical geometry, and then combines the digital surface model (DSM) to correct points in the fisheye image to their correct positions on a pixel-by-pixel basis, thereby achieving fisheye image orthorectification. To validate the feasibility of the proposed orthorectification model, an indoor calibration field was established. Experimental validation was then conducted using two fisheye image datasets: an indoor dataset acquired in the calibration field with a digital single-lens reflex (DSLR) camera and an outdoor dataset acquired with an unmanned aerial vehicle (UAV). The results of the two groups of experiments demonstrate that the proposed model can effectively orthorectify fisheye images with ground accuracies of 0.055 m and 0.097 m in x and y direction, respectively. Full article

Given the increasing relevance of sustainability certification in food supply chains and, at the same time, rising confusion among consumers about the multitude of labels on food products, concerns about the value of sustainability certification occur frequently. This paper aims to investigate consumers’ evaluation and purchase intentions, and willingness-to-pay (WtP) for blockchain-enabled sustainability certification in coffee. Utilizing a questionnaire guided by an extended model of Ajzen’s theory of planned behavior (TPB), an online survey was conducted with n = 400 German consumers. Data were analyzed using structural equation modeling and cluster analysis. The results revealed perceived behavioral control (PBC) and subjective norms (SN) as the most influential factors on WtP, whereas intention to buy is shaped by PBC and environmental concerns. Notably, trust in blockchain technology did not emerge as a significant direct predictor, suggesting it operates as a background condition rather than a behavioral driver. Three distinct clusters were identified with concise preference, intention, and WtP profiles, highlighting heterogeneous consumer motivations. The study contributes to the literature in three ways: it provides the first consumer-behavioral evidence from the German market; it demonstrates that blockchain-specific trust constructs do not constitute independent behavioral drivers, suggesting that adoption follows generic TPB mechanisms; and it empirically differentiates intention and WtP as distinct psychological outcomes driven by different construct sets. Full article

The microstructure of semicrystalline bioresorbable polymers is central to their biomedical performance because the crystalline content influences both the mechanical stability and the degradation behaviour. Experimental studies have shown that crystallinity evolves concurrently with mass loss during enzymatic degradation. However, most existing models represent the material as a single homogeneous structure, preventing them from capturing this microstructural evolution or the state-selective mechanisms that drive it. We present a one-dimensional partial differential equation model for the enzymatic degradation of thin films, which treats the crystalline and amorphous states as distinct reactive components. Calibrated to poly($\epsilon$-caprolactone) (PCL) degraded by Candida antarctica lipase in vitro, the model accurately reproduces both the observed weight-loss profile and the concurrent decline in crystallinity. Parameter uncertainty analysis indicates that while there are varying degrees of confidence in individual parameter values, the overall model predictive uncertainty is well constrained. Parameter sensitivity analysis shows that the amorphous catalytic rate (the rate at which the enzyme degrades the amorphous region) is the dominant driver of degradation dynamics. The identified model parameters are used to explore the role of film thickness on the rates of mass and crystallinity loss. It was found that thin films remain largely reaction-limited, whereas thicker specimens become increasingly transport-influenced, with slower degradation and delayed structural evolution in the material interior. The model provides a useful tool to explore the effect of changing PCL film thickness on degradation rate and crystallinity-related properties without extensive experimentation. Full article