Study of Structures and Electronic Properties of Pdn–1Pb and Pdn （n≤8） Clusters

Geometric and electronic properties of Pdn–1Pb and Pdn (n≤8) clusters have been studied by using density functional theory with effective core potentials, focusing on the differences between mono- and bimetallic clusters. The average bond length of Pdn–1Pb (n≤8) bimetallic clusters is longer than that of pure palladium clusters except for n = 2 and 3. The most stable structure of Pdn–1Pb (n≤7) is the singlet where there is at least a Pd or Pb atom on its excited state. The energy gaps of Pd–Pb binary clusters are narrower than those of Pdn clusters, and then the chemical activity is strengthened when Pdn clusters are doped with Pb.     

关于超高分子量聚丙烯超拉伸膜的结构性能的研究——Ⅱ.形态结构变化对力学性能的影响

用X-射线衍射、动态力学测定等手段研究了不同拉伸倍数的超高分子量聚丙烯薄膜的力学性能的变化.以X-射线衍射法并基于串联力学模型的假设得到的各样品的表观晶区模量E_c~(app)约为34-38GPa.样品模量E_b随拉伸倍数增加而逐渐增大,其变化趋势与非晶区取向因子的变化相类似,说明非晶区取向是左右样品模量的重要因素.室温下,69倍拉伸样品的模量为27GPa,约为表观结晶模量的3/4,且其值在-150-160℃的温度范围内没有急剧变化,说明超拉伸明显改善了材料的力学性能及热稳定性.在各拉伸样品中,考虑伸直链结晶生成的可能性,利用并串联力学模型对伸直链结晶的体积分数做了估算,并对X-射线衍射法所得表观结晶模量进行了修正,认为室温下聚丙烯的真正晶区模量约为47GPa.     

四甲基对联苯二胺光敏化聚苯乙烯砜及其模型化合物二苄基砜分解机理的研究

N、N、 N’、N’-四平基对联苯二胺(NTMB)和 3、3’、5、5’-四甲基对联苯二胺(TMB)可以有效地光敏化二苄基砜(DBS)分解和聚苯乙烯砜(PSS)降解。敏化作用是按电子转移机理进行的,电子转移过程可以由NTMB的单重激发态,也可以由三重激发态发生。由三重态电子转移产生的三重态离子自由基对进一步反应生成产物的效率比单重态离子自由基对的效率高10倍。     

Predictions of moiré excitons in twisted two-dimensional organic–inorganic halide perovskites

Recent breakthrough in synthesizing arbitrary vertical heterostructures of Ruddlesden–Popper (RP) perovskites opens doors to myriad quantum optoelectronic applications. However, it is not clear whether moiré excitons and flat bands can be formed in such heterostructures. Here, we predict from first principles that twisted homobilayers of RP perovskite, MA₂PbI₄, can host moiré excitons and yield flat energy bands. The moiré excitons exhibit unique and hybridized characteristics with electrons confined in a single layer of a striped distribution while holes localized in both layers. Nearly flat valence bands can be formed in the bilayers with relatively large twist angles, thanks to the presence of hydrogen bonds that strengthen the interlayer coupling. External pressures can further increase the interlayer coupling, yielding more localized moiré excitons and flatter valence bands. Finally, electrostatic gating is predicted to tune the degree of hybridization, energy, position and localization of moiré excitons in twisted MA₂PbI₄ bilayers.

Excitonic states in twisted MA₂PbI₄ bilayers were calculated by first-principles calculations.     

On the Kernel of Restriction of Characters*

Let G be a finite group, H be a proper subgroup of G, and S be a unitary subring of C. The kernel of the restriction map S[Irr(G)] → S[Irr(H)] as a ring homomorphism is studied. As a corollary, the main result in [Isaacs, I. M. and Navarro, G., Injective restriction of characters, Arch. Math., 108, 2017, 437–439] is reproved.     

Tensor products of coherent configurations

A Cartesian decomposition of a coherent configuration ✗ is defined as a special set of its parabolics that form a Cartesian decomposition of the underlying set. It turns out that every tensor decomposition of ✗ comes from a certain Cartesian decomposition. It is proved that if the coherent configuration ✗ is thick, then there is a unique maximal Cartesian decomposition of ✗; i.e., there is exactly one internal tensor decomposition of ✗ into indecomposable components. In particular, this implies an analog of the Krull–Schmidt theorem for the thick coherent configurations. A polynomial-time algorithm for finding the maximal Cartesian decomposition of a thick coherent configuration is constructed.     

非对称碰撞约束下形状记忆合金梁的随机响应与分岔

形状记忆合金(SMA)是二十一世纪具有形状记忆效应的新型智能材料.针对具有非对称约束的SMA梁,本文构造了碰撞振动系统.在无碰撞和有碰撞两种情况下,利用随机平均法给出了近似解析结果.数值模拟作为验证解析结果的工具.结果表明,系统能量的概率响应曲线具有非光滑特性.当约束位置发生变化时,系统会出现随机P分岔和D分岔.     

The distribution of 4-full numbers

Let Q(x) denote the number of 4-full numbers not exceeding x. It is well known that $$Q(x) = \sum\limits_{j = 4}^7 {r_j x^{1/j} + R(x)}$$ where $$r_j = \mathop {res}\limits_{s = 1/j} (F(s)/s), F(s) = \mathop \prod \limits_P \left( {1 + \frac{{p^{ - 4s} }}{{1 - p^{ - s} }}} \right)$$ and R(x) is the remainder. This paper proves that $$R(x) \ll x^{3626/35461 + \varepsilon }$$ where ε is any positive number.