Solvability for nonlinear elliptic equation with boundary perturbation

The solvability of nonlinear elliptic equation with boundary perturbation is consid- ered.The perturbed solution of original problem is obtained and the uniformly valid expansion of solution is proved.     

2.45GHz下常用有机试剂复介电常数的测量与研究

1986年加拿大的R．Gedye和R．J．Giguere等发现了微波可以显著加快有机合成,他们发现用微波辐射可使反应速率和产率有不同程度的提高。由于微波作用机理的特殊性,微波化学对很多化学领域带来了冲击。但是,微波与化学反应体系之间相互作用的一些重大问题还未得到解决,如微波加热过程中化学反应系统的非线性反射、非均匀加热等。解决这类问题,首先必须了解化学反应过程中混合物的电学性质与磁学性质,而物质的宏观电学和磁学性质都用其介电常数和磁导率来描述。对于大部分是非磁性材料的有机试剂,微波与反应体系相互作用的特性集中体现在体系的等效复介电常数上。了解各种常用试剂的复介电常数,可以进一步了解各种化学试剂对微波的吸收和反射的情况。而很多试剂的复介电常数无法从现有文献中得到。本文利用谐振腔微扰法测定了在2．45GHz室温下各类常用有机试剂的复介电常数,结果显示：醇类试剂复介电常数实部与虚部都较大;酮类试剂复介电常数实部相对较大,而虚部较小;酸类试剂复介电常数实部和虚部都较小;烷烃和苯类试剂实部,虚部更小。同时,随着碳链增加,所有试剂的复介电常数的实部与虚部均有下降趋势。这些测试和分析结果将为微波辅助有机合成提供了有益参考。     

对称理论在解若干非线性问题中的应用

将摄动理论和对称约化理论结合起来对研究扰动非线性方程具有重要的意义. 本文利用近似对称约化理论研究了扰动mKdV方程, 得到了该方程的各阶近似约化方程和级数约化解. 本文还讨论了同伦近似对称方法在求解不可积系统中的应用以及利用对称和守恒律的关系求解非线性系统的无穷多守恒律等问题.     

Ab initio quantum-chemical calculations of interactions of ions and hydrides of alkali metals with C3H6 and C4H8 molecules

Calculations of the C₃H₆ · LiH, C₄H₈ · M⁺, and C₄H₈ · MH systems and of C₂H₂ · MH complexes (M = Li or Na) were carried out by the unrestricted Hartree-Fock-Roothaan (UHF) method with partial optimization of the geometry using fixed geometric parameters of the C₃H₆ and C₄H₈ molecules. The standard 3-21G and 6-31G* basis sets were used. Unlike the C₃H₆ · LiH structure, the C₄H₈ · M⁺ and C₄H₈ · MH systems are typical complexes. It was found that the C₄H₈ · M⁺, C₄H₈ · MH, and C₂H₂ · MH complexes are similar in coordination of M⁺ ions and MH molecules by carbon atoms in spite of considerable differences in the interatomic distances (–1 A) between these atoms in the C₄H₈ and C₂H₂ molecules. The heats of formation (Q), which were calculated in the UHF/6-31G* approximation and using second- and fourth-order Möller-Plesset perturbation theory taking into account the electron correlation energy in the MP2/6-31G*. MP4(SDQ)/6-31G*, and MP4(SDTQ)/6-31G* approximations, satisfy the following relationships: Q(C₂H₃ · MH) < Q(C₄H₈ · MH) < Q(C₄H₈ · M⁺). It was observed that in going from Li to Na the corresponding values of Q tend to decrease.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya. No. 7, pp. 1636–1640, July, 1996.     

Vibrational isotope effect by the low rank perturbation method

Mathematical formalism of the Low Rank Perturbation method (LRP) is applied to the vibrational isotope effect in the harmonic approximation with a standard assumption that force field does not change under isotopic substitutions. A pair of two n-atom isotopic molecules A and B which are identical except for isotopic substitutions at ρ atomic sites is considered. In the LRP approach vibrational frequencies ω _k and normal modes of the isotopomer B are expressed in terms of the vibrational frequencies ν _i and normal modes of the parent molecule A. In those relations complete specification of the normal modes is not required. Only amplitudes at sites τ affected by the isotopic substitutions and in the coordinate direction s (s = x, y, z) are needed. Out-of-plane vibrations of the (H,D)-benzene isotopomers are considered. Standard error of the LRP frequencies with respect to the DFT frequencies is on average . This error is due to the uncertainty of the input data (± 0.5 cm⁻¹) and in the absence of those uncertainties and in the harmonic approximation it should disappear. In comparing with experiment, one finds that LRP frequencies reproduces experimental frequencies of (H,D)-benzene isotopomers better () than scaled DFT frequencies () which are designed to minimize (by frequency scaling technique) this error. In addition, LRP is conceptually and numerically simple and it also provides a new insight in the vibrational isotope effect in the harmonic approximation.     

弹性接触问题线性互补法的摄动原理

为使弹性摩擦问题的线性互补法得到收敛性保证,提出一个摄动原理,证明了通过“摆脱摄动误差”可得到原离散模型的精确解。     

STABILITY OF DISPLACEMENT TO THE SECOND FUNDAMENTAL PROBLEM IN PLANE ELASTICITY

In this article, by using the stability of Cauchy type integral when the smooth perturbation for integral curve and the Sobolev type perturbation for kernel density happen, we discuss the stability of the second fundamental problem in plane elasticity when the smooth perturbation for the boundary of the elastic domain （unit disk） and the Sobolev type perturbation for the displacement happen. And the error estimate of the displacement between the second fundamental problem and its perturbed problem is obtained.     

关于非线性矩阵方程$X^s-A^*X^{-t}A=Q$的Hermitian正定解及其扰动估计

In this paper, the Hermitian positive definite solutions of the nonlinear matrix equation X^s - A^＊X^-tA = Q are studied, where Q is a Hermitian positive definite matrix, s and t are positive integers. The existence of a Hermitian positive definite solution is proved. A sufficient condition for the equation to have a unique Hermitian positive definite solution is given. Some estimates of the Hermitian positive definite solutions are obtained. Moreover, two perturbation bounds for the Hermitian positive definite solutions are derived and the results are illustrated by some numerical examples.     

空中交通管理中的地面等待策略研究

就现代空中交通管理中地面等待策略 (GDP)的发展和现状作了简要的总结概括 ,阐述了地面等待对空中交通流量管理的影响与意义 ,分类分析了地面等待策略 ,同时从众多理论研究中归纳出了几种典型模型和求解方法 ,并对各种模型、方法进行了比较分析 ,最后提出了地面等待策略的发展趋势和方向 .     

A singularly perturbed reaction diffusion problem forthe nonlinear boundary condition with two parameters

A class of singularly perturbed initial boundary value problems of reaction diffusion equations for the nonlinear boundary condition with two parameters is considered. Under suitable conditions, by using the theory of differential inequalities, the existence and the asymptotic behaviour of the solution for the initial boundary value problem are studied. The obtained solution indicates that there are initial and boundary layers and the thickness of the boundary layer is less than the thickness of the initial layer.