也谈关于参照系的选取——对“椭圆摆的一种实现方法”一文的商榷

本文旨在指出相关文献中关于质点轨迹结果中的错误,并利用不同于相关文献的惯性参照系,给出修正和改进后的结果．     

Studies of closed orbit correction and slow orbit feedback for the SSRF storage ring

Details of the active ways to suppress Closed Orbit Distortion （COD）, including bending magnet sorting and survey and alignment of the magnets, are discussed based on the studies of affections to the COD by the bending magnet field error and the misalignment of quadrupoles. The closed orbit correction and the Slow Orbit Feed Back （SOFB） system for the SSRF storage ring are presented in this paper. With these available methods, better results were obtained during the commissioning period with 3 GeV beam energy.     

Orbit response matrix analysis and lattice periodicity restoration of the SSRF storage ring

In this paper, we present numerically and experimentally the linear beam-optics distortion in the SSRF storage ring and the correction of optics by using a number of quadrupole magnets installed in the storage ring. The measured orbit-response matrices were fitted to the model-response matrices to obtain the β and the dispersion functions in the storage ring. By readjusting the currents of quadrupole-magnet power supplies, we were able to successfully restore the optics parameters to values very close to the design ones, with rms deviations around 1%. This periodicity restoration is verified with the β function measurement.     

Spin–orbit coupling and semiclassical electron dynamics in noncentrosymmetric metals

Spin–orbit coupling of electrons with the crystal lattice plays a crucial role in materials without inversion symmetry, lifting spin degeneracy of the Bloch states and endowing the resulting nondegenerate bands with complex spin textures and topologically nontrivial wavefunctions. We present a detailed symmetry-based analysis of the spin–orbit coupling and the band degeneracies in noncentrosymmetric metals. We systematically derive the semiclassical equations of motion for fermionic quasiparticles near the Fermi surface, taking into account both the spin–orbit coupling and the Zeeman interaction with an applied magnetic field. Some of the lowest-order quantum corrections to the equations of motions can be expressed in terms of a fictitious “magnetic field” in the momentum space, which is related to the Berry curvature of the band wavefunctions. The band degeneracy points or lines serve as sources of a topologically nontrivial Berry curvature. We discuss the observable effects of the wavefunction topology, focusing, in particular, on the modifications to the Lifshitz–Onsager semiclassical quantization condition and the de Haas-van Alphen effect in noncentrosymmetric metals.     

在有心力场中行星运行轨道稳定性的证明

从粒子的基本运动方程出发,利用非线性动力学的方法证明了行星在有心力场中运行轨道的稳定性,得到结论:粒子在有心力F=-k2m2r-n的作用下运行时,轨道稳定的条件是n<3.     

一类生化反应微分方程的定性分析

对一类生化反应模型x=δ-ax-xpyq,y=xpyq-by(δ>0,b>0,a>0,p 1,q>1)进行了研究.讨论了系统平衡点的稳定性态,对系统极限环的位置做出了估计.同时讨论了系统无环的充分条件以及极限环存在惟一性条件.     

Emissive or Nonemissive? A Theoretical Analysis of the Phosphorescence Efficiencies of Cyclometalated Platinum(II) Complexes

We herein report a theoretical analysis based on a density functional theory/time‐dependent density functional theory (DFT/TDDFT) approach to understand the different phosphorescence efficiencies of a family of cyclometalated platinum(II) complexes: [Pt(NCN)Cl] ( 1 ; NCN=1,3‐bis(2‐pyridyl)phenyl^?), [Pt(CNN)Cl] ( 2 ; CNN=6‐phenyl‐2,2′‐bipyridyl^?), [Pt(CNC)(CNPh)] ( 3 ; CNC=2,6‐diphenylpyridyl^2?), [Pt(R‐CNN)Cl] ( 4 ; R‐CNN=3‐(6′‐(2′′‐naphthyl)‐2′‐pyridyl)isoquinolinyl^?), and [Pt(R‐CNC)(CNPh)] ( 5 ; R‐CNC=2,6‐bis(2′‐naphthyl)pyridyl^2?). By considering both the spin–orbit coupling (SOC) and the electronic structures of these complexes at their respective optimized singlet ground (S₀) and first triplet ( ) excited states, we were able to rationalize the experimental findings that 1) 1 is a strong emitter while its isomer 2 is only weakly emissive in CH₂Cl₂ solution at room temperature; 2) although the cyclometalated ligand of 3 has a higher ligand‐field strength than that of 1 , 3 is nonemissive in CH₂Cl₂ solution at 298 K; and 3) extension of π conjugation at the lateral aryl rings of the cyclometalated ligands of 2 and 3 to give 4 and 5 , respectively, leads to increased emission quantum yields under the same conditions. We found that Jahn–Teller and pseudo‐Jahn–Teller effects are operative in complexes 2 and 3 , respectively, on going from the optimized S₀ ground state to the optimized excited state, and thus lead to large excited‐state structural distortions and hence fast nonradiative decay. Furthermore, a strong‐field ligand may push the two different occupied d orbitals so far apart that the SOC effect is small and the radiative decay rate is slow. This work is an example of electronic‐structure‐driven tuning of the phosphorescence efficiency, and the DFT/TDDFT approach is demonstrated to be a versatile tool for the design of phosphorescent materials with target characteristics.     

Quantum‐chemical study of the singlet oxygen emission

Intensity distribution in rotational lines of the 0–0 band of the a¹Δ_g → X³Σ transition in the oxygen molecule at λ = 1270 nm is studied by quadratic response (QR) method in a framework of multiconfiguration self‐consisted field (MCSCF) theory. The distance dependence of the transition magnetic moment and the (0–0)/(0–1) bands intensity ratio are calculated. A short review of previous theory of the red and infrared atmospheric oxygen bands and of their enhancement by collisions is presented to analyze and compare the new results. Enhancement of these bands in O₂ collisions with Li₂ and N₂ molecules is calculated by QR method. Diamagnetic species simulate solvent molecules of different optical polarizability. Specific influence of collisions on vibronic bands is stressed. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Magnitude of Finite‐Nucleus‐Size Effects in Relativistic Density Functional Computations of Indirect NMR Nuclear Spin–Spin Coupling Constants

A spherical Gaussian nuclear charge distribution model has been implemented for spin‐free (scalar) and two‐component (spin–orbit) relativistic density functional calculations of indirect NMR nuclear spin–spin coupling (J‐coupling) constants. The finite nuclear volume effects on the hyperfine integrals are quite pronounced and as a consequence they noticeably alter coupling constants involving heavy NMR nuclei such as W, Pt, Hg, Tl, and Pb. Typically, the isotropic J‐couplings are reduced in magnitude by about 10 to 15 % for couplings between one of the heaviest NMR nuclei and a light atomic ligand, and even more so for couplings between two heavy atoms. For a subset of the systems studied, viz. the Hg atom, Hg₂²⁺, and Tl? X where X=Br, I, the basis set convergence of the hyperfine integrals and the coupling constants was monitored. For the Hg atom, numerical and basis set calculations of the electron density and the 1s and 6s orbital hyperfine integrals are directly compared. The coupling anisotropies of TlBr and TlI increase by about 2 % due to finite‐nucleus effects.     

<Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript>-singular dichotomy for orbital measures of classical simple Lie algebras

We prove that the G-invariant orbital measures supported on adjoint orbits in the Lie algebra of a classical, compact, connected, simple Lie group satisfy a smoothness dichotomy: Either μ ^k is singular to Lebesgue measure or μ ^k ∈ L ². The minimum k for which μ ^k ∈ L ² is specified and is also the minimum k such that the k-fold sum of the orbit has positive measure. S. K. Gupta appreciates the hospitality of the Department of Pure Mathematics at the University of Waterloo where some of this research was done. K. E. Hare was supported in part by NSERC.