On warped product manifolds satisfying some curvature conditions

We determine curvature properties of pseudosymmetric type of certain warped product manifolds, and in particular of generalized Robertson–Walker spacetimes, with Einsteinian or quasi-Einsteinian fibre.     

基于非线性时间序列分析经验模态分解和小波分解异同性的研究

基于经验模态分解(EMD）的希尔伯特变换（HT），是对非线性时间序列基于EMD进行分解， 然后通过HT获得频谱.利用理想时间序列和青藏高原古里雅冰芯¹⁸O时 间序列 ，系统地分析比较了EMD和小波分解(WD）以及HT和小波变换在非线性时间序列处理中的优劣 ，并针对它们各自的缺点提出了可能改进的设想.研究结果表明，将基于EMD的方法和基于WD 的方法有机结合起来应用，可以更有效地识别原时间序列的特征信息. 关键词： 经验模态分解 小波分解 理想时间序列 古里雅冰芯     

A remark on the disconnected nature of Lagrange equations in the context of a linear-scaling implementation of the coupled-cluster energy gradients

It is known that the Λ-tensor (an array of Lagrange multipliers), necessary for evaluating analytic energy gradients in the coupled-cluster theory, is diagrammatically disconnected in general. This means that the number of non-negligible elements in the Λ-tensor grows faster than linearly with the number of calculated particles. At a formal level, when evaluating the gradients of the coupled-cluster energy, this could prevent obtaining a linear scaling of the operational cost with respect to the number of correlated particles. It is shown that in ground/excited-state coupled-cluster calculations, based on localized orbitals, the disconnected part of the Λ-tensor, as well as the disconnected part of the left-hand excited-state eigenvector, can be ignored, thus justifying the use of standard screening techniques employed in linear-scaling schemes.     

The spin-isospin decomposition of the nuclear symmetry energy from low to high density

The energy per particle BA in nuclear matter is calculated up to high baryon density in the whole isospin asymmetry range from symmetric matter to pure neutron matter.The results,obtained in the framework of the Brueckner-Hartree-Fock approximation with two-and three-body forces,confirm the well-known parabolic dependence on the asymmetry parameterβ=(N?Z)/A(β^2 law)that is valid in a wide density range.To investigate the extent to which this behavior can be traced back to the properties of the underlying interaction,aside from the mean field approximation,the spin-isospin decomposition of BA is performed.Theoretical indications suggest that theβ^2 law could be violated at higher densities as a consequence of the three-body forces.This raises the problem that the symmetry energy,calculated according to theβ^2 law as a difference between BA in pure neutron matter and symmetric nuclear matter,cannot be applied to neutron stars.One should return to the proper definition of the nuclear symmetry energy as a response of the nuclear system to small isospin imbalance from the Z=N nuclei and pure neutron matter.     

单原子催化剂Ir1/MoS2表面上的NH3吸附与直接分解的第一性原理

NH₃的催化分解一直是制备高纯度氢的有效途径之一,因此具有良好的催化活性的贵金属被广泛的应用于催化解离的研究中.然而,由于纯金属催化剂的利用效率低,增加催化成本.最近的研究发现单原子催化剂Ir₁/MoS₂以其突出的优势被认为是一种潜在的能替代现有贵金属催化剂的材料.本文采用密度泛函理论与周期性平板模型相结合的方法,研究了NH₃在单原子催化剂Ir₁/MoS₂上的吸附与活化.结果表明:NH₃的优势吸附位为Ir原子的顶位,构型为倾斜结构(atop),NH₃与体系表面的金属Ir成键,吸附能达到1.63 eV,是化学吸附;进一步分析了NH₃直接催化分解的反应路径,给出了相应的反应热、活化能,结果显示NH₃在atop位的解离比脱附有利,第一步脱氢反应活化能最小,N-H键易断裂,第二步反应能垒较高,此步为整个反应的决速步.     

On some meaningful inner product for real Klein—Gordon fields with positive semi-definite norm

A simple derivation of a meaningful, manifestly covariant inner product for real Klein—Gordon (KG) fields with positive semi-definite norm is provided, which turns out — assuming a symmetric bilinear form — to be the real-KG-field limit of the inner product for complex KG fields reviewed by A. Mostafazadeh and F. Zamani in December 2003, and February 2006 (quant-ph/0312078, quant-ph/0602151, quant-ph/0602161). It is explicitly shown that the positive semi-definite norm associated with the derived inner product for real KG fields measures the number of active positive and negative energy Fourier-modes of the real KG field on the relativistic mass shell. The very existence of an inner product with positive semi-definite norm for the considered real, i.e. neutral, KG fields shows that the metric operator entering the inner product does not contain the charge-conjugation operator. This observation sheds some additional light on the meaning of the C operator in the CPT inner product of PT-symmetric quantum mechanics defined by C.M. Bender, D.C. Brody and H.F. Jones.     

甲硅烷的分解复合的对称性

本文基于原子分子反应静力学证明甲硅烷SiH4的分解方式Ⅱ是对称性允许的,而分解方Ⅰ是对称性不许可的.     

Symmetry and general symmetry groups of the coupled Kadomtsev--Petviashvili equation

In this paper, the Lie symmetry algebra of the coupled Kadomtsev--Petviashvili (cKP) equation is obtained by the classical Lie group method and this algebra is shown to have a Kac--Moody--Virasoro loop algebra structure. Then the general symmetry groups of the cKP equation is also obtained by the symmetry group direct method which is proposed by Lou et al。 From the general symmetry groups, the Lie symmetry group can be recovered and a group of discrete transformations can be derived simultaneously. Lastly, from a known simple solution of the cKP equation, we can easily obtain two new solutions by the general symmetry groups.     

Simulation of SIMS for monomer and dimer of lignin under the assumption of thermal decomposition using QMD method

The thermal decomposition of the monomer and dimer of lignin has been simulated by a quantum molecular dynamics (DMD) method. In the calculation, we controlled the total energy of the system using Nóse-Hoover thermostats in the total energy range of 0.69-0.95 eV, and the sampling position data with a time step of 0.5 fs were carried out up to 3000 (1.5 ps) or 5000 (2.5 ps) steps in ab initio and semiempirical MO methods, respectively. We obtained the thermally decomposed fragments with positive, neutral and negative charges from SCF MO calculation at each data of the last MD step, and simulated the fragment distribution of the monomer and dimer lignins from the last step in 30-40 runs. Simulated mass numbers of positively and negatively charged fragments for lignin monomer and dimer showed considerably good accordance with the experimental results in TOF-SIMS observed by Saito and co-workers.     

Spin and Pseudospin Symmetries of Dirac Equation and the Yukawa Potential as the Tensor Interaction

Considering of a tensor interaction in Dirac equation removes the degeneracy in spin and pseudospin doublets and consequently leads to results consistent with the experimental data. Here, instead of the commonly used Coulomb or linear terms, we investigate a tensor interaction of Yukawa form. We obtain arbitrary state solutions of Dirac equation under vector, scalar and tensor Yukawa potentials via a physical approximation and the Nikiforov-Uvarov methodology. The solutions are discussed in detail.     

Approximate homotopy similarity reduction for the generalized Kawahara equation via Lie symmetry method and direct method

<正>This paper studies the generalized Kawahara equation in terms of the approximate homotopy symmetry method and the approximate homotopy direct method.Using both methods it obtains the similarity reduction solutions and similarity reduction equations of different orders,showing that the approximate homotopy direct method yields more general approximate similarity reductions than the approximate homotopy symmetry method.The homotopy series solutions to the generalized Kawahara equation are consequently derived.     

模态分解法在非恒同耦合系统同步研究中的推广

通过改变耦合函数将模态分解法进行了推广,应用于非恒同耦合系统同步的研究.详细研究了周期吸引子、概周期吸引子等非恒同耦合系统的同步,得到了同步的局部渐近稳定性条件.并进行了数值模拟,发现同步时动力学现象丰富.概周期吸引子耦合系统会出现稳定的周期、概周期同步解,由于耦合周期吸引子耦合系统会出现多个稳定的周期同步解,且其吸引域差别较大,均出现了同步的多值性.同时也验证了该方法的正确性.     

Spin and Pseudospin Symmetries of Dirac Equation and the Yukawa Potential as the Tensor Interaction

Considering of a tensor interaction in Dirac equation removes the degeneracy in spin and pseudospin doublets and consequently leads to results consistent with the experimental data. Here, instead of the commonly used Coulomb or linear terms, we investigate a tensor interaction of Yukawa form. We obtain arbitrary state solutions of Dirac equation under vector, scalar and tensor Yukawa potentials via a physical approximation and the Nikiforov-Uvarov methodology. The solutions are discussed in detail.     

The construction of conserved quantities for linearly coupled oscillators and study of symmetries about the conserved quantities

In this paper, the conserved quantities are constructed using two methods. The first method is by making an ansatz of the conserved quantity and then using the definition of Poisson bracket to obtain the coefficients in the ansatz. The main procedure for the second method is given as follows. Firstly, the coupled terms in Lagrangian are eliminated by changing the coordinate scales and rotating the coordinate axes, secondly, the conserved quantities are obtain in new coordinate directly, and at last, the conserved quantities are expressed in the original coordinates by using the inverse transform of the coordinates. The Noether symmetry and Lie symmetry of the infinitesimal transformations about the conserved quantities are also studied in this paper.     

耦合Burgers方程的对称性及对称约化

对称性分析是自然科学研究中的重要方法之一. 利用对称性分析研究了一个描述两层流体体系的模型即耦合Burgers方程的对称性. 利用对称性给出了这个模型的四种对称性约化并给出了这些约化方程的一些特殊的严格解,如有理解、行波孤立子解和非行波孤立子解. 关键词： 对称性约化 耦合Burgers方程 孤立子     

Ground state for CH2 and symmetry for methane decomposition

Using the different level of methods B3P86, BLYP, B3PW91, HF, QCISD、 CASSCF （4,4） and MP2 with the various basis functions 6-311G^＊＊, D95, cc-pVTZ and DGDZVP, the calculations of this paper confirm that the ground state is X^-3B1 with C2v group for CH2. Furthermore, the three kinds of theoretical methods, i.e. B3P86、 CCSD（T, MP4） and G2 with the same basis set cc-pVTZ only are used to recalculate the zero-point energy revision which are modified by scaling factor 0.989 for the high level based on the virial theorem, and also with the correction for basis set superposition error. These results are also contrary to X^-3∑^-g for the ground state of CH2 in reference. Based on the atomic and molecular reaction statics, this paper proves that the decomposition type （1） i.e. CH4 →CH2＋H2, is forbidden and the decomposition type （2） i.e. CH4→CHa＋H is allowed for CH4. This is similar to the decomposition of SiH4.     

HOF分子电离态的运动方程耦合簇研究

采用单双激发运动方程耦合簇(EOM-CCSD)以及多个包含迭代三激发在内的运动方程耦合簇变体(EOM-CCSDT-i,i=1a,1b,2,3和EOM-CC3)计算了HOF价层垂直电离势(VIP).在EOM-CCSD水平上优化出各价层电离态结构,得到绝热电离势(AIP),进一步计算出谐振频率.同时对称匹配簇组态相互作用(SAC/SAC-CI)也被应用到部分计算.结果显示:EOM-CC3、EOM-CCSDT-3计算的VIP接近于全三激发运动方程耦合簇EOM-CCSDT结果;EOM-CC与SAC-CI值基本一致;同时发现HOF光电子能谱实验在2A'态指认上有误并重新进行归属.HOF的第三VIP应为16.9 e V,而非光电子能谱实验测得的16.0 e V.     

引出口的几何参数对团簇形成影响的DSMC研究

利用直接模拟蒙特卡洛方法(DSMC),模拟了气体凝聚团簇源的引出口尺寸和中心位置不同的条件下,Cu团簇的尺寸分布以及模拟了随着时间的增长,腔内团簇数目的变化.模拟结果表明:引出口的直径越大,产生大团簇的比例越小;在引出口的直径相同的情况下,引出口的中心位置偏离坐标原点比在原点产生的大团簇的比例要大;随着时间的增长,腔内团簇数目先变多后变少.     

The molecular symmetry group of the CO dimer and the assignments of the intermolecular vibrations

Vibrational assignments for some of the lowest energy levels of the CO dimer have been derived purely spectroscopically on the basis of the molecular symmetry, nuclear spin statistics, observed selection rules, and sequence of the transition doublets. Most of the previous assignments of Surin et al. [L.A. Surin, D.N. Fourzikov, T.F. Giesen, S. Schlemmer, G. Winnewisser, V.A. Panfilov, B.S. Dumesh, G.W.M. Vissers, A. van der Avoird, J. Phys. Chem. A 111 (2007) 12238-12247] are confirmed in the present work, and are supported by much clear evidences. One significant revision of that analysis in the present work is identification of the torsional (out-of-plane) excited state, which had been assigned previously to an excited state of the geared (in plane) internal rotation.     

混合团簇Cu12A(A=Fe、Co、Ni)结构及能量特性的密度泛函研究

以Cu13非紧致低对称性基态结构及四种13原子高对称性(Ih、Oh、D5h、D3h)密堆积结构为初始构型,通过不等价位原子替换,利用密度泛函理论系统研究了Cu12A (A=Fe、Co、Ni)混合团簇的结构及能量特性.结果表明:Cu12 A(A=Fe、Co)团簇的基态结构均以Ih替换结构为主,且均倾向于中心位置替代的高对称性结构,而Cu12Ni团簇基态则为与Cu13类似的非紧致低对称性结构;Fe、Co、Ni三者对Cu13基态各不等价位替代结构稳定性序列基本相同,而对四种高对称性结构相应中心替代构型稳定性均高于表面替代构型(且Fe、Co均明显强于Ni);对各混合团簇基态结构均无明显同分异构现象.