This work explores generalized Ulam-type stability for a family of time-lag discrete systems governed by two-order difference operators. First and foremost, we put forward strict mathematical formulations of Hyers–Ulam-based generalized stability adapted to the above-mentioned two-order time-delay discrete frameworks, which expand existing stability theories for lower-order discrete dynamic models. Afterwards, utilizing the discrete matrix delay exponential approach alongside the discrete Grönwall inequality, we rigorously deduce adequate criteria that ensure such generalized stability characteristics for the investigated systems, with core theoretical deductions elaborated thoroughly. In the end, a numerical case is designed to demonstrate the correctness and applicability of our derived theoretical outcomes and further verify the reliability of the established analytical strategies.
Experimental evidence shows that the immune system plays a crucial role in clearing acute hepatitis B virus (HBV) infection. This study develops a mathematical model to investigate the immune response to HBV and the coexistence of liver cancer within the liver cell population. The model is validated using published patient data from the acute phase of infection. The invasion threshold for disease transmission, represented by the basic reproduction number R0, is derived for populations of uninfected macrophages both in the presence and absence of cancer cells. The basic reproduction number R0 is defined as the number of new HBV and liver cancer cases generated by a single infected macrophage introduced into a fully susceptible population of liver cells. This threshold is then extended to incorporate two treatment controls: nucleotide (nucleoside) analogues (NAs) and interferon-based therapies yielding the control reproduction number Rc. Stability analyses of the virus-free and virus-persistence equilibrium states are performed, and numerical simulations are used to support the analytical results. The influence of different immune components on disease progression is also examined. Simulation results predict the time at which T helper-1 cells exceed cytotoxic T lymphocytes (CTLs), referred to as the time to chronicity, which increases with the proliferation rate of interleukin-10 ρ3. Further analysis indicates that interleukin-10 promotes HBV persistence by suppressing immune activity, allowing viral evasion and the establishment of chronic infection through inhibition of CTLs responsible for clearing infected cells. To evaluate treatment strategies, antiviral therapies including nucleoside analogues and interferon are incorporated into the model. Results indicate that effective control occurs when Rc<1, highlighting the importance of combined therapies that suppress viral production and prevent new infections. For example, a nucleotide drug efficacy of approximately 74% together with interferon therapy efficacy of 71% reduces Rc to 0.0875, demonstrating effective disease control.
Variable memory effects are essential for accurately modeling nonlocal phenomena in applied mathematics, physics, and engineering. Motivated by this observation, we develop a new class of variable-order postquantum fractional integral inequalities based on the Riemann–Liouville (RL)-type p,q-fractional integral operator with a q-shifting structure. Unlike the existing results restricted to constant fractional orders, the proposed framework allows the order to vary with the independent variable, enabling the description of nonuniform and evolving memory effects. A postquantum variable-order multiparameter fundamental identity on finite intervals is established, from which new generalized Hermite–Hadamard-, midpoint-, trapezoidal-, Simpson-, and Bullen-type inequalities are derived. The results are developed under several generalized convexity assumptions, including convex and α,m-convex functions, thereby extending the applicability of the theory. Many known constant-order postquantum inequalities are recovered as special cases. Numerical simulations, graphical illustrations, and an application to special means are presented to demonstrate the effectiveness of the proposed framework.
This study examines the relationship between environmental uncertainty and ESG performance, with a focus on the moderating roles of ESG controversies and gender diversity on the board. It utilizes an unbalanced panel dataset of 315 Chinese and US banks from 2011 to 2022. By employing a two-step system GMM and 2SLS estimations, this study finds that environmental uncertainty adversely influences ESG performance. The findings also suggest a U-shaped relationship between environmental uncertainty and ESG performance, indicating an adverse effect of environmental uncertainty on ESG performance, which is initially negative but weakens throughout environmental uncertainty and turns positive when the environment is highly uncertain. However, ESG controversies moderate these effects, as does the moderating role of gender board diversity, especially in US banks. Gender diversity helped mitigate the adverse impacts of uncertainty on ESG performance, though this effect is weaker in Chinese banks. The findings offer significant policy insights for bank managers, policymakers, and regulators aiming to improve ESG strategies in the face of crises and global uncertainties.
This preliminary feasibility study explores an innovative intervention approach that combines a multidimensional virtual reality (VR)-based drawing game with electroencephalogram (EEG) monitoring to enhance emotional regulation in children with autism spectrum disorder (ASD). Traditional interventions, primarily relying on behavioral therapy and pharmacological treatments, often fail to adequately address the unique emotional and cognitive needs of this population. VR-based drawing technology, with its immersive and highly interactive nature, offers children a novel space for nonverbal expression and self-regulation, thereby expanding therapeutic possibilities. The study focuses on examining the effects of VR drawing activities on emotional responses and neural activity patterns, particularly by using EEG to track real-time changes in brainwave activity, aiming to identify specific neural markers—such as alpha, beta, and theta waves—associated with emotional regulation, thus informing personalized intervention strategies. Preliminary results suggest promising potential for the integration of VR and EEG in improving emotional regulation among children with ASD. However, as a small-scale exploratory study, these findings are still preliminary and require further validation through large-scale randomized controlled trials incorporating VR and EEG technologies to advance the development of more effective and individualized interventions. Overall, the study indicates that integrating creative expression with neuroscience tools holds significant promise in therapeutic settings, although these conclusions need confirmation through larger, controlled studies.
This paper develops and analyzes a nine-compartment discrete colorectal cancer model governed by a Caputo variable-order difference operator. The model describes the interactions among epithelial cells, adenomatous polyps, oncogenes, tumor suppressor genes, APC mutations, KRAS mutations, microsatellite instability, inflammatory cells, and myofibroblasts. The variable-order framework is used to represent stage-dependent memory effects in colorectal cancer progression. The existence and uniqueness of solutions are established by using a Banach fixed-point argument, while positivity and uniform boundedness are proved to ensure biological feasibility of the model. Equilibrium points and a basic reproduction number are derived, and local stability is investigated through a variable-order spectral-angle criterion. Numerical simulations are performed to study the influence of memory variation on the model dynamics. A comparative analysis is also presented for the integer-order, constant fractional-order, and variable-order cases. Finally, the normalized model output is compared qualitatively with available colorectal cancer incidence data, showing that the proposed framework can capture the general observed trend while preserving flexibility through time-varying memory.
Against the backdrop of the deep penetration of social media into social life, networked sentiment polarization has become an important challenge for public opinion research and governance analysis. To address the reactive and lagging nature of traditional public opinion response strategies, this study proposes a large language model-driven multiagent simulation framework for modeling networked sentiment dynamics and comparing regulation strategies. Based on multidimensional user profiles, including user identity, sentiment tendency, personality traits, and reading habits, the framework simulates content generation and interactive behaviors such as commenting, liking, and reposting, thereby forming a feedback loop between agent behaviors and the public opinion environment. This study introduces the "rate of change in sentiment entropy" as a core metric to quantify sentiment fluctuation intensity. On this basis, static and dynamic regulation strategies are designed and compared. Experiments based on two real-world Weibo public opinion events show that the proposed simulation environment can, to a certain extent, reproduce the dynamic characteristics of real public opinion data in terms of semantic content, stylistic features, sentiment evolution, and interaction behavior. The regulation experiments further reveal a "pulse-rebound" pattern and suggest that information-source credibility and adaptive triggering mechanisms play important roles in the recovery and stabilization of the simulated sentiment system. Overall, this study provides a controlled simulation environment and analytical reference for sentiment evolution modeling and regulation strategy comparison.
World Heritage Sites generally face the core contradiction between tourism economic development and heritage resource protection. Due to the lagging data collection and limitations of static analysis, traditional management models struggle to accurately quantify the dynamic balance between economic value-added and ecological protection. Addressing the identification challenge of the chain effect triggered by the cluster development of home stays, this study proposes a three-in-one technical framework of "sensory network-dynamic simulation-decision support." Based on the LoRa low-power wide-area network, a multinode monitoring system is constructed to break through the bottleneck of real-time data collection in karst landforms, achieving high-precision positioning of tourist behavior with 1.37-2.68 m accuracy and second-level dynamic tracking of consumption trajectories. Coupling system dynamics models with nonlinear threshold analysis, this study identifies the critical inflection point of home stay cluster density for economic value-added in karst landform heritage sites. This threshold identification complements existing studies on heritage carrying capacity and cluster optimization, and at this threshold, the growth rate of tourism revenue reaches a theoretical peak, the decay rate of heritage integrity is minimized, and the efficiency of protection input-output is significantly improved. Empirical verification in ancient villages of southern Anhui shows that the dynamic regulation mechanism achieves second-level delay in emergency response, technology-enabled scenarios effectively stimulate the synergistic effect of the tertiary industry, the return visit rate of tourists increases by over 50%, and the added value of the local industrial chain doubles. The research results have established a "monitoring-simulation-decision" closed-loop management paradigm, which effectively integrates contemporary theories of heritage tourism economics, destination competitiveness, smart tourism ecosystems, and data-driven analysis, The empirical results from Xidi and Hongcun are consistent with cross-case findings on heritage tourism governance in ancient village, supporting the broader applicability of this framework to karst heritage sites with similar cluster characteristics.
In the present work, two distinct Runge-Kutta methods based on the conformable derivative were introduced for solving fractional differential equations of the first order. Both proposed methods were defined as second- and fourth-order and derived from Taylor series expansions and integral quadrature. Illustrative examples were discussed for the validity and efficiency of the methods. The absolute error graphs demonstrated the exceptional efficiency of the proposed methods and their greater accuracy than that of the conformable derivative. Furthermore, some approaches that provide more precise approximations than the fractional Runge-Kutta method were discovered.
The current study elucidates the influence of product diversification strategies and technological R&D investments on the resilience of Chinese high-tech listed companies in the context of US trade sanctions. Our findings reveal an inverse U-shaped relationship between enterprise product diversification and resilience. R&D investment positively affects resilience but with diminishing returns. Notably, R&D investments amplify the inverted U-shaped effect of product diversification on firm resilience, particularly when product diversification falls within the “double threshold.” Furthermore, non-state-owned holding enterprises exhibit a more pronounced impact of product diversification on resilience compared to state-owned counterparts. Our research not only examines the impact of these strategies on enterprise resilience but also clarifies how different strategic choices influence the response and consequences of enterprises facing systemic risks. We shed light on the varying impacts of external systemic risks on businesses. These insights provide valuable guidance for enterprises aiming to bolster their resilience and sustain steady development under the influence of trade complexity. Methodologically, this study integrates a discrete-time dynamic resilience framework with event-study and panel-regression approaches, modeling how firms transition across resilience states—resistance, recovery, and adaptation—in response to sequential sanction shocks. This discrete-dynamics perspective contributes a novel bridge between dynamic systems theory and empirical corporate strategy research.
The Randi & cacute; index is a classical degree-based topological index that captures branching features of a graph and has broad applications in chemical graph theory and related network models. Roman domination is a defense-inspired covering concept in which vertices are assigned protective labels so that every unprotected vertex is adjacent to a strongly protected one, and the Roman domination number measures the minimum total defensive weight needed. In this paper, we investigate how these two invariants interact on trees. We establish new sharp lower bounds for the Randi & cacute; index of a tree expressed in terms of its order and its Roman domination number, and we characterize all trees attaining equality. We further derive a matching upper bound in the same parameters and again determine the extremal structures. In particular, we show that among trees with fixed order and Roman domination number, the star uniquely attains the minimum Randi & cacute; index, while the path uniquely attains the maximum. A comparative analysis with previously known bounds demonstrates that the new lower bound is consistently tighter and tracks the exact Randi & cacute; index more closely, especially for larger trees. We conclude with an open problem on extending these extremal results to unicyclic and bicyclic graphs.
To enhance the emergency response capacity of the digital technology infrastructure engineering supply chain and reduce the independent costs and risks faced by enterprises during emergency situations, this paper constructs a game model involving key stakeholders: regulatory agencies, resource suppliers, and service operators. It analyzes the relationships among emergency response capacity, regulatory subsidy rate, and emergency benefits. The findings show that a collaborative cooperation mechanism can significantly improve the supply chain's emergency response capacity. In the process of enhancing emergency capabilities, reducing emergency costs should be the top priority, followed by improving the efficiency of emergency data utilization. Further analysis reveals a negative correlation between the proportion of corporate income distribution and the improvement of emergency capacity. When the distribution ratio reaches two-thirds, the regulatory subsidy rate in noncooperative games no longer affects the improvement of emergency capacity. The optimal subsidy rate is jointly influenced by the proportion of emergency benefits and the income distribution structure. Under the Stackelberg leader-follower game model, the optimal subsidy rate by the regulatory agency is the same for both enterprises.
A global stability analysis of fractional-order memristor fuzzy BAM neural networks with time-varying delays and leakage terms is covered in this paper. Sufficient conditions are established to guarantee uniform stability of fractional-order fuzzy BAM neural networks and to derive the equilibrium point, which ensures asymptotic stability on a global scale, using the theory of fractional-order calculus, the lemma of fractional Barbalat, and the characteristics of fuzzy logic operators. In order to validate the effectiveness of the theoretical conclusions, two numerical examples are provided to illustrate the value of the outcome.
To enhance the stability of the agricultural product supply chain (APSC) under adverse weather conditions, this study examines contract coordination and government subsidy mechanism. First, we develop a two-echelon APSC including a farmer and a company and establish stochastic profit functions to reflect the impact of adverse weather on agricultural product quality. Then, we construct Stackelberg game models based on different contracts (wholesale price contract, revenue-sharing contract, and “revenue-sharing + franchise fee” contract) and government subsidies (output subsidy and sale subsidy). Finally, we conduct numerical analysis to compare the effects of various contracts and government subsidies on APSC decision-making, as well as the influence of various subsidies on contract coordination. The research demonstrates that adverse weather can deviate APSC performance from the optimum. However, contract coordination and government subsidies enhance supply chain performance. The revenue-sharing contract can achieve supply chain coordination, but at a higher revenue-sharing ratio, the profit of the company declines. The “revenue-sharing + franchise fee” contract not only achieves supply chain coordination but also improves profits for all parties. Furthermore, output subsidy exhibits a broader coordination scope than the sale subsidy under the “revenue-sharing + franchise fee” contract. Regardless of the contract type, output subsidy generally leads to higher overall social welfare compared to sale subsidy, while sale subsidy is higher in terms of fund utilization efficiency.
A promising solution to the challenge of sustainability and environmental protection lies in promoting the adoption and use of new information and communication technologies (ICTs) and advancing gender equality. ICTs can contribute to environmental protection by transforming production methods and processes into cleaner technologies, through energy savings, or by interacting with institutions and governance. This article seeks to fill a gap in the existing literature by describing a number of theoretical mechanisms and providing empirical evidence of the diffusion of green technologies and its interaction with institutional quality. Using a cross-sectional distributed lag (CS-DL) model across 40 African countries over the period 2000-2020, the results indicate that a reduction in CO2 emissions is generally associated with greater diffusion of digital technologies. The results also suggest that an improvement in the institutional quality of African countries is associated with better environmental protection. Furthermore, the results show that a reduction in gender inequalities is associated with better performance in terms of green innovation. In addition, regulations aimed at encouraging the transition to renewable energy are likely to contribute to improving the environmental performance of African countries.
Aiming at the problem of multi-industry comprehensive evaluation, this paper discusses a comprehensive evaluation method based on principal component and class coverage discriminant analysis. This method adopts principal component analysis and the standard value of industry performance to classify the sample data, and the original sample data are divided into five levels, namely, excellent, good, average, poor, and very poor, and a comprehensive evaluation model is constructed by using the idea of class coverage and nearest neighbor principle. To verify the effect of the model, the paper collected the relevant data of 108 listed companies in 4 industries in 2022. The sample data were divided into a training group and a test group, three schemes were set up, and the comprehensive evaluation model was established by using the methods discussed in the paper, respectively. Then, a comparative analysis was conducted with Fisher discriminant analysis, k-nearest neighbor discriminant analysis, and nonlinear discriminant analysis method based on the cover class problem. The experimental results show that compared to the common supervised classification comprehensive evaluation method, the proposed comprehensive evaluation method has better stability and classification accuracy.
Corporate green transformation represents a critical pathway toward achieving high-quality economic development and fulfilling the "dual carbon" targets. Concurrently, environmental, social, and governance (ESG) ratings are emerging as a core market-based governance mechanism to steer corporate sustainable development trajectories. This study empirically investigates the effect of ESG ratings on corporate green transformation and its underlying mechanisms, using panel data from Chinese A-share-listed companies from 2009 to 2022. The findings reveal the following: First, ESG ratings significantly promote corporate green transformation. This conclusion remains robust after a series of endogeneity and robustness tests, including the instrumental variable method. Second, the cost of debt financing, institutional investor attention, and green technology innovation are identified as mediating channels. Specifically, ESG ratings facilitate corporate green transformation by reducing the cost of debt financing (resource pathway), attracting the attention of institutional investors (governance pathway), and fostering green technology innovation (capability pathway). Third, the enabling effect of ESG ratings on corporate green transformation exhibits significant heterogeneity; the promotional effect is more pronounced for state-owned enterprises, large-scale firms, and companies in nonheavy-polluting and high-technology industries. Therefore, to fully unleash the empowering effect of ESG ratings on corporate green transformation, it is crucial to enhance the transmission mechanisms through capital markets, corporate governance, and corporate capabilities.
Video platforms have significantly broadened the marketing and advertising channels available to automobile manufacturers, leading to reduced transaction costs and increased profits for participants. Through building a dynamic automobile manufacturer competition model with bounded rationality, we have revealed the following conclusions: Adjustment speed, research and development (R&D) level, advertising level, and risk aversion all affect the automobile manufacturer competition system. Specifically, adjustment speed and R&D level increase system instability, while advertising level and risk aversion enhance system stability. Regarding their impacts on competition, a higher R&D level raises the prices and profits of automobile manufacturers, whereas advertising levels and risk aversion reduce them. The time-delayed feedback control (TDFC) mechanism contributes to the stability of the overall system.
Amid rapid digital transformation and accelerated AI advancements, healthcare data utilization has gained global prominence. Empirical evidence demonstrates that public trust is pivotal to sustainable healthcare data sharing, with transparency being its key determinant. This study investigates the transparency-trust relationship through evolutionary game theory. A tripartite stochastic evolutionary game model is developed, incorporating Gaussian white noise to capture real-world complexity. Through analyzing interactions among data platforms, users, and patients, four key findings emerge: (1) Enhancing the regulatory efficiency and penalty intensity of data platforms can drive the system towards an effective equilibrium. (2) Both external regulatory pressure and long-term trust benefits are influential factors that encourage data users to choose TU. (3) The dynamic feedback mechanism of “risk speculation—patient withdrawal—strategy shift—system equilibrium” serves as the intrinsic driving force for the system’s self-repair and stability. (4) The intrinsic motivation for patients to choose participation is multidimensional; both privacy and security protection and the benefits derived from data sharing are influential factors driving patients to adopt PA.
Corruption behaves like a social contagion that evolves through interaction, influence, and institutional memory. To capture this complexity, we develop a deterministic corruption-transmission model governed by a piecewise fractional framework that combines the Caputo and modified Atangana-Baleanu-Caputo (mABC) derivatives. This dual-operator structure describes both short-term and long-term memory effects within a unified formulation. Analytical results confirm the existence and stability of solutions, while numerical experiments reveal faster stabilization and smoother convergence compared with classical and single-fractional models. The findings demonstrate that the proposed piecewise mABC framework offers a realistic and flexible mathematical tool for predicting corruption behavior and designing effective intervention strategies.
