成果1：

公司教师杨云雁与清华大学林勇教授，山东财经大学张梦杰教授合作的论文《 Fractional Laplace operator and related Schrödinger equations on locally finite graphs》在Calculus of Variations and Partial Differential Equations上发表.

链接：https://doi.org/10.1007/s00526-025-03074-7

Abstract：In this paper, we first define a discrete version of the fractional Laplace operator (-△)⁸through the heat semigroup on a stochastically complete, connected, locally finite graph. Moreover, we introduce a fractional Sobolev space, which is necessary when we study problems involving (-△)⁸.Thirdly, we define the fractional divergence, and then give another form of (-△)⁸, which leads to a formula of integration by parts. Finally, using the mountain-pass theorem and the Nehari manifold, we obtain multiplicity solutions to a discrete fractional Schrödinger equation. We caution the readers that though these existence results are well known in the continuous case, the discrete case is quite different.

成果2：

公司教师赖秀兰与其员工滕宇合作的论文《Modeling Combination Therapies and T Cell Exhaustion Dynamics in the Tumor Under Immune Checkpoint Blockade》在期刊Bulletin of Mathematical Biology上发表

链接：https://doi.org/10.1007/s11538-025-01507-0

Abstract：Chronic antigen exposure in the tumor microenvironment drives CD8+T cell exhaustion, marked by increased inhibitory receptors and diminished effector functions. Immune checkpoint blockade seeks to prevent or reverse exhaustion, but its success relies on the pre-existing state of tumor-infiltrating T cells. To investigate this, we developed a mathematical model examining: (1) how T cell exhaustion disrupts tumor-immune equilibrium, (2) anti-PD-L1 efficacy across exhaustion states, and (3) efficacy of next-generation therapies (e.g., IFNα-anti-PD-L1, PD1-IL2v). Stability analysis and simulations reveal that tumor PD-L1 expression critically influences immune dynamics, particularly the bistability of tumor-free and tumorous states. High PD-1 expression and exhaustion rates correlate with growth of tumor and impaired expansion of less-exhausted CD8+T cells. While anti-PD-L1 efficacy depends on baseline exhaustion, severe exhaustion enables immune escape. Next-generation therapies enhancing cytotoxicity and sustaining less-exhausted T cell populations show improved tumor control, suggesting combination strategies may overcome resistance.

成果3：

公司教师赵文彬与厦门理工公司吴国春教授合作的论文《Global well-posedness and vanishing viscosity limit of the compressible elastic system in three dimensions》在数学期刊《Journal of Differential Equations》发表。

链接：https://www.sciencedirect.com/science/article/pii/S0022039625008769

Abstract: The compressible elastodynamics is a typical example of systems with different wave speeds, which are difficult to be solved due to lack of symmetries. In general, the nonlinear interactions among the pressure waves are so strong that the global existence of classical solutions cannot be expected. In this article we investigate a specific example, namely the compressible Mooney–Rivlin materials, of which both the interactions among the pressure waves and among the shear waves satisfy the null conditions respectively. With delicate analysis of the linear system, we manage to identify all the good unknowns in a simpler form which are essential to exploit the null conditions for extra time decay. The approach to the a priori energy estimates applies to both inviscid and viscous systems, and enables us to justify the vanishing viscosity limit result.