Rings whose cyclic modules are lifting and ⊕-supplemented

It is proved that a semiperfect module is lifting if and only if it has a projective cover preserving direct summands. Three corollaries are obtained: (1) every cyclic module over a ring R is lifting if and only if every cyclic R-module has a projective cover preserving direct summands; (2) a ring R is artinian serial with Jacobson radical square-zero if and only if every (2-generated) R-module has a projective cover preserving direct summands; (3) a ring R is a right (semi-)perfect ring if and only if (cyclic) lifting R-module has a projective cover preserving direct summands, if and only if every (cyclic) R-module having a projective cover preserving direct summands is lifting. It is also proved that every cyclic module over a ring R is ⊕-supplemented if and only if every cyclic R-module is a direct sum of local modules. Consequently, a ring R is artinian serial if and only if every left and right R-module is a direct sum of local modules.     

A geometric realization of quantum groups of type D

We geometrize quantum groups of type D in the spirit of Beilinson et al. (1990) [1].     

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.     

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     

基于流固耦合的锚索涡激振动抑制方法研究

悬浮隧道锚索的涡激振动会加剧锚索的疲劳破坏,进而影响悬浮隧道的使用寿命和安全.文章在海洋立管涡激振动抑制研究的基础上,考虑悬浮隧道锚索倾斜角度和来流方向的影响,采用流固耦合的数值方法,对整流罩方法和三控制杆方法的抑制效果进行了分析.结果表明,在顺来流方向,两种方法均具有良好的抑振效果;锚索有倾斜的情况下,三控制杆方法的效果会有所提升;但在来流方向改变时,整流罩方法具有较强的适应性.