Based on boundary rationality and relative profit maximization, quantum game theory is applied to develop a dynamic model of the quantum Cournot duopoly game. We investigate the effect of quantum properties on game stability and nonlinear dynamics. The results show that quantum entanglement can improve the model’s stability and control the generation of bifurcation and chaos when comparing the classical game and the game without considering relative profit maximization. It facilitates the player’s choice of quantum entanglement to control the chaos that emerges in the production output. Numerical simulations verify the chaotic properties of the game by means of bifurcations, maximum Lyapunov exponents, and phase diagrams. The results show that quantum entanglement has different effects on different games.

In this paper, we extend the entropy scheme for hyperbolic conservation laws to one-dimensional convection-diffusion equation. The operator splitting method is used to solve the convection-diffusion equation that is divided into conservation and diffusion parts, in which the first-order accurate entropy scheme is applied to solve the conservation part and the second accurate central difference scheme is applied to solve the diffusion part. Numerical tests show that the L∞ error achieves about second-order accuracy, but the L1 error reaches about forth-order accuracy.

Images captured under weak illumination typically suffer from low brightness and contrast, severe color distortion, and significant noise contamination, which not only degrade human visual perception but also hinder the performance of high-level vision tasks. Low-light image enhancement aims to improve visual quality and provide favorable conditions for subsequent image processing. To address the challenges of non-uniform illumination and loss of details in dark regions, we propose a two-stage denoising diffusion model (two-stage DDM). Specifically, we design a convolution-based Retinex decomposition module to achieve fast and robust image decomposition, followed by a two-stage diffusion-based denoising process that further enhances global image details, brightness, and contrast. In addition, we introduce a feature enhancement module to strengthen the representational capacity of the reflectance component. To evaluate the robustness and generalization ability of the proposed model, extensive experiments are conducted on the LOLv1, LOLv2-real, and LSRW datasets. Experimental results demonstrate that the proposed two-stage DDM achieves competitive performance with state-of-the-art methods, producing enhanced images with more natural and spatially uniform brightness, along with noticeably improved visual quality.