Spin–orbit coupling in oxygen containing diradicals

Intermediate diradicals which occur in the Paterno–Büchi photocycloaddition and in the Norrish type I photoreactions have been calculated taking into account the spin–orbit coupling (SOC) between the singlet (S) and triplet (T) states. Reaction paths for the photocycloaddition of formaldehyde to ethene and the diradical products of the α-cleavage of cyclohexanone have been optimized by the MNDO CI method for a number of different singlet and triplet states. SOC integrals are calculated by an effective one-electron approximation. Intermediate diradicals in the Paterno–Büchi reaction and the SOC effects are also studied ab initio with CAS SCF geometry optimization in a TZV basis set. Both methods predict a large SOC matrix element between the S and T states in the course of the C–C attack, while the SOC integral is two orders of magnitude smaller for the diradical produced in the C–O attack. In the Norrish type I photoreaction the oxygen atom also produces some nonzero contribution to the SOC integral which governs intersystem crossing in a ·C–C· diradical. For the diradicals produced by the α-cleavage of cyclohexanone a vibronic interaction is responsible for the SOC mixing between the lowest S and T states. The importance of one-center versus two-center SOC contributions in diradicals is briefly discussed.     

Hypersurfaces of prescribed mean curvature enclosing a given body

Given a smooth domain Ω in ℝ ^m+1 with compact closure and a smooth integrable functionh: ℝ ^m+1→ℝ satisfyingh(x)≥H _∂Ω (x) on ∂Ω whereH _∂ω denotes the mean curvature of ∂Ω calculated w.r.t. the interior unit normal we show that there is a setA⊂ℝ ^m+1 with the properties andH _∂A=h on ∂A.     

合肥电子储存环基本参数的测量

 为了给改造后的合肥储存环留下参考数据,同时为了找到储存环存在的物理问题,储存环特性参数首次被系统测量,它们是动量扩张因子、色散函数、自然色品、校正色品和中心频率。     

Dynamics and formation of vortices collapsed from ring dark solitons in a two-dimensional spin–orbit coupled Bose–Einstein condensate

We consider the dynamics and formation of vortices from ring dark solitons in a two-dimensional Bose–Einstein condensate with the Rashba spin–orbit coupling based on the time-dependent coupled Gross–Pitaevskii equation. Compared with previous results, the system exhibits complex dynamical behaviors in the presence of the spin–orbit coupling. With the modulation of the spin–orbit coupling, not only the lifetime of ring dark solitons is greatly prolonged, but also their attenuation kinetics is significantly affected. For two shallow ring dark solitons with the equal strength of the spin–orbit coupling, the radius of ring dark solitons increases to a maximum value over time and then shrinks into a minimum value. Due to the effect of the snake instability, ring dark solitons split into a series of ring-like clusters of vortex pairs, which perform complex oscillations. This indicates that the system is strongly dependent on the presence of the spin–orbit coupling. Furthermore, the effect of different initial modulation depths on the dynamics of ring dark solitons is investigated.     

人造地球卫星运动方程的代数动力学算法数值解

代数动力学算法首次被用于求人造地球卫星运动方程的数值解，在四阶算法下，与Runge-Kutta算法和辛算法的计算结果作了比较.结果表明，代数动力学算法对于人造地球卫星长期轨道的计算有较高的精度.并讨论了地球四极和八极带谐项对卫星轨道的影响. 关键词： 人造地球卫星运动方程 代数动力学算法数值解 地球四极和八极带谐项对卫星轨道的影响     

自适应光学系统对实际大气湍流波前的时域校正效果

引入时域校正因子（系统团环校正波前残余误差与系统开环时的湍流波前扰动误差之比）和系统测量信噪比,分析了自适应光学系统对实际大气湍流扰动的时域校正效果与湍流功率指数、湍流功率谱转折频率、系统测量信噪比、系统时间延迟以及系统闭环带宽的关系,并给出了系统的最佳闭环带宽。此外还分析了弱光61单元自适应学系统的时域校正效果。     

Equilibrium,pseudoequilibrium and sliding-mode heteroclinic orbit in a Filippov-type plant disease model

Plant diseases have caused tremendous crop losses and have massive impacts on food security and environment. Modeling the spread of plant diseases and understanding the dynamics of the resulting plant disease models may provide practical insights on designing effective control measures. In this paper, by incorporating cultural strategies and economic threshold policy, we present a Filippov-type plant disease model. The resulting model has state dependent discontinuous right-hand side and thus non-smooth analysis and generalized Lyapunov approach are employed for model analysis. We show that the model exhibits the phenomena of stable equilibrium, unstable pseudoequilibrium as well as sliding-mode heteroclinic orbit. Biological implications of our results in implementing control strategies for plant diseases are also discussed.     

Statistical inference and modelling of momentum in stock prices

The following results are obtained, (i) It is possible to obtain a time series of market data {y(t)} in which the fluctuations in fundamental value have been compensated for. An objective test of the efficient market hypothesis (EMH), which would predict random correlations about a constant value, is thereby possible, (ii) A time series procedure can be used to determine the extent to which the differences in the data and the moving averages are significant. This provides a model of the form y(t)-y(t-l)=0.5{y(t- l)-y(t-2)}+ε(t)+0.8ε(r-1) where ε(t) is the error at time t, and the coefficients 0.5 and 0.8 are determined from the data. One concludes that today's price is not a random perturbation from yesterday's; rather, yesterday's rate of change is a significant predictor of today's rate of change. This confirms the concept of momentum that is crucial to market participants. (iii) The model provides out-of-sample predictions that can be tested statistically. (iv) The model and coefficients obtained in this way can be used to make predictions on laboratory experiments to establish an objective and quantitative link between the experiments and the market data. These methods circumvent the central difficulty in testing market data, namely, that changes in fundamentals obscure intrinsic trends and autocorrelations. This procedure is implemented by considering the ratio of two similar funds (Germany and Future Germany) with the same manager and performing a set of statistical tests that have excluded fluctuations in fundamental factors. For the entire data of the first 1149 days beginning with the introduction of the latter fund, a standard runs test indicates that the data is 29 standard deviations away from that which would be expected under a hypothesis of random fluctuations about the fundamental value. This and other tests provide strong evidence against the efficient market hypothesis and in favour of autocorrelations in the data. An ARIMA time series finds strong evidence (9.6 and 21.6 standard deviations in the two coefficients) that the data is described by a model that involves the first difference, indicating that momentum is the significant factor. The first quarter's data is used to make out-of-sample predictions for the second quarter with results that are significant to 3 standard deviations. Finally, the ARIMA model and coefficients are used to make predictions on laboratory experiments of Porter and Smith in which the intrinsic value is clear. The model's forecasts are decidedly more accurate than that of the null hypothesis of random fluctuations about the fundamental value.     

Comment on ‘Ab initio study: the potential energy curves and rovibrational spectrum of low-lying excited states of HCl+ cation’ (Molecular Physics, 114:19, 2817–2823)

In a recent article, Y. Liu, X. Cheng, H. Cheng, J. Cheng and X. Song [Mol. Phys., 114:19, 2817–2823] report on the calculation of potential energy curves and the derivation of spectroscopic constants and line intensities for the lowest energy electronic states of HCl⁺. There are several shortcomings in the article; the most notable being the incorrect ordering of the ²П_3/2 and ²П_1/2 state energies, erroneous selection rules, which lead to the absence of a Q-branch in their predicted spectra, incorrect Höln–London factors, and a missing appendix.     

Full four‐component relativistic calculations of the one‐bond 77Se–13C spin‐spin coupling constants in the series of selenium heterocycles and their parent open‐chain selenides

Four‐component relativistic calculations of ⁷⁷Se–¹³C spin–spin coupling constants have been performed in the series of selenium heterocycles and their parent open‐chain selenides. It has been found that relativistic effects play an essential role in the selenium–carbon coupling mechanism and could result in a contribution of as much as 15–25% of the total values of the one‐bond selenium–carbon spin‐spin coupling constants. In the overall contribution of the relativistic effects to the total values of ¹J(Se,C), the scalar relativistic corrections (negative in sign) by far dominate over the spin‐orbit ones (positive in sign), the latter being of less than 5%, as compared to the former (ca 20%). A combination of nonrelativistic second‐order polarization propagator approach (CC2) with the four‐component relativistic density functional theory scheme is recommended as a versatile tool for the calculation of ¹J(Se,C). Solvent effects in the values of ¹J(Se,C) calculated within the polarizable continuum model for the solvents with different dielectric constants (ε 2.2–78.4) are next to negligible decreasing negative ¹J(Se,C) in absolute value by only about 1 Hz. The use of the locally dense basis set approach applied herewith for the calculation of ⁷⁷Se–¹³C spin‐spin coupling constants is fully justified resulting in a dramatic decrease in computational cost with only 0.1–0.2‐Hz loss of accuracy. Copyright © 2014 John Wiley & Sons, Ltd.