Differential equations with almost periodic or conditionally periodic coefficients: Recurrence and reducibility

Recurrence of an individual trajectory of a linear nonautonomous differential equation on a compact Lie group for the case of an almost periodic or conditionally periodic dependence of the right-hand side on time is proved. The relation between recurrence and reducibility is examined.Translated fromMatematicheskie Zametki, Vol. 64, No. 2, pp. 229–237, August, 1998.This research was supported by the Russian Foundation for Basic Research under grants No. 96-01-00378 and No. 96-15-96072.     

On the Category of Koszul Modules of Complexity One of an Exterior Algebra

In this paper, we prove that there is a natural equivalence between the category F1（x） of Koszul modules of complexity 1 with filtration of given cyclic modules as the factor modules of an exterior algebra A = ∧V of an m-dimensional vector space, and the category of the finite-dimensional locally nilpotent modules of the polynomial algebra of m - 1 variables.     

二元广义外代数的Hochschild同调群

设Aq=k／(x2,xy+qyx,y2)是含有两个变量的广义外代数,基于Buch- weitz等人构造的极小投射双模解,广义外代数的各阶Hochschild同调群的维数被清晰地计算．     

Limit sets for maps of the circle

A trick which reduces some questions concerning the dynamics of self-maps of the circle to similar questions about self-maps of the interval is suggested and applied to answer two questions of Block and Coppel.     

部分基因继承技术对带有对称编码的基因算法的影响

进一步讨论了带有对称编码的基因算法中采用的部分基因保留技术对算法性能的影响，确定了最佳基因保留量（２５％）及其选择范围（２０％～５０％），对算法的计算机实验所得到的结果表明，如果不采用这项技术，带有对称编码的基因算法的性能就会降低，所得到的解的质量就会下降。     

Exponential meshes and three‐dimensional computation of a magnetic field

We describe the simulation of an exterior problem using a magnetic field deriving from magnetostatics, with a numerical method mixing the approaches of C. I. Goldstein and L.‐A. Ying. This method is based on the use of a graded mesh obtained by gluing homothetic layers in the exterior domain. On this mesh, we use an edge elements discretization and a recently proposed mixed formulation. In this paper, we provide both a theoretical and numerical study of the method. We establish an error estimate, describe the implementation, propose some preconditioning techniques and show the numerical results. We also compare these results with those obtained from an equivalent boundary elements approach. In this way, we retain that our method leads to a practical numerical implementation, a saving of storage, and turns out to be an alternative to the classical boundary elements method. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 595–637, 2003     

基于补偿控制的无人地面车辆轨迹跟踪方法

针对无人地面车辆轨迹跟踪精度不高,鲁棒性差的问题,提出了一种基于补偿控制的算法。该算法分为运动学和动力学两部分：基于方向角调整策略的运动学控制律能确保无人地面车辆有效跟踪参考轨迹;基于PD与模型参考模糊滑模自适应控制相结合控制的动力学控制律能有效补偿建模不精确和外界扰动带来的影响。仿真结果表明：该算法能够有效跟踪参考轨迹,控制量分配合理且鲁棒性较好。     

Influence of collision energy and reagent vibrational excitation on the dynamics of the reaction H + LiH

We present a detailed quasiclassical trajectory (QCT) study of the dynamics corresponding to the reaction H + LiH proceeding via depletion and H‐exchange paths on a new potential energy surface of the electronic ground state. The effects of collision energy and reagent initial vibrational excitation on the reaction probability and cross sections are studied over a wide range of collision energies. The QCT‐calculated reaction probability and cross sections are in good agreement with previous time‐dependent wave packet results. More importantly, we found that the vibrational excitation of LiH molecule inhibits the LiH depletion reaction, whereas it promotes the H‐exchange reaction. In addition, the differential cross sections calculated for the depletion reaction at different collision energies and excitation states indicate a strong forward scattering of the product molecule H₂. © 2013 Wiley Periodicals, Inc.     

Functional and Basis Set Dependence for Time-Dependent Density Functional Theory Trajectory Surface Hopping Molecular Dynamics: Cis-Azobenzene Photoisomerization

Within three functionals (TD-B3LYP, TD-BHandHLYP, and TD-CAM-B3LYP) in combination with four basis sets (3-21g, 6-31g, 6-31g(d), and cc-pvdz), global switching (GS) trajectory surface hopping molecular dynamics has been performed for cis-to-trans azobenzene photoisomerization up to the S₁(nπ*) excitation. Although all the combinations show artificial double-cone structure of conical intersection between ground and first excited states, simulated quantum yields and lifetimes are in good agreement with one another; 0.6 (±5%) and 40.5 fs (±10%) by TD-B3LYP, 0.5 (±10%) and 35.5 fs (±4%) by TD-BHandHLYP, and 0.44 (±9%) and 35.2 fs (±10%) by TD-CAM-B3LYP. By analyzing distributions of excited-state population decays, hopping spots, and typical trajectories with performance of 12 functional/basis set combinations, it has been concluded that functional dependence for given basis set is slightly more sensitive than basis set dependence for given functional. The present GS on-the-fly time-dependent density functional theory (TDDFT) trajectory surface hopping simulation can provide practical benchmark guidelines for conical intersection driven excited-state molecular dynamics simulation involving in large complex system within ordinary TDDFT framework. © 2019 Wiley Periodicals, Inc.