We investigate traveling wave fronts for an acid-mediated tumor invasion model with density-dependent degenerate diffusion. The model is a partially diffusive PDE–ODE system of Gatenby–Gawlinski type, in which the tumor diffusion coefficient D(U) is allowed to be a general decreasing function satisfying D(1)=0. This degeneracy causes the traveling wave equation for the tumor component to lose uniform ellipticity near the healthy state, and hence standard arguments for nondegenerate reaction diffusion systems are not directly applicable. To overcome this difficulty, we introduce a nonlinear change of variables which removes the degeneracy from the highest-order term of the tumor equation. For each fixed admissible tumor profile, the acid profile is represented by a Green kernel, while the healthy-tissue profile is obtained from an explicit integral formula. The transformed tumor profile is then constructed as the stationary limit of a uniformly parabolic auxiliary problem. By combining comparison principles, local Schauder estimates, carefully chosen super- and sub-solutions, and the Schauder fixed-point theorem, we prove the existence of traveling wave fronts for every wave speed θ≥2rD(0). The resulting wave connects the tumor-dominant state (0,1,1) at z=−∞ to the healthy state (1,0,0) at z=+∞. We further establish strict pointwise bounds, monotonicity of all wave components, and one-sided exponential asymptotic estimates in both the transformed variable and the original traveling-wave variable.
A semicomplete multipartite digraph is a digraph obtained from a complete multipartite graph by replacing each edge uv with either a 2-cycle between u and v or a single directed edge, serving as a natural generalization of tournaments and semicomplete digraphs. In such a digraph D, a quasi-spanning trail is defined as a trail that includes at least one vertex from every partite set of D. The digraph D is called weakly quasi-eulerian-connected if for any distinct vertices x,y, there exists either an (x,y)-quasi-spanning trail or a (y,x)-quasi-spanning trail. It is called strongly quasi-eulerian-connected if both trails exist simultaneously for any pair of distinct vertices. In this paper, we completely characterize weakly and strongly quasi-eulerian-connected semicomplete multipartite digraphs and prove the following results: (1) A strong semicomplete multipartite digraph D is weakly quasi-eulerian connected if and only if D does not belong to the exceptional class D3 of semicomplete 3-partite digraphs; (2) Every 2-arc-strong semicomplete multipartite digraph is inherently strongly quasi-eulerian-connected; (3) A semicomplete multipartite digraph is strongly quasi-eulerian-connected if and only if D is strong and not in an exceptional class Dc. These results generalize the conclusions of Liu, Liu, Zhang and Chen on tournaments and Bang-Jensen, Havet and Yeo on semicomplete digraphs. Specifically, they extend the following known results: A tournament is weakly eulerian-connected if and only if it is strong; Every 2-arc-strong tournament is strongly eulerian-connected; A strong tournament is strongly eulerian-connected if and only if it does not belong to an exceptional class T; Every 2-arc-strong semicomplete digraph is strongly eulerian-connected.
Fluorescence molecular tomography (FMT) is a sensitive optical imaging technology widely used in biomedical research. However, the ill-posed nature of the inverse problem makes FMT reconstruction highly challenging, limiting the quality of the reconstructed images. Although existing iterative optimization and deep learning-based methods can improve reconstruction quality to some extent, the former relies on global regularization and fails to capture local sparse features, while the latter implicitly learns sparsity through network architectures but lacks explicit constraints, limiting the accurate recovery of fluorescent source regions. To address these limitations, we propose an explicitly sparse guided diffusion reconstruction framework, termed ESGDiff-FMT, to enhance the reconstruction of fluorescent sources. First, we propose an asymmetric conditional embedding strategy implemented via a dual-path cross-gating module, which incorporates multi-projection fluorescence signals as stable conditions into the diffusion process and effectively fuses fluorescence signals with reconstructed image features, thereby enhancing their consistency. Second, we introduce the sparsity-aware smooth weighted loss, which adaptively increases the gradient contribution of fluorescence regions while suppressing background interference, explicitly guiding the model to optimize the features of the fluorescent source regions iteratively. Numerical simulations, physical phantom, and in vivo experiments demonstrate that the proposed ESGDiff-FMT achieves superior performance in morphological reconstruction and background noise suppression, even without relying on large-scale datasets.
Abstract Steel corrugated pipes are gradually being adopted to protect polyethylene water supply pipes crossing mining goaf areas due to their strong adaptability, uniform stress distribution, and rapid construction. Therefore, it is important to accurately analyze the mechanical response of buried corrugated pipes in mining goaf areas. Based on a water supply project for a mining goaf area in northwestern China, this paper systematically investigates the stress and deformation performance of buried corrugated pipes underground subsidence. First, the deformation law of ground subsidence in the mining goaf area is predicted by the probability integral method combined with the survey data. Second, for the pipeline size beyond the standard, an engineering practical calculation method for the mechanical response of the corrugated pipe in the mining goaf area is proposed, and the validity of the method is verified by numerical simulation. Finally, the law of parameter variation on the mechanical response of corrugated pipe is systematically discussed, and the optimized design suggestion of the pipe is given. The results show that the stress and deformation of buried corrugated pipe can be obtained by considering the displacement form of the pipe as angular displacement and extending the single-waveform stiffness correction factor in the standard. The calculated values are basically consistent with the numerical simulation, which demonstrates that the method proposed in this paper is effective. As the wall thickness increases, the stress of the pipe decreases significantly, but the deformation remains almost constant. The stress and deformation of the pipe decrease with the increase of the dip angle of the coal seam. As the angle between the pipeline direction and the mining direction increases, the stress on the pipe gradually increases, but the deformation changes are small, which is the same as the influence of the soil friction angle on the pipe. The stress and deformation of the pipe are minimized when the wave distance is 0.23 m and the wave height is 64 mm. The research results can provide reference for the design and safety assessment of buried corrugated pipes in mining goaf areas.
Low seed germination rate is a great challenge in the breeding and production of many crops. Although traditional methods such as physics and chemistry can promote the germination of some seeds, the fact that some seeds have difficulty in germinating still exists. Recent research indicates that endophytic fungi (fungi that live symbiotically with plant seeds) play a crucial role in breaking dormancy and promoting seed germination. This paper is a review of the latest developments in endophytic fungi promoting seed germination. It covers the molecular mechanisms by which endophytic fungi regulate the synthesis of hormones within seeds to affect germination, including the regulation of gibberellin, abscisic acid, auxin, ethylene, jasmonic acid, and brassinolide synthesis. It also discusses how endophytic fungi induce plants to produce defense enzymes to promote seed germination, as well as how they regulate secondary metabolites in seeds to affect germination. Finally, it provides an outlook on the development of this field. This review will offer scientific references for seed research and provide green and sustainable ideas for solving efficient breeding with endophytes in agriculture.
