Groups,group actions and fields definable in first‐order topological structures

Given a group (G, ·), G?M^m, definable in a first‐order structure $\mathcal {M}=(M,\ldots )Given a group (G, ·), G?M^m, definable in a first‐order structure $\mathcal {M}=(M,\ldots )$ equipped with a dimension function and a topology satisfying certain natural conditions, we find a large open definable subset V?G and define a new topology τ on G with which (G, ·) becomes a topological group. Moreover, τ restricted to V coincides with the topology of V inherited from M^m. Likewise we topologize transitive group actions and fields definable in $\mathcal {M}$. These results require a series of preparatory facts concerning dimension functions, some of which might be of independent interest.     

Dynamic evolution of transverse energy flow in focused asymmetric optical vector-vortex beams

We present here controlled generation of asymmetric optical vector-vortex beams using a two-mode optical fiber and study the dynamic evolution of the transverse energy flow (TEF) when focused through a spherical lens. The dependence of the TEF on various factors such as the vortex charge, vortex anisotropy and polarization structure around the vortex core is explored. It is found that the TEF is directly proportional to the phase gradient and its direction is governed by the vortex charge. The presence of C-point polarization singularity in the beam and the polarization structure around it results in vibrational phase gradient which is the major factor deciding the TEF in vector-vortex beams.     

Sm1－xGdxA12低温下的磁性

分别测量了Sm1-xGdxAl2在低温下不同外加磁场时的电阻和磁化率.实验 结果表明，铁磁性物质Sm1-xGdxAl2在居里温度以下时，自旋磁矩和轨 道磁矩反平行有序排列，且对温度的依赖关系不同，导致在磁性抵消点出现自旋铁磁有序而 总磁矩为零的磁现象.并发现外加强磁场时自旋 轨道发生翻转. 关键词： Sm1-xGdxAl2 铁磁有序 自旋磁矩 轨道磁矩     

Af+AB星型聚合体系的统计热力学

应用统计力学和热力学原理研究了 A_f+AB星型聚合体系的性质. 首先从两种不同的角度给出了与聚合反应相应的配分函数, 并据此得到反应体系的平衡自由能、质量作用定律及数量分布函数, 进而得到了体系的平衡状态方程和比热. 在此基础上, 以反应体系的回转半径为例研究了溶剂效应对星型高分子空间尺度的影响.     

基于哈密顿动力系统新变分原理的保辛算法之二：算法保辛性质证明

文献[1]给出了哈密顿系统的一个新的变分原理,并基于此变分原理,通过选择一个时间步长两端不同广义位移或广义动量为独立变量,给出了四种不同类型的求解哈密顿动力系统的数值方法。本文将分别证明这四类数值方法都是保辛的数值方法。     

Ionization Energies and Dyson Orbials of Allyl Alcohol and Allyl Mercaptan Conformers

The conformers of allyl alcohol and allyl mercaptan were studied with B3LYP/aug-cc-pVTZ method. Their relative energies were calculated at MP3, MP4(SDQ), and CCSD(T) levels. The most stable conformers for these two molecules are Gauche-gauche' (Gg'). The theo-retical photoelectron spectra simulated with the calculated ionization energies demonstrate that there are at least four conformers in allyl alcohol and four conformers in allyl mercaptan in the gas-phase experiments. The Dyson orbitals of the highest occupied molecular orbital (HOMO) and the next HOMO (HOMO-1) of allyl mercaptan Gg' conformer show strongly mixing n_S and π_C=C characteristics, which may be due to the resonance and inductive effects between π_C=C and n_S in HOMO-1 and HOMO.     

State-of-the-art and prospects for orbital dynamics and control near small celestial bodies

小天体探测是未来深空探测的重点领域之一, 而小天体附近轨道动力学与控制问题是小天体探测任务迫切需要解决的关键问题. 该问题涉及形状不规则小天体附近的动力学环境建模与小天体附近轨道动力学机理. 本文从不规则形状小天体引力场的建模、小天体附近的自然轨道动力学、小天体附近的受控轨道动力学3 个方面综述了小天体附近轨道动力学与控制的研究现状与发展趋势, 并分析了小天体附近轨道动力学所面临的挑战与难题, 最后对我国未来小天体探测任务可能涉及的轨道动力学与控制问题的发展方向进行了展望.     

Methyl orbital signatures in 2-amino-1-propanol

Electron density distributions of 2-aminoethanol (2AE) and 2-amino-1-propanol (2AP) are calculated in both the coordinate and the momentum spaces using the B3LYP/TZVP method. Using the dual space analysis, molecular orbital signatures of the methyl substituent in 2AP are identified with respect to 2AE. Relaxations of the geometry and the valence orbital in 2AP are found to be due to the insertion of the methyl group. Five orbitals, not four orbitals, are identified as the methyl signatures. They are orbital 5a in the core shell, orbitals 9a and 10a in the inner valence shell, and orbitals 15a and 16a in the outer valence. In the inner valence shell, the attachment of methyl to 2AE causes a splitting of its orbital 8a into orbitals 9a and 10a of 2AP, whereas in the outer valence shell, the methyl group results in the insertion of an additional orbital pair of 15a and 16a. The frontier molecular orbitals 21a, 20a, and 19a are found to have no significant role in the methylation of 2AE.     

Conformation effects on the molecular orbitals of serine

This paper calculates the five most stable conformers of serine with Hartree--Fock theory, density functional theory (B3LYP), Moller--Plesset perturbation theory (MP4(SDQ)) and electron propagation theory with the 6-311++G(2d,2p) basis set. The calculated vertical ionization energies for the valence molecular orbitals of each conformer are in agreement with the experimental data, indicating that a range of molecular conformations would coexist in an equilibrium sample. Information of the five outer valence molecular orbitals for each conformer is explored in coordinate and momentum spaces using dual space analysis to investigate the conformational processes, which are generated from the global minimum conformer Ser1 by rotation of C₂--C₃ (Ser4), C₁--C₂ (Ser5) and C₁--O₂ (Ser2 and Ser3). Orbitals 28a, 27a and 26a are identified as the fingerprint orbitals for all the conformational processes.     

Hamiltonian and Path Integral Quantization of the Conformally Gauge-Fixed Polyakov D1 Brane Action in the Presence of a Scalar Dilation Field

The conformally gauge-fixed Polyakov D1 brane action in the presence of a scalar dilaton field is seen to be a constrained system in the sense of Dirac. In the present work we study its Hamiltonian and path integral quantization in the instant-form of dynamics using the equal world-sheet time framework.