A note on some piecewise-linear difference equations with Mersenne-type periodic solutions

This paper studies solutions of some piecewise-linear difference equations. In two particular cases, a descent argument is used to show that all solutions are periodic with either prime period 3(2 ^k  ? 1) or 6(2 ^k  ? 1) for some k ≥ 1. The existence of solutions with such periods is also considered.     

Rotational excitation of CH<Subscript>4</Subscript> by He atoms

Quantum close-coupling and coupled-state approximation scattering calculations for rotational energy transfer of rotationally excited CH₄ due to collisions with He are presented for collision energies between 10⁻⁷ and 3000 cm⁻¹ using the MP4 potential of Calderoni et al. [J. Chem. Phys. 121, 8261 (2004)]. State-to-state cross sections and rate coefficients from selected initial rotational states of CH₄ in symmetries A, E, and F are studied from the ultra-cold to the thermal regime. Comparison of the cross sections with available theoretical results and experimental data show good agreement. Applications to astrophysics and cold laboratory environments are briefly addressed.     

ESI‐MS/MS of expanded porphyrins: a look into their structure and aromaticity

Electrospray mass spectrometry/mass spectrometry was used to investigate the gas‐phase properties of protonated expanded porphyrins, in order to correlate those with their structure and conformation. We have selected five expanded meso‐pentafluorophenyl porphyrins, respectively, a pair of oxidized/reduced fused pentaphyrins (22 and 24 π electrons), a pair of oxidized/reduced regular hexaphyrins (26 and 28 π electrons) and a regular doubly N‐fused hexaphyrin (28 π electrons). The gas‐phase behavior of the protonated species of oxidized and reduced expanded porphyrins is different. The oxidized species (aromatic Hückel systems) fragment more extensively, mainly by the loss of two HF molecules. The reduced species (Möbius aromatic or Möbius‐like aromatic systems) fragment less than their oxidized counterparts because of their increased flexibility. The protonated regular doubly fused hexaphyrin (non‐aromatic Hückel system) shows the least fragmentation even at higher collision energies. In general, cyclization through losses of HF molecules decreases from the aromatic Hückel systems to Möbius aromatic or Möbius‐like aromatic systems to non‐aromatic Hückel systems and is related to an increase in conformational distortion. Copyright © 2016 John Wiley & Sons, Ltd.     

O3+与H2碰撞中解离电子俘获过程的全量子计算

利用全量子的分子轨道强耦合方法,我们研究了基态的O3+(2s22p2P)与氢分子碰撞的解离电荷转移过程.分子轨道强耦合计算中采用了自旋耦合价带理论计算的三原子分子势能面和径向耦合矩阵元.对氢分子的自身转动,我们采用无限阶的冲量近似方法.在入射离子能量为0.1 eV/u到500 eV/u的能量区间,我们得到了非解离碰撞过程的振动态选择单电子俘获截面和解离碰撞过程的单电子俘获微分截面,发现解离碰撞截面大约占非解离过程的10%.这表明在实际的应用中,必须包含解离俘获过程的贡献.