A FULLY DISCRETE IMPLICIT-EXPLICIT FINITE ELEMENT METHOD FOR SOLVING THE FITZHUGH-NAGUMO MODEL

This work develops a fully discrete implicit-explicit finite element scheme for a parabolic-ordinary system with a nonlinear reaction term which is known as the FitzHugh-Nagumo model from physiology. The first-order backward Euler discretization for the time derivative, and an implicit-explicit discretization for the nonlinear reaction term are employed for the model, with a simple linearization technique used to make the process of solving equations more efficient. The stability and convergence of the fully discrete implicit-explicit finite element method are proved, which shows that the FitzHugh-Nagumo model is accurately solved and the trajectory of potential transmission is obtained. The numerical results are also reported to verify the convergence results and the stability of the proposed method.     

Dredging the Charge-Carrier Transfer Pathway for Efficient Low-Dimensional Ruddlesden-Popper Perovskite Solar Cells

Low-dimensional Ruddlesden-Popper (LDRP) perovskites still suffer from inferior carrier transport properties. Here, we demonstrate that efficient exciton dissociation and charge transfer can be achieved in LDRP perovskite by introducing γ-aminobutyric acid (GABA) as a spacer. The hydrogen bonding links adjacent spacing sheets in (GABA)₂MA₃Pb₄I₁₃ (MA=CH₃NH₃⁺), leading to the charges localized in the van der Waals gap, thereby constructing “charged-bridge” for charge transfer through the spacing region. Additionally, the polarized GABA weakens dielectric confinement, decreasing the (GABA)₂MA₃Pb₄I₁₃ exciton binding energy as low as ≈73 meV. Benefiting from these merits, the resultant GABA-based solar cell yields a champion power conversion efficiency (PCE) of 18.73 % with enhanced carrier transport properties. Furthermore, the unencapsulated device maintains 92.8 % of its initial PCE under continuous illumination after 1000 h and only lost 3 % of its initial PCE under 65 °C for 500 h.     

On weakly nil-clean rings

We obtain the structure of the rings in which every element is either a sum or a difference of a nilpotent and an idempotent that commute. This extends the structure theorems of a commutative weakly nil-clean ring, of an abelian weakly nil-clean ring, and of a strongly nil-clean ring. As applications, this result is used to determine the 2-primal rings R such that the matrix ring \(\mathbb{M}_n (R)\) is weakly nil-clean, and to show that the endomorphism ring End _D (V) over a vector space V _D is weakly nil-clean if and only if it is nil-clean or dim(V) = 1 with D?= ?₃.     

Residue and dissipation of zinc thiazole in tobacco field ecosystem

A high-performance liquid chromatography with ultraviolet (HPLC-UV) detection method after derivatisation was developed for the first time for the novel fungicide zinc thiazole residue in tobacco samples. Field trials in two different locations were conducted to investigate the dissipation and residue of zinc thiazole in tobacco leaves and soil. The average recoveries of zinc thiazole were in the range of 82.5%–93.9% with relative standard deviations (RSDs) of 1.2%–9.1%. The zinc thiazole showed a rapid dissipation rate in fresh tobacco leaves with the half-lives of 1.1–1.6 days. The terminal residues of zinc thiazole in cured tobacco leaves and soil were 2.8–28.0 mg kg^?1and <0.05 mg kg^?1, respectively. The results could be used to establish the maximum residue limits (MRLs) and provide guidance for the scientific use of zinc thiazole in agriculture.     

集值或单值增算子变分不等式的有限维近似

将非线性变分不等式的有限维近似理论用来处理带集值增算子的变分不等式,得到近似解的存在性及收敛性定理。对一种特殊的单值情形,给出了收敛性理论及误差估计。     

CNC车床的故障概率模型

本文从ＣＮＣ车床的故障数据的采集入手,建立了ＣＮＣ车床的故障数据库。应用模糊综合评价的方法对ＣＮＣ车床的故障模型进行了分析     

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多元非参数分位数回归常常是难于估计的, 为了降低维数同时保持非参数估计的灵活性, 人们常常用单指标的方法模拟响应变量的条件分位数. 本文主要研究单指标分位数回归的变量选择. 以最小化平均损失估计为基础, 我们通过最小化具有SCAD惩罚项的平均损失进行变量选择和参数估计. 在正则条件下, 得到了单指标分位数回归SCAD变量选择的Oracle性质, 给出了SCAD变量选择的计算方法, 并通过模拟研究说明了本文所提方法变量选择的样本性质.