Solution of ODE u＂ ＋ p（u）（u＇）^2＋ q（u） = 0 and Applications to Classifications of All Single Travelling Wave Solutions to Some Nonlinear Mathematical Physics Equations

Under the travelling wave transformation, some nonlinear partial differential equations such as Camassa-Holm equation, High-order KdV equation, etc., are reduced to an integrable ODE expressed by u＂ ＋p（u）（u＇）^2 ＋ q（u） = 0 whose generai solution can be given. Furthermore, combining complete discrimination system for polynomiai, the classifications of all single travelling wave solutions to these equations are obtained. The equation u＂＋p（u）（u＇）^2＋q（u） = 0 includes the equation （u＇）^2 = f（u） as a special case, so the proposed method can be also applied to a large number of nonlinear equations. These complete results cannot be obtained by any indirect method.     

最近物理学综述评论文献题录

88-145.r共振物理学:十年以后. ycnexu φu3.Hayk,152 (1987),No. 3,361—398.参92.88-146.电磁响应函数的一般性质.ycnexu　φu3.Hayk,152(1987),No.3,399— 422.参 37.88-147.离子晶体的热释电性、压电性、弯电性及热极 化效应.ycnexu　φu3.Hayk, 152(1987),No.3,423—448.参38.88-148.向温性液晶的表面物理.ycnexu φu3.Hayk,152(1987),No.3,449— 477.参 146.88-149.托卡玛克中边际等离[子]体物理学.ycnexu φu3.Hayk,152(1987),No. 3,479—492.参56.88-150 光散射和吸收相干旋光谱学中的干涉现象: 全息多维光谱学.ycnexu　φu3. …     

Cu + 掺杂口氧化铝光谱性能的研究

用离子交换工艺对提拉法生长的N a + 节氧化铝进行处理得到的c u+ 掺杂p 氧化铝在紫外光激发下孤立C u+ 和IC u+一c u+ 1 二聚物的发射光谱. 在双掺情况下, 伴随C u+ 掺入的阳离子(K + , 人g +) 提高了孤立C u+ 对{C u+一C u+ } 发射强度的比率, 发射带峰位也略有偏移, 在C u+ / K 十掺杂样品中新发现一个很强的3 9 知m 的荧光峰. 文章提供了单掺和双掺C u+ 一p 氧化铝的吸收、发射和激发谱数据并对各荧光发射带的机制进行了讨论。 关键词：     

AlO自由基在辐射场中的物理和光谱特性

AlO自由基在金属有机化学、催化材料、燃烧化学及天体物理学等领域受到人们的广泛关注,研究外辐射场下对AlO自由基的物理特性和光谱特征的影响将有助于更深入理解和增强在相关领域的应用。采用密度泛函理论B3PW91方法,在6-311+G(3df,2p)基组水平上优化了不同辐射场(-0.04~0.04 a.u.)下AlO自由基的基态稳定构型,用同样方法计算了该构型的分子结构、总能量、能隙以及红外光谱、拉曼光谱、紫外可见吸收光谱受外辐射场的影响。结果表明,分子结构与辐射场有关。在外辐射场变化范围(-0.04~0.04 a.u.),自由基总能先小幅度增大(-0.03 a.u.达到最大值)后大幅度单调减小;分子键长在负辐射场(-0.04~0 a.u.)没有明显变化,但在(0~0.04 a.u.)正辐射场下单调变长;偶极矩先减小(-0.03 a.u.达到最小值)后增大;而能隙先不断增大(-0.04^-0.02 a.u.),在(-0.02~0.03 a.u.)辐射场能隙基本稳定,随后单调下降。正辐射场(0~0.04 a.u.)对AlO自由基的振动频率和红外强度的影响较大, AlO自由基在0.04 a.u.辐射场下的红外光谱红移74 cm^-1,其对应光谱强度是未加辐射场的80倍;正辐射场(0~0.04 a.u.)的拉曼光谱红移较明显,在0.04 a.u.红移78 cm^-1;负辐射场(0^-0.04 a.u.)对拉曼光谱影响也较大,在-0.03 a.u.辐射场下具有很强的拉曼活性是未加辐射场的688倍;正辐射场(0~0.04 a.u.)下AlO自由基的紫外可见吸收光谱中原来无辐射场下的最大吸收峰(170 nm)蓝移了22 nm且吸收幅度减至一半,在负辐射场范围内(0^-0.04 a.u.)该吸收峰也辐有蓝移其强度也有减弱趋势;AlO自由基的无辐射场下第二个最大紫外可见峰在正辐射场作用下,其波长从282 nm一直递减蓝移13 nm和吸收强度递增至2.2倍,负辐射场范围内(0^-0.04 a.u.)该吸收峰红移10 nm和吸收强度递增了6.2倍,超过了无辐射场下最大吸收波长强度。     

Accurate One-Centre Method for Hydrogen Molecule Ions in Strong Magnetic Field

An accurate one-centre method for the hydrogen molecule ion is tested. The slow convergence and singularities at the nuclear positions that are problems in the general one-centre method axe solved well by employing the optimal radial and angular B-spline basis. Therefore, the accuracy of the one-centre method is improved observably. For the ground state of the H2^＋ in the free field, 7 ×10^-8 accuracy is obtained, which rivals the best one-centre calculation before. As a test, the nuclear distances and the total energies of the 1σ g,u, 1πu, 1δ9,u and 2σg states of the H2^＋ for the magnetic field strength B = 1 a.u. are also obtained. Compared to other results, five-digit accuracy at least can be arrived even for the antibonding states 1σu and 1σu, whose equilibrium distances R is very large.     

新型复合物Li…HF,Li…FH,Li…H2O和Li…NH3的一阶超极化率的从头算理论研究

在MP2/6-311 G(2df,2pd)水平上优化得到了几种小型碱金属—极性分子复合物的结构,利用有限场方法[HF,MP2,MP3,MP4(SDQ)]在15种基组上分别计算了它们的偶极矩(μ),极化率(α0),各向异性极化率(Δα)和一阶超极化率(β0).在MP4(SDQ)/6-311 G(2df,2pd)理论水平上,各复合物分子一阶超极化率分别为:Li…HF,β0=3957.575 a.u.;Li…FH,β0=12939.614 a.u.;Li…NH3,β0=34881.899a.u.;Li…H2O,β0=39820.410 a.u..而分子HF,NH3,H2O的一阶超极化率的值分别为1.224 a.u.,35.560 a.u.,20.130 a.u..结果表明,复合物分子中的额外电子对分子非线性光学性质有巨大的贡献.     

也谈对称重陀螺的运动特征

苏云荪同志在[1]和[2]中用能图法讨论了对称重陀螺的运动特征,[2]尤为详细.这两篇文章给出了对称重陀螺各种类型的运动方式及其实现条件,此项工作是值得肯定的.不过,我们以为就用通常的三次式的方法也能得到[2]的所有结果. 为了便于对照,本文援用[1]和[2]的记号.章动角、进动角和自转角分别记作θ, 和 .对称重陀螺有三个运动积分即绕对称轴的动量矩、绕竖直轴的动量矩、能量.我们不妨认为a 是正的. 通常把(2)改写为 式中 而u=cos θ是用以代替变数θ的一个变数. 再以(4)代入(3)即得u2=U(u),这里U　(u)是三次式教本中都指出U(u)有一个零点u…     

Geometrical structures,vibrational frequencies,force constants and dissociation energies of isotopic water molecules （H2O,HDO, D2O,HTO, DTO,and T2O） under dipole electric field

The dissociation limits of isotopic water molecules are derived for the ground state. The equilibrium geometries, the vibrational frequencies, the force constants and the dissociation energies for the ground states of all isotopic water molecules under the dipole electric fields from -0.05 a.u. to 0.05 a.u. are calculated using B3P86/6-311++G(3df,3pf). The results show that when the dipole electric fields change from -0.05 a.u. to 0.05 a.u., the bond length of H-O increases whereas the bond angle of H-O-H decreases because of the charge transfer induced by the applied dipole electric field. The vibrational frequencies and the force constants of isotopic water molecules change under the influence of the strong external torque. The dissociation energies increase when the dipole electric fields change from -0.05 a.u. to 0.05 a.u. and the increased dissociation energies are in the order of H2O, HDO, HTO, D2O, DTO, and T2O under the same external electric fields.     

Invariant Sets and Exact Solutions to Nonlinear Diffusion Equations with x-Dependent Convection and Absorption

In this paper, we introduce a new invariant set Eo={u：ux=f＇（x）F（u）＋ε[g＇（x）-f＇（x）g（x）]F（u）×exp（-∫^u1/F（z）dz）}where f and g are some smooth functions of x, ε is a constant, and F is a smooth function to be determined. The invariant sets and exact sohltions to nonlinear diffusion equation ut = （ D（u）ux）x ＋ Q（x, u）ux ＋ P（x, u）, are discussed. It is shown that there exist several classes of solutions to the equation that belong to the invariant set Eo.     

Spatially Resolved N2（A3Σ＋u, ν=0） Decay Studies in the Pulsed Direct-Current Nitrogen Discharge using the Laser-Induced-Fluorescence Technique

We focus on the investigation of the spatial distribution and temporal evolution of N2（A3Σ＋u, ν=0） in a very early afterglow of a pulsed dc nitrogen discharge. The results indicate that a fast quenching process of N2（A3Σ＋u, ν=0） exists in the very early afterglow. We study the dependence of this fast quenching process on the discharge pressure 20–40 torr. It seems that this fast quenching behavior of N2（A3Σ＋u, ν=0） found in our experiment can be ascribed to the combined action of pooling reaction and collisions with N atoms through N2（A3Σ＋u）＋N2（A3Σ＋u）→ N2＊＋N2（N2＊=N2（B3Πg, C3Πu, C＇3Πu, C＂5Πu）） and N2（A3Σ＋u）＋N（4S）→N（2P）＋N2, respectively. Meanwhile, the decay studies of N2（A3Σ＋u, ν=0） near the anode and cathode infer that the production of N（4S） atoms does not distribute uniformly along the axis of the discharge gap at relatively low pressure, and this effect becomes gradually inconspicuous with the increasing discharge pressure.     

Global Structure Stability of Riemann Solution of Quasilinear Hyperbolic System of Conservation Law in Presence of Boundary： Shocks and Contact Discontinuities

In this paper, we investigate a class of mixed initial-boundary value problems for a kind of n × n quasilinear hyperbolic systems of conservation laws on the quarter plan. We show that the structure of the pieeewise C^1 solution u = u（t, x） of the problem, which can be regarded as a perturbation of the corresponding Riemann problem, is globally similar to that of the solution u = U（x/t） of the corresponding Riemann problem. The piecewise C^1 solution u = u（t, x） to this kind of problems is globally structure-stable if and only if it contains only non-degenerate shocks and contact discontinuities, but no rarefaction waves and other weak discontinuities.     

荷电标量分子对光子与光子散射振幅贡献的精确解析表达式

计算了荷电标量介子的圈图对光子与光子散射的四阶极化张量和圆极化散射振幅的贡献,得到了它们依赖于三个超越函数B(u),T(u)和I(u,v)的精确解析表达式.     

Two Types of New Solutions to KdV Equation

It is common knowledge that the soliton solutions u（x, t） defined by the bell-shape form is required to satisfy the following condition lira u（x, t） = u（±∞, t） = 0. However, we think that the above condition can be modified as lim u（x, t） = u（±∞, t）^x→ = c, where c is a constant, which is called as a stationary height of u（x, t） in the present paper.^x→∞ If u（x, t） is a bell-shape solitary solution, then the stationary height of each solitary wave is just c. Under the constraint c = 0, all the solitary waves coming from the N-bell-shape-sollton solutions of the KdV equation are the same-oriented travelling. A new type of N-soliton solution with the bell shape is obtained in the paper, whose stationary height is an arbitrary constant c. Taking c ≥ 0, the resulting solitary wave is bound to be the same-oriented travelling. Otherwise, the resulting solitary wave may travel at the same orientation, and also at the opposite orientation. In addition, another type of singular rational travelling solution to the KdV equation is worked out.     

Invariant Sets and Exact Solutions to Higher-Dimensional Wave Equations

The invariant sets and exact solutions of the （1 ＋ 2）-dimensional wave equations are discussed. It is shown that there exist a class of solutions to the equations which belong to the invariant set E0 = {u ： ux = vxF（u）,uy = vyF（u） }. This approach is also developed to solve （1 ＋ N）-dimensional wave equations.     

S2(B 3∑u-→X3∑g-(v''''≥18,0))弥散谱带的自旋-轨道从头计算

采用从头计算方法从理论上解释了实验中双原子分子S2(B3∑u-→X3∑g-)吸收谱中谱带(18,0)开始出现的弥散现象.计算了包含自旋-轨道耦合(SOC)的B3∑u-和排斥的15∏u,23∑u+态的电子势能曲线.对于(18,0)谱带开始弥散,给出了与其他文献不同的物理解释.计算结果表明B3∑u-与15∏u,23∑u+态的SOC作用导致预解离对谱带的弥散起着决定作用,并与实验结果作了比较,符合很好.     

S_2(B~3Σ_u~-→X~3Σ_g~-(ν′≥18,0))弥散谱带的自旋-轨道从头计算

采用从头计算方法从理论上解释了实验中双原子分子S_2(B~3Σ_u~-→X~3Σ_g~-吸收谱中谱带(18,0)开始出现的弥散现象.计算了包含自旋-轨道耦合(SOC)的B3Σu-和排斥的15Πu,23Σu 态的电子势能曲线.对于(18,0)谱带开始弥散,给出了与其他文献不同的物理解释.计算结果表明B3Σu-与15Πu,23Σu 态的SOC作用导致预解离对谱带的弥散起着决定作用,并与实验结果作了比较,符合很好.     

Multireference calculation of lifetime of A~2Π_u state in nitrogen-molecule cation

This paper utilizes multireference configuration interaction theory to calculate the lifetime of A2Πu state for nitrogen molecular ion N+2.It obtains the transition moment function for A2Πu→X2Σ+ g,Franck-Condon factors between vibrational levels of the two states.The calculated lifetimes are 16.81,14.62,13.10,12.18,11.40,and 11.64 μs forv'= 0,1,2,3,4,5 vibrational levels of A2Πu state,respectively,which are in excellent agreement with available experimental values.     

Momentum transfer dependence behaviors of ionization and dissociation of oxygen

The decay pathways of the structured ionization region of oxygen at different momentum transfers,i.e.,0,0.23 a.u.(atomic unit),and 0.91 a.u.,are studied by measuring the ion and the scattered electron coincidently.It is found that the dipole-forbidden superexcited states of(2σu)-1(c4Σu-)npσu 3Σg-← X3Σg-decay into different channels according to the principal quantum number n.The broad ridge above 35 eV,which may be due to inner-valence excited states of(2σg)-1nλ or multiply excited states,is observed both at small and large momentum transfers,and its decay channel of O++ O is dominant.