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Can the accelerated development of ecological civilization promote the sustainable development of green innovation?This paper investigates the effects of ecological civilization demonstration zones (ECDZs) on green innovation resilience. Based on a sample of 237 prefecture-level cities across 31 provinces in China from 2011 to 2021, our double dual machine learning and spatial difference-in-differences model indicates that ECDZs significantly enhance urban green innovation resilience. Our findings also reveal a spatial spillover effect of ECDZ—the development of ECDZs in one city significantly improves the resilience of green innovation in neighboring cities. The spatial spillover effect reaches its maximum in the fifth year. Our analysis of the underlying mechanisms suggests that ECDZs promote urban green innovation resilience through the advancement of digitalization, green consciousness, and new quality productivity. We also conduct an analysis of heterogeneity based on geographical locations and levels of policy support, and the results show that the impact of ECDZs on urban green innovation resilience is mainly observed in western, inland, and strongly policy-supported regions. The findings of this study provide crucial insights and valuable guidance for developing national environmental conservation policies and programs.

In this paper, we studied a generalized Nash equilibrium problem where the constraint conditions were limited to a certain probability. The existence of an equilibrium solution for the vector-valued optimization problem was verified using Ky Fan's inequality and Lusin's theorem, considering the conditions of lower semi-continuity and concavity. Based on the study of the variational inequality method, we proposed a new algorithm to solve the problem. Furthermore, we analyzed the convergence of the algorithm. Finally, we applied the model to examine the economic benefits of digital currency issuance, corroborating the algorithm's effectiveness with a concrete numerical example.

As a major emerging economy, China government debt burden on local governments remains substantial, so enhance fiscal self-sufficiency and debt sustainability is so important. Utilizing panel data spanning from 2004 to 2020 across 29 provincial-level governments in China, this study employs the SYS-GMM approach to empirically validate the significant negative impact of digital infrastructure development on governments’ fiscal self-sufficiency rates. Furthermore, the research shows the significant positive mediating role of technological expenditure efficiency between digital infrastructure and fiscal self-sufficiency, implying that digital infrastructure can enhance fiscal self-sufficiency by augmenting technological innovation efficiency. Under the moderating effect mechanism, fiscal decentralization positively moderates the relationship between digital infrastructure and fiscal self-sufficiency. Heterogeneity analysis reveals that the impact of digital infrastructure on fiscal self-sufficiency is more pronounced in high-density regions. At the same time, its effect is less significant in low-density areas, indicating regional disparities in China’s digital infrastructure development. The contribution of this study is grounded in fiscal decentralization theory, policy recommendations advocate granting local governments greater autonomy over tax categories and broadening their fiscal revenue. Concurrent efforts should be directed towards deepening reforms in the fiscal and taxation systems, as well as budget management mechanisms.

Frequent natural disasters challenge relief network efficiency. This paper introduces a stochastic relief network with limited path capacity, develops an equilibrium model based on cumulative prospect theory, and formulates it as a stochastic variational inequality problem to enhance emergency response and resource allocation efficiency. Using the NCP function, Lagrange function, and random variables, the model dynamically monitors disasters, enabling rational resource allocation for quick decision-making. Compared to traditional methods, our model significantly improves resource scheduling and reduces disaster response costs. Through a random network example, we validate the model's effectiveness in aiding intelligent decision-making for relief plans and resource allocation optimization.

Lake ecosystems on the Tibetan Plateau (TP) are highly susceptible to external input owing to their fragile environment. However, less study has been done to focus the direct influences of anthropogenic activities on the lake sediments by human activities. In this study, we performed the first large-scale investigation to use the fecal stanol proxies in lake surface sediments to assess the impact of human and herbivorous feces on TP lakes. The 75 investigated lakes were divided into three types (I, II, and III) according to cluster analysis of the fecal stanol ratios R1′ and R2′. Fecal stanols in type I lake surface sediments originate from a mixture of herbivorous and human feces; fecal stanols in type II lake surface sediments primarily originate from herbivorous feces with minimal human feces. In contrast, fecal stanols in type III lake surface sediments are mainly derived from herbivorous feces (coprostanol concentration > 100 ng/g), a mixed source of herbivorous feces and cholesterol reduction (coprostanol concentration of 10–100 ng/g), and in situ reduction of cholesterol (coprostanol concentration

Variational inequalities theory is a potent tool that can be employed to tackle diverse optimization problems, with applications spanning physics, economics, finance and beyond. Solving the uncertain variational inequalities (UVI) has emerged as a prominent research topic in academia. However, conventional regularization methods for solving UVI are subject to certain limitations on the convergence rate of the algorithm. To overcome this challenge, we opt a class of regularized gap functions which is lower semi-continuous and $\phi $ -bounded true convex properties. We establish an expected value equivalent optimization model and demonstrate that the exponential convergence of the regularized gap function. Furthermore, we investigate the subdifferential of the lower semi-continuous and $\phi $ -bounded true convex functions (LSTCOS) and develop a deviation between the LSTCOS and its closed convex hull. By utilizing their deviations, we transform the convergence rate of the UVI solution to the uniform exponential convergence of LSTCOS. Finally, we prove that the UVI solution uniformly converges at an exponential rate based on the generalized equation.

This paper describes a kind of linear quadratic uncertain stochastic hybrid differential game system grounded in the framework of subadditive measures, in which the system dynamics are described by a hybrid differential equation with Wiener–Liu noise and the performance index function is quadratic. Firstly, we introduce the concept of hybrid differential games and establish the Max–Min Lemma for the two-player zero-sum game scenario. Next, we discuss the analysis of saddle-point equilibrium strategies for linear quadratic hybrid differential games, addressing both finite and infinite time horizons. Through the incorporation of a generalized Riccati differential equation (GRDE) and guided by the principles of the Itô–Liu formula, we prove that that solving the GRDE is crucial and serves as both a sufficient and necessary precondition for identifying equilibrium strategies within a finite horizon. In addition, we also acquire the explicit formulations of equilibrium strategies in closed forms, alongside determining the optimal values of the cost function. Through the adoption of a generalized Riccati equation (GRE) and applying a similar approach to that used for the finite horizon case, we establish that the ability to solve the GRE constitutes a sufficient criterion for the emergence of equilibrium strategies in scenarios extending over an infinite horizon. Moreover, we explore the dynamics of a resource extraction problem within a finite horizon and separately delve into an H∞ control problem applicable to an infinite horizon. Finally, we present the conclusions.

In this paper, a Stieltjes integral approximation method for uncertain variational inequality problem (UVIP) is studied. Firstly, uncertain variables are introduced on the basis of variational inequality. Since the uncertain variables are based on nonadditive measures, there is usually no density function. Secondly, the expected value model of UVIP is established after the expected value is discretized by the Stieltjes integral. Furthermore, a gap function is constructed to transform UVIP into an uncertain constraint optimization problem, and the optimal value of the constraint problem is proved to be the solution of UVIP. Finally, the convergence of solutions of the Stieltjes integral discretization approximation problem is proved.

For this paper, we consider the almost sure exponential stability of uncertain stochastic Hopfield neural networks based on subadditive measures. Firstly, we deduce two corollaries, using the Itô–Liu formula. Then, we introduce the concept of almost sure exponential stability for uncertain stochastic Hopfield neural networks. Next, we investigate the almost sure exponential stability of uncertain stochastic Hopfield neural networks, using the Lyapunov method, Liu inequality, the Liu lemma, and exponential martingale inequality. In addition, we prove two sufficient conditions for almost sure exponential stability. Furthermore, we consider stabilization with linear uncertain stochastic perturbation and present some exceptional examples. Finally, our paper provides our conclusion.

Abstract No previous study has involved uncertain delay differential equations with jump. In this paper, we consider the uncertain delay differential equations with V-jump, which is driven by both an uncertain V-jump process and an uncertain canonical process. First of all, we give the equivalent integral equation. Next, we establish an existence and uniqueness theorem of solution to the differential equations we proposed in the finite domain and the infinite domain, respectively. Once more, the concept of stability for uncertain delay differential equations with V-jump is proposed. In addition, the sufficient condition for stability theorem is derived. To judge existence, uniqueness, and stability briefly, we provide some examples in the end.

A convex combined expectations regularized gap function with uncertain variable is presented to deal with uncertain nonlinear variational inequality problems (UNVIP). The UNVIP is transformed into a minimization problem through an uncertain weighted expected residual function. Moreover, the convergence of the global optimal solutions of the uncertain weighted expected residual minimization model is given through the integration by parts method under the compact space of the uncertain event. The limiting behaviors of the transformed model are analyzed. Furthermore, a compact approximation method is proposed in the unbounded uncertain event space. Through analysis of the convergence of UWERM model and reasonable hypothesis, the compact approximation method is verified under the circumstance of Holder continuity.

In this paper, we consider nonlinear variational inequality problems with fuzzy variables. The fuzzy variables were introduced to deal with the variational inequality containing noise for which historical data is not available. The fuzzy expected residual minimization (FERM) problems were established. We discussed the S C 1 property of the FERM model. Furthermore, results of convergence analysis were obtained based on an approximation model of the FERM model. The convergence of global optimal solutions and the convergence of stationary points were analysed.

In this paper, a n-person credibilistic non-cooperative game with risk aversion is investigated in the fuzzy environment. Firstly, optimistic value criterion is applied to modeling players’ risk aversion. We define a α-optimistic Nash equilibrium for this games. The existence of α-optimistic Nash equilibrium strategies is proposed. Then a Bayesian α-optimistic Nash equilibrium is given by assuming α to be not common knowledge and its existence theorem is also proved. Moreover, we present a sufficient and necessary condition to find the Bayesian α-optimistic Nash equilibrium. Finally, an example is given to illustrate the usefulness of the proposed game. [ABSTRACT FROM AUTHOR]