In this paper a bilateral boundary control strategy is developed based on the infinite-dimensional backstepping method for a linear $(1+1+1)\times(1+1+1)$ one-dimensional hyperbolic partial differential equation system in which one state exhibits zero transport speed. The proposed approach ensures the global exponential stability of the closed-loop system in the $L^2$ norm. Addressing the limitation that traditional backstepping fails in the presence of zero transport speed (potentially leading to unbounded controller gains), the Volterra transformation is introduced only in the subsystem with nonzero transport speed, while the zero transport speed state remains unchanged. The state with nonzero transport speed is treated as an external input to the subsystem with zero transport speed, thereby guaranteeing its input-to-state stability. Bilateral boundary control implies that actuators are installed at both ends of the spatial domain. Since the actuators act on both boundaries, the existing Lyapunov functionals are not directly applicable. To overcome this, a modified quadratic Lyapunov functional is constructed to rigorously prove the exponential stability of the target system. Numerical simulation results further verify the effectiveness of the proposed control strategy.

This study proposes a solution based on the newsboy model for the fruit supply chain problem in Xinjiang and other places far from the consumer market. The study finds that the choice of dealers to sell fresh fruit or processed products has a significant impact on the supply chain, and their decision depends on a key threshold: When the ratio of the value of processed products to the value of fresh fruit itself is lower than a certain threshold, processing is not recommended; Otherwise, processing is recommended to save transportation costs. Land transfer has transformed the original three-level supply chain into a two-level supply chain, improving operational efficiency. Further analysis of the study found that whether a repurchase contract or a revenue sharing contract is used for supply chain coordination, the threshold for the proportion of fresh fruit sales will be reduced, thereby expanding the feasible range of fresh fruit sales options.

This paper introduces a panel data structure containing firm-specific micro characteristics into the vector autoregressive model with exogenous variables (VARX) and thereby constructs a high-dimensional panel vector autoregressive (HPVAR) volatility forecasting model to characterize the dynamic features of realized volatility. First, to address the difficulty of lag-order selection in high-dimensional volatility series, an improved hierarchical own-other (IHOO) regularization method is proposed to achieve structured regularization and lag-order selection simultaneously in a high-dimensional setting. Next, a proximal gradient descent (PGD) algorithm with adaptive step sizes, together with Bayesian optimization, is employed for parameter estimation and hyperparameter selection. An upper bound for the in-sample mean squared forecasting error (MSFE) is further derived under regularity conditions. Finally, empirical analysis is conducted using high-frequency volatility data from the U.S. and Hong Kong stock markets. The results show that: 1) After firm-specific characteristics and external shocks are incorporated, HPVAR achieves higher forecasting accuracy than VAR and VARX; 2) IHOO produces better forecasting performance than hierarchical lag own-other (HLagO) and Lasso; and 3) Heatmaps of autoregressive lag coefficient matrices and estimated maximum-lag matrices indicate that the proposed model maintains both high forecasting performance and good interpretability under high dimensionality.

In this paper, we review the time-harmonic wave modes of the Helmholtz equation subject to quasi-periodic boundary conditions in two-dimensional layered periodic structures. Using the spectral theory of periodic ordinary differential operators and the Bloch theory for elliptic partial differential equations, we present the wave modes for electromagnetic wave propagation under TE polarization in three different types of inhomogeneous periodic layered materials: periodic media depending only on the horizontal coordinate, periodic media depending only on the vertical coordinate, and general biperiodic media. By employing the finite energy property of wave propagation, we characterize the radiating modes of the periodic Helmholtz equation in infinite inhomogeneous media, thereby laying a mathematical foundation for model analysis and numerical computations.

Zero-one biochemical reaction networks are widely recognized for their importance in analyzing signal transduction and cellular decision-making processes. Degenerate networks reveal non-standard behaviors and mark the boundary where classical methods fail. Their analysis is key to understanding exceptional dynamical phenomena in biochemical systems. Therefore, the authors focus on investigating the degeneracy of zero-one reaction networks. It is known that one-dimensional zero-one networks cannot degenerate. In this work, the authors identify all degenerate two-dimensional zero-one reaction networks with up to three species by an efficient algorithm. By analyzing the structure of these networks, the authors arrive at the following conclusion: If a two-dimensional zero-one reaction network with three species is degenerate, then its steady-state system is equivalent to a binomial system.

In Isogeometric Analysis (IGA), constructing high-quality analysis-suitable computational domain parameterizations is a crucial issue. In recent years, learning-based parameterization methods have attracted attention with the development of machine learning and deep learning. This paper proposes a novel learning-based domain parameterization method for IGA. The proposed method employs Physics-Informed Neural Networks (PINNs) to solve Partial Differential Equations (PDEs) associated with parameterizations. To achieve high-quality parameterizations, the loss function incorporates both angular distortion and area distortion during the construction process. Furthermore, the authors introduce a penalty function-based Jacobian regularization strategy that enhances network training stability and ensures the generation of analysis-suitable parameterizations. After training the network, the authors use tensor-product B-splines to fit the results and construct the parameterizations. Numerical examples demonstrate that the proposed method achieves superior orthogonality and uniformity compared to existing deep learning-based parameterization approaches for complex planar computational domains. Additionally, the proposed method can be extended to volume parameterizations for 3D computational domains.

Floater-Hormann barycentric rational interpolation is a family of interpolation methods with high approximation precision. Based on Floater-Hormann barycentric rational interpolation, researches have provided algorithms for solving ODEs. Since barycentric rational interpolation function has one uniform expression $r(x)$ on the entire interval, when there are local changes in interpolation data, $r(x)$ changes globally. When solving ODEs, the coefficient matrix of linear equations obtained based on $r(x)$ is dense, which brings complexities for solving equations. To overcome these problems, a weighted piecewise barycentric rational interpolation method is established in this work. Regarding the interpolation case, when there are local changes in data, the interpolation function obtained by the proposed method only changes locally. When solving two-point boundary value problems based on weighted piecewise barycentric rational interpolation method, number of non-zero elements in the obtained coefficient matrix reduces with the increase of ``pieces''. Especially, under specific conditions for dividing pieces, the coefficient matrix reduces to a 3-diagonal matrix. Experiments show that, this kind of weighted piecewise barycentric rational interpolation method has some advantages for both interpolation and solving two-point boundary value problems.

Faced with supplier adulteration, downstream enterprises need to find a balance between incentives and supervision to ensure the reliability and consistency of product quality. This paper constructs an innovative supply chain incentive model that integrates incentive mechanisms and supervision measures, aiming to more accurately characterize the comprehensive management efforts of managers under a specific incentive intensity. The model introduces two key variables: Variance (uncertainty in supplier performance) and distortion (deviation between supplier behavior and enterprise expectations), and analyzes how they affect incentive intensity. Unlike traditional research, this paper finds that incentive intensity does not depend directly on the level of uncertainty, but on the management cost required to reduce uncertainty. The study shows that enterprises can significantly improve the integration effect of incentives and supervision by reducing total costs or reducing the ratio of variance to distortion. The research in this paper provides a new theoretical basis and practical guidance for enterprises to optimize management strategies in complex supply chain environments.

In actuarial science and financial risk management, accurately characterizing the quantile function in the tail of a risk distribution is of critical importance for the measurement and control of extreme risks. Traditional risk measures often exhibit large estimation biases and insufficient robustness under small-sample conditions or unknown distributions. To enhance the stability and consistency of risk estimation, this paper proposes a credibility-based estimation method for the quantile function, grounded in a Bayesian framework and the linear minimum mean squared error principle. The proposed method constructs an analytical credibility estimation model, effectively avoiding the computational complexity associated with high-dimensional posterior quantiles, and establishes a unified estimation framework applicable to multiple types of risk measures. Theoretical analysis demonstrates that the proposed estimator possesses desirable statistical properties, including conditional consistency, mean squared error convergence, and asymptotic normality. Numerical simulations further indicate that the method exhibits superior stability and accuracy compared to conventional empirical estimators in small-sample scenarios. Finally, the author conducted an empirical analysis using daily data from six representative stocks in the Chinese stock market to evaluate the proposed estimation method. The results show that the method remains robust under conditions of high volatility and noise, adapts well to different market environments, and provides a reliable and practical approach for tail risk measurement.

In this paper, we propose a geometric primitives detection and fitting method for 3D point clouds based on genetic algorithm. This method uses genetic algorithm to achieve geometric element detection and fitting by optimizing the fitness function including approximation error, number of patches, and patch size. The main process of genetic algorithm is initialization, mutation, crossover, and selection, and the entire process is designed to minimize the fitness function. Obtaining a good result of primitive detection and fitting is very time-consuming. The main challenge of this method is to design a fitness function that balances the number of surface patches and the fitting effect, as well as the specific operation of genetic algorithm that accelerates the algorithm speed, and visualize the segmentation results. The feasibility and effectiveness of this method have been verified in many complex examples. Compared with existing methods, the results of this paper have smaller approximation errors and fewer patches.

Multidimensional system reduction is often converted to the equivalence between multivariate polynomial matrices and their Smith forms. This paper focuses on the unimodular equivalence of a class of multivariate polynomial matrices to their Smith forms. A criterion for the unimodular equivalence of such matrices and their Smith forms is proposed, with the result extended to non-square and rank-deficient cases. Finally, a general algorithm for reducing such matrices to their Smith forms is presented and an example is provided to illustrate the algorithm.

This paper investigates the output regulation problem for uncertain variable-coefficient heat equations with matched boundary disturbances. The thermal system is governed by an uncertain parabolic partial differential equation (PDE) with mixed boundary conditions, characterized by unknown spatially varying diffusion coefficients and subject to smooth uncertain boundary disturbances that may potentially be unbounded in magnitude. We propose a robust control strategy that synergistically combines linear feedback design with the Twisting second-order sliding mode control algorithm, properly reformulated and integrated within an infinite-dimensional framework. The well-posedness of the closed-loop system, formulated as a differential inclusion, is established through maximal monotone operator theory. Furthermore, by employing a nonstandard Lyapunov functional and under the condition that the controller tuning parameters satisfy certain fundamental inequalities, we prove the global asymptotic stability of the closed-loop system in an appropriate Sobolev space. Numerical simulations in the experimental section validate the effectiveness of the proposed controller design.

The rational allocation of basic education resources is essential to achieving educational equity and improving educational quality, while the enhancement of human capital is a core driving force for building a strong education system. Based on annual provincial panel data from 2000 to 2022, this paper employs fixed-effects models and difference-in-differences (DID) models to examine the effects of the accessibility, quality, and balanced allocation of basic education resources on human capital accumulation. The results show that the accessibility of basic education resources has a long-term positive effect on the stock of human capital, with the most significant effect observed at the junior high school stage. The effects of the quality of basic education resources on human capital quality vary across educational stages. The mechanism analysis indicates that high-quality education resources further enhance regional human capital quality by attracting inflows of highly educated individuals. The balanced allocation of basic education resources also plays a positive role in improving the structure of human capital, especially at the junior high school stage. In addition, the DID analysis further confirms the positive effect of policies promoting the balanced development of education on human capital accumulation.

The gradient method is one of the simplest and most fundamental computational methods for solving optimization problems. Since all gradient methods find the next iterate along the steepest descent direction, the difference among various gradient methods lies in the choice of step size. The BB step size is one of the most renowned choices for step size in gradient methods. In this paper, by interpreting the BB step as a step size based on onedimensional subspace approximation, we construct new step sizes based on two-dimensional and three-dimensional subspace approximations. These new step sizes possess favorable theoretical properties and are expected to be developed into effective numerical methods.

This paper mainly discusses the long-time behavior of solutions to a class of degenerate heat-beam coupled partial differential dynamical systems. The model consists of two parts: One part is described by a degenerate heat equation, and the other part is described by the Timoshenko beam equation. These two parts are coupled together at a common boundary through certain transmission conditions. Based on the frequency domain analysis method, this paper provides a refined estimate of the polynomial stability of solutions to this type of coupled system under smooth initial conditions and determines an explicit relationship between the decay rate of the system and the degree of heat degeneracy.

This study explores in depth the impact mechanism of state-owned institutional investors' shareholding on corporate investment efficiency, especially in the context of mixed ownership reform. Combining theoretical analysis and empirical testing, it reveals the key role of state-owned institutional investors in improving corporate investment efficiency. Research has shown that an increase in the shareholding ratio of state-owned institutional investors has a significant promoting effect on improving the investment efficiency of enterprises. In addition, factors such as corporate governance level, enterprise size, industry competition level, and cash flow volatility also have a direct impact on the investment efficiency of enterprises. Further research has found that digital transformation and green innovation of enterprises play an important intermediary role between the shareholding of state-owned institutional investors and the efficiency of enterprise investment. State owned institutional investors accelerate the process of digital transformation and green innovation by providing financial support, strategic guidance, and resource allocation. Digital transformation can improve information processing capabilities and optimize resource allocation efficiency, while green innovation can indirectly enhance the investment efficiency of enterprises by improving resource utilization efficiency and enhancing market competitiveness, enabling state-owned institutional investors to hold shares can indirectly improve the investment efficiency of enterprises. This article not only enriches the relevant research on the economic consequences of state-owned institutional investors, but also provides a new theoretical perspective for understanding the mechanism of improving investment efficiency of enterprises. At the same time, it provides important theoretical basis and policy inspiration for deepening the reform of state-owned enterprises, optimizing the layout of state-owned capital, and enhancing the overall competitiveness of enterprises in the new era.

The rapid expansion of shared mobility services has introduced innovative solutions for urban transportation. Ride-hailing platforms, facilitated through user-friendly smartphone applications, seamlessly connect individual preferences with immediate vehicle availability. In carpooling services, passengers can share a ride in the same vehicle, setting their respective destinations as waypoints to increase vehicle utilization. This study proposes a carpooling and dispatching model for ride-hailing services based on a self-attention reinforcement learning network. Initially, a carpooling travel topology network is constructed, considering factors like passenger pick-up and drop-off times and locations. An on-demand algorithm is designed to identify ride-hailing orders suitable for carpooling. Subsequently, a self-attention reinforcement learning network is employed for order dispatching optimization. Through the implementation of policy gradient techniques for learning and training, the integration of masking methods ensures the efficacy of order dispatching. Leveraging the strengths of “offline training & online decision-making”, the proposed strategy tackles the challenges of enhancing the real-time responsiveness of large-scale ride-hailing dispatching services. Finally, the real-world case study is conducted based on ride-hailing orders in Beijing, China. Results underscore the efficiency of the order dispatching algorithm in achieving near-optimal route selections while reaching a real-time demand response. Although carpooling slightly increases passenger waiting times, it significantly boosts ride-hailing operational efficiency, alleviates traffic congestion, and mitigates environmental pollutants.

This paper investigates the adaptive tracking control problem for Auto-Regressive Moving Average (ARMA) systems with quantized observations, explicitly focusing on reference signals composed of non-periodic sequences. The authors propose an adaptive tracking control scheme integrating an adaptive controller with a stochastic approximation-type estimation algorithm. Different from the control scheme for Finite Impulse Response (FIR) systems, the estimation part not only estimates the unknown system parameters but also the unknown system outputs. Next, based on the certainty equivalent principle, the adaptive controller is designed using the above two estimates instead of the actual parameters and system outputs. To tackle the inherent coupling between the two estimates, the authors introduce a novel approach that combines the Lyapunov function method with a backward-shifted polynomial method featuring time-varying coefficients. This approach assists in establishing the mean square convergence of the estimates with a convergence rate of $O\left(\frac{1}{k}\right)$ under suitable conditions of the step size coefficient. Additionally, this paper shows that the designed adaptive control law can achieve asymptotically optimal tracking of non-periodic reference signals in the mean square sense. Finally, a numerical simulation is presented to validate the theoretical results obtained in this paper.

In this paper, the authors address the problem of almost sure polynomial stabilization for a class of highly nonlinear stochastic systems via sampled-data feedback. The considered systems fall within a general framework that includes two key features: (a) Continuous-time irreducible Markov chain- the authors introduce a continuous-time irreducible Markov chain to describe systems that can undergo sudden alterations in their parameters and structures. This flexibility allows us to model real-world scenarios more accurately; (b) Diffusion and drift coefficients with polynomial growth - unlike existing literature that primarily focuses on systems with bounded delays, the authors investigate the stabilization conditions for highly nonlinear stochastic systems with pantograph delay, an unbounded delay. Specifically, the authors analyze systems where the diffusion and drift coefficients satisfy a polynomial growth condition. To achieve the proposed goal, the authors employ $M$-matrix theory and Lyapunov functions as basic tools. The main results establish that the system can attain almost sure polynomial stabilization through a subtly and innovatively designed sampled-data feedback. The authors validate the theoretical findings with numerical simulations, demonstrating the effectiveness of the proposed approach. This work contributes to the understanding of stabilization in highly nonlinear stochastic systems, particularly those with unbounded delays, and broadens the practical applicability of stochastic modeling.

To explore the impact of various groups and methods on rumor propagation, the authors propose a 'Double-Refutation $(DR)$ and Double-Blocking $(DB)$' rumor control strategy. This strategy combines external refutation via media reports, internal refutation by counteracting individuals, and both continuous and impulse blocking methods. By leveraging multi-synergy and aiming to minimize control costs, the authors propose stochastic optimal hybrid control strategies for rumor containment. Additionally, to enhance the response speed of the control strategy, the authors introduce an ensemble learning algorithm as a substitute for theoretical solutions. Numerical simulations demonstrate that the trained ensemble learning control algorithm can quickly identify sub-optimal control strategies for rumor spreading, with costs only 4.1% higher than those of the optimal control theory.

In this paper, the controllability of signed multi-agent networks based on the consensus protocol is studied from the perspective of topological structure. Firstly, based on the eigenvectors of Laplacian matrix and the leader-follower structure, the necessary and sufficient algebraic condition for the controllability of undirected signed topologies is obtained. According to the condition, for the composite topologies obtained by connecting two sub-topologies, two methods are proposed to construct controllable composite topologies by connecting the controllable sub-topologies. In addition, based on uncontrollable undirected signed topologies, the same sign double controllability destructive nodes (SSDCDN) and inverse sign double controllability destructive nodes (ISDCDN) are defined for the first time. By analyzing the characteristics of these nodes, the necessary and sufficient condition for the controllability on multi-leader undirected signed topological graphs is obtained. Finally, on the basis of the existing results, the design methods of two special types of uncontrollable signed sub-topologies connected with controllable signed sub-topologies to form controllable composite signed topologies are proposed.

China's policy implementation and technological evolution of the energy industry exert a substantial global influence in confronting climate challenges. Given the notable regional differences in China's economic development and resource endowments, there are significant distinctions in the distribution structures and evolutionary trajectories of energy industry technologies among various regions. This study constructs the global-China multi-region integrated assessment model, namely WITCH-China, aiming to explore the optimal evolutionary paths of energy industry technology development and carbon emissions for the selected 30 regions in China under the global temperature control scenarios. And the technological optimization evolution of energy industry is comprehensively evaluated. The findings reveal that: 1) Under policy scenarios, the consumption of coal and oil show a significant downward trend, wind and solar energy experiences a sharp increase, and the proportion of non-fossil energy consumption will exceed fossil energy for the first time in 2050. 2) Carbon emissions gradually decline with the decrease in fossil energy consumption, but due to the improvement of energy efficiency and the popularization of clean energy technology, the decline of carbon emissions gradually slows down. 3) There are obvious differences in the trend of energy consumption structure in different regions, and clean resource-rich areas, such as Qinghai, Xinjiang, Inner Mongolia, Gansu, etc., have greater development potential in clean energy, and the clean substitution potential of wind power and solar energy is the most significant. Finally, the study puts forward relevant policy suggestions for the development of China's energy industry.

This paper proposes a class of spatial varying-coefficient autoregressive models with autocorrelated errors. The proposed framework simultaneously incorporates spatial correlation in the response variable and spatial autocorrelation in the error term within the spatial varying-coefficient setting, thereby jointly capturing both heterogeneity and dependency structures in spatial data to better reflect their complex characteristics. To overcome the endogeneity issue of the model, an effective three-stage estimation method is proposed that integrates local linear estimation, generalized method of moments (GMM), and profile least squares estimation methods, and the asymptotic properties of the estimators are derived. The Monte Carlo simulation results indicate that the estimation method for the studied model demonstrates good efficacy under finite samples. Empirical analysis based on the Boston housing price data further shows that this model significantly enhances the explanatory power of spatial economic phenomena.

This paper applies the Cheng projection to the support vector machine (SVM) in handling missing data. In the process of handling missing data, each sample with missing values is replaced by its Cheng projection in the original space. Additionally, two classification algorithms for handling linearly separable and nonlinearly separable datasets with missing data are presented. For linearly separable datasets with missing data, Cheng kernel function is introduced, and an SVM classification algorithm that improves the linear kernel function to the Cheng kernel function is proposed. For nonlinearly separable datasets, a generalized Gaussian Radial Basis Function kernel is introduced and an SVM classification algorithm for handling missing data is given. For both algorithms, two comparative experiments are conducted to demonstrate their effectiveness.

Both actuator faults and time delays degrade the performance of control systems. Although fault-tolerant mechanisms are commonly used in advanced control systems, no results are available in investigating the adaptive tracking problem of stochastic nonlinear time-delay systems in the presence of Markovian jump actuator faults. After establishing some mathematical fundamentals for stochastic differential delayed equations with multi-Markovian switching, this issue is tackled in this article, by proposing a novel adaptive backstepping fault-tolerant controller. Uncertainties caused by random actuator faults, unknown time-varying delays, the Wiener noise of unknown covariance as well as the unknown plant parameters are handled skillfully in a unified stochastic framework. By constructing a suitable Lyapunov-Krasovskii functional, it is proved that all closed-loop signals are bounded in probability, and the tracking error can converge into an arbitrarily small residual set in the sense of mean quartic value. In addition, the range of reference signals is greatly enlarged by comparison with the conventional backstepping controller. Two simulation examples are presented to illustrate the proposed theoretical findings.

In recent years, artificial cilia have attracted widespread research interest due to their enormous application prospects in the fields of medicine and environmental therapy. Deformation is a key issue to consider in the design and preparation of artificial cilia, however the corresponding mathematical analysis is still lacking. This paper introduces a multi-agent model for the magnetic artificial cilium, where each agent denoting a bead is influenced by the external magnetic field and neighboring agents. Then, the authors provide the existence and uniqueness of the solution to the proposed model, and give a stability condition for avoiding magnetic chain breakage and collisions between adjacent magnetic beads. To our best knowledge, it is the first mathematical result on the stability of magnetic bead chain. Finally, simulations are conducted to verify the proposed theoretical result.

In this paper, we develop an approach to the problem of closing lemma based on KAM normal form. The new approach differs from existing $C^1$ perturbation approach and spectral approach, and can handle the high regularity, high dimensional cases and even Riemannian metric perturbations. Moreover, the proof is constructive and effective. We apply the method to the original nearly integrable setting of Poincaré and confirm several old and new conjectures with weak formulations. First, for Poincaré's original setting of nearly integrable systems, we prove that for typical perturbations, periodic orbits are asymptotically dense as the size of perturbation tends to zero. Second, we prove that typical smooth perturbation of the geodesic flow on the flat torus has asymptotically dense periodic orbits, which partially solves an open problem since Pugh-Robinson's $C^1$-closing lemma. Third, we prove that for typical Hamiltonian or contact perturbation of the geodesic flows of the ellipsoid has asymptotically dense orbit on the energy level, which enhances the recent researches on strong closing lemma, and also confirms partially a conjecture of Fish-Hofer in this setting and a problem of Arnold. We also discuss the relation of our models to the recent researches on many-body localization in physics.

It is well-known that there are global small data smooth solutions for the 3-D semilinear Klein-Gordon equations $\square u+u=F(u, \partial u)$ with cubic nonlinearities. However, for the short pulse initial data $\left(u, \partial_t u\right)(0, x)=\left(\delta^{\nu+1} u_0\left(\frac{x}{\delta}\right), \delta^\nu u_1\left(\frac{x}{\delta}\right)\right)$ with $\nu \in \mathbb{R}$ and $\left(u_0, u_1\right) \in C_0^{\infty}(\mathbb{R})$, which are a class of large initial data, we establish that when $\nu \leq-\frac{1}{2}$, the solution $u$ can blow up in finite time for some suitable choices of ($u_0, u_1$) and cubic nonlinearity $F(u, \partial u)$; when $\nu>-\frac{1}{2}$, the smooth solution $u$ exists globally. Therefore, $\nu=-\frac{1}{2}$ is just the critical power corresponding to the global existence or blowup of smooth short pulse solutions for the cubic semilinear Klein-Gordon equations.

This paper is a review of $K$-theory methods in solid state physics. Our goal is to demonstrate that $K$-theory is a natural language for the mathematical description of solid bodies. Our main tool is the $K$-theory of $C^*$-algebras. We follow Kitaev's idea that the symmetry algebras of solid bodies belong to the class of Clifford algebras which reduces the quantization problem for solid states to the representation theory of Clifford algebras.

This paper presents a primal-dual prediction-correction (PD-PC) method for solving linearly constrained time-varying convex optimization problems, which frequently arise in control, signal processing, and online learning applications. The proposed method establishes a novel integration of primal-dual gradient dynamics with a discrete-time prediction-correction structure, specifically designed for problems with time-dependent linear constraints. A tunable memory parameter is introduced in the prediction phase to perform linear extrapolation using past iterates, enabling a flexible trade-off between the amount of historical information stored and the computational cost of correction. In the correction phase, primal and dual variables are updated via gradient descent-ascent iterations, thus maintaining the computational efficiency of a first-order method without requiring Hessian or high-order derivative computations. Theoretical analysis shows that the method achieves $\mathcal{O}(h^2)$ asymptotic tracking accuracy for both primal and dual variables, matching the state-of-the-art performance among first-order methods even in unconstrained settings. Numerical experiments on problems with both time-invariant and time-varying constraints validate the theoretical findings and demonstrate the method's effectiveness.

The cooperative output regulation problem for unknown linear multi-agent systems has been studied by both policy-iteration method and value-iteration method via distributed internal model approach. However, the original results were limited to single-input single-output linear multi-agent systems under the assumption that the communication digraph is acyclic. Recently, the authors have extended the existing result to multi-input multi-output linear multi-agent systems over a general static and connected digraph by a more efficient value-iteration method. Since the policy-iteration method is simpler and has a much faster convergence rate than the value-iteration method, in this paper, the authors further apply the policy-iteration method to the cooperative output regulation problem of unknown multi-input multi-output multi-agent systems over a general static and connected digraph. Compared with the existing policy-iteration method, the proposed policy-iteration approach not only drastically reduces the computational cost, but also significantly weakens the solvability conditions. Moreover, by introducing a virtual exosystem, the proposed policy-iteration approach eliminates the need for employing a distributed observer. As a result, the data collection can start at any time, and the computing cost for each agent is also reduced.

Using ESG rating data of Sino-Securities Index Information Service from 2009 to 2020, this paper examines the impact of listed companies' ESG rating on the level of stock price, financial and operational risk in the next year. The study finds that better ESG rating has a significant inhibitory effect on all three risk levels of enterprises in the next year. Specifically, for the risk of stock price crash, ESG rating higher than the benchmark level, as a strong market signal, has a more significant reduction in the risk level of stock price crash. The trading volume of individual stocks, which reflects the attention of investors, has an intermediary effect on ESG to reduce the risk of enterprise stock price crash. ESG of large-scale enterprises that occupy an important position in the market and attract more attention from investors has a stronger inhibitory effect on the risk of stock price crash; In addition, the negative relationship between ESG and the risk of stock price crash is more significant after the implementation of the “Environmental Protection Law”. For financial risk, ESG has a marginal diminishing effect on reducing corporate financial risk, and the improvement of ESG rating from low to medium can improve the level of corporate financial risk. At the same time, enterprises' voluntary disclosure of non-financial information could strengthen the inhibitory effect of ESG on financial risks. For operational risk, ESG rating has a marginal diminishing effect on reducing operational risk; At the same time, the nature of equity has a moderating effect on the reduction of operating risks by ESG rating. Compared with private enterprises, ESG has a stronger inhibition effect on the operation risk of state-owned enterprises. Finally, the sub-sample heterogeneity test results based on the length of enterprise life in this paper show that the inhibitory effect of ESG rating on risk is stronger for enterprises with a long establishment age, but weaker for enterprises with a short establishment age.

Based on investor behavior data from the Eastmoney Guba, this paper employs the effective transfer entropy method to investigate whether the mediating role of stock forums in the stock market better represents investor attention or sentiment. The findings reveal that: 1) Investor attention in stock forums conveys more valuable information flows to the stock market, providing a more accurate representation of investor behavior; 2) The net comment volume, as a key indicator of investor attention, exhibits strong information flow correlations with the stock market, significantly influencing stock volatility, with its effect extending up to one month into the future; 3) Across posts with different sentiments (positive, neutral, and negative), investor attention consistently transmits information flows that predict stock volatility, while investor sentiment lacks significant incremental value in transmitting information flows to the market. This study further underscores the mediating role of stock forums in capturing investor attention, particularly highlighting the unique predictive value of net comment volume, offering investors a novel perspective on analyzing online stock forum data. Future research should focus on integrating more comprehensive datasets and conducting in-depth explorations to enhance the accuracy of market forecasts and the scientific rigor of investment decision-making.

Focusing on the supply side of vehicle charging service, this study proposes two differential game models for charging pile operation decision-making, with the government, operator, and third-party platform (hereinafter referred to as the platform) as the participants. The two differential game models are decentralized (i.e., operators and platforms aim to maximize their own interests) and centralized (i.e., operators and platforms aim to maximize the overall interests of both). The results show that under the equilibrium state with fixed revenue distribution ratios between operator and platform, compared with the decentralized decision-making mode, the centralized decision-making mode can improve the efforts of operator and platform, service quality and social benefit. When the platform is relatively weak and has a lower share of revenue, adopting the centralized decision-making mode can achieve a Pareto improvement in the revenues of both operator and platform; conversely, when the platform is relatively strong and has a higher share of revenue, adopting the decentralized decision-making mode can increase the revenues of both operator and platform. This indicates that as platform develops from weak to strong, the decision-making mode of the charging service market may shift from centralized to decentralized. At this time, the proportion of government policy support will increase, and social benefit and service quality may decrease.

In this paper, the stability and robustness of a recurrent neural network (RNN) controller with saturation function and ReLU function as activation function are analyzed for first-order linear uncertain systems. The necessary conditions for the closed-loop system to converge to the non-zero target and the suffcient conditions for exponential stability are provided. The quantitative relationships between the recurrent neural network controller’s parameters and the robustness of the initial state value, the target value and the unknown parameter of the plants are analyzed. The analysis results show that the RNN controllers with ReLU function as the activation function have stronger robustness.

The registration-based system represents a pivotal reform in China’s capital market development. The inquiry system reform aims to transfer pricing authority more substantially to market participants and enhance IPO pricing effciency. Consequently, systematic research evaluating IPO pricing effciency and the effects of inquiry system reforms under the registration-based framework have attracted considerable scholarly attention. This paper employs a bilateral stochastic frontier model to measure IPO pricing effciency across 2365 listed companies in China’s A-share market from 2016 to 2023, and empirically verifies the systematic impact of inquiry system reforms on IPO pricing under the registration-based system. Research findings indicate that during 2016–2023, underpricing effects dominated overpricing effects in A-share market initial offerings, with overall pricing 7.06% below reasonable levels, exhibiting distinct characteristics across different boards, years, ownership structures, and break-even status. The inquiry system reform generally elevated initial offering prices, primarily driven by the distinctive characteristics of the STAR Market, while other boards demonstrated declining trends. During the registration-based system expansion phase, significant competitive dynamics emerged between the STAR Market and ChiNext Board, while reform effects on the main board remained limited. Furthermore, the study identifies two critical transmission pathways explaining these impacts: The number of inquiry institutions and the effectiveness of price quotations. Based on these conclusions, this paper proposes targeted recommendations for regulatory authorities to guide future inquiry system reforms.

Sparsity is a crucial assumption in high-dimensional modeling, as only a small subset of variables typically exert significant influence on the response in high-dimensional regression analysis. Based on varying coeffcient models, this paper proposes a varying sparse coeffcient mixed-effects quantile regression (VSCMEQ) model for longitudinal data, which incorporates variable selection. In this model, the coeffcient functions are estimated using B-splines, and penalties are imposed on both random and fixed effects to investigate the influence of relevant important factors, including varying effects and constant effects. Finally, the proposed method is applied to the Primary Biliary Cirrhosis (PBC) dataset to analyze disease progression, identifying the influence of significant factors on disease progression (biomarkers) at different quantiles.

This paper considers the supply interruption of a supply chain composed by two suppliers and one retailer, where one supplier is an integrated supply and marketing supplier and the other supplier is a pure supplier, and the retailer makes replenishment from the latter supplier and makes and emergency order from the former when the supply is interrupted. For this system, we mainly investigate the retail price decision and the emergency replenishment from the supply and retailing integrated supplier in the case of a supply interruption with a random end time from the second supplier. Based on maximizing the benefits of each member in the supply chain, we establish an optimization model, and its solution is obtained via a theoretical analysis which gives the optimal decision for each member of the supply chain. Some numerical experiments are made which give the impact analysis of main parameters on the optimal decision of each member of the supply chain and their benefits for the supply interruption period.

Trend filtering is a widely used method for extracting long-term trends and eliminating short-term noise from time series data. In order to accurately capture the global change pattern and local fluctuation of the potential trend, this paper proposes the generalized trend filtering model with composite $\ell_0$ constraint (L0CTF) based on the primitive function representing sparsity, and the optimality theory is analyzed. However, solving the L0CTF model is a challenging task because of the combinatorial property and indivisibility of the composite $\ell_0$ function. Therefore, based on the properties of composite $\ell_0$ function, this paper reformulates the L0CTF model as a mixed integer programming problem with special ordered sets of type 1 and analyzes its equivalence with L0CTF in the sense of global optimal solution. Finally, experimental results on simulated and real data sets show that the proposed method is superior to some mainstream trend filtering methods in extracting potential trends.