General Formulae for Two Pseudo-differential Operators

Some general formulas in the Sato theory related to the nonisospectral KP and mKP hierarchies are derived for simplifying calculations.     

摄动有限体积法重构近似高精度的意义

研讨有限体积(FV)方法重构近似高精度的作用问题.FV方法中积分近似采用中点规则为二阶精度时,重构近似高精度(精度高于二阶)的意义和作用是一个有争议的问题.利用数值摄动技术[1,2]构造了标量输运方程的积分近似为二阶精度、重构近似为任意阶精度的迎风型和中心型摄动有限体积(PFV)格式.迎风PFV格式无条件满足对流有界准则(CBC),中心型PFV格式为正型格式,两者均不会产生数值振荡解.利用PFV格式求解模型方程的数值结果表明:与一阶迎风和二阶中心格式相比,PFV格式精度高、对解的间断分辨率高、稳定性好、雷诺数的适用范围大,数值地"证实"重构近似高精度和PFV格式的实际意义和好处.     

New construction of special Lagrangian submanifolds in T^＊R^n equipped with the standard metric

A class of twisted special Lagrangian submanifolds in T~*R~n and a kind of austere submanifold from conormal bundle of minimal surface of R~3 are constructed.     

模糊随机参数二维声场数值计算

解决声场参数同时具有模糊性和随机性的问题,实现模糊随机声场声压响应的预测,引入了信息熵理论,利用信息熵的等效转换,将模糊随机声场转化为纯随机声场或者纯模糊声场进行求解,推导了基于摄动法的二维随机声场和模糊声场的有限元计算公式。以模糊随机参数下的二维管道声场模型和某轿车二维声腔模型为例进行了数值计算,所得结果与蒙特卡洛法(Monte Carlo Method)所预测声压变化范围基本一致,同时,转化为纯随机声场和纯模糊声场所求得声压响应变化范围也基本一致,说明了本文方法计算结果的准确性。因此本文方法能很好地应用于模糊随机参数下二维声场的预测,具有重要的工程应用价值。     

带摩擦的弹性接触问题广义变分不等原理的简化证明

在弹性摩擦接触问题中 ,从变分原理出发来研究接触问题 ,可以将摩擦力纳入问题的能量泛函 .为了得到摩擦约束弹性接触问题的能量泛函 ,日前大多是用拉格朗日乘子法 ,但拉格朗日方法用在变分不等问题中 ,要利用非线性泛函分析和凸分析来证明 ,证明复杂 .本文利用向量分析的工具及巧妙的变换 ,对带摩擦约束的弹性接触问题的广义变分不等原理进行了严格的证明 ,由于只用到向量分析 ,简化了证明 .     

具有相交性质的近小扭转映射的不变环面的保持性

In this paper we investigate the nearly small twist mappings with intersection property. With a certain non-degenerate condition, we proved that the most of invariant tori of the original small twist mappings will survive afer small perturtations. The persisted invariant tori are close to the unperturbed ones when the perturbation are small. The orbits reduced by those mappings are quasi-periodic in the invariant tori with the frequences closing to the original ones.     

AsH(X~3∑~-)及AsH_2(X~2B_1)自由基的分子结构与解析势能函数

运用Gaussian 03程序包中的单双迭代三重激发耦合簇理论和相关一致五重基优化了AsH_2的基态结构,并在优化结构的基础上计算了它的离解能和振动频率.结果表明:AsH_2基态的平衡构型具有C_(2v)对称性,键长R_(As-H)=0,1508 nm,键角∠HAsH=91.2231°,离解能D_e(Has-H)=2.8795 eV,振动频率ν_1(α_1)=1013.3361 cm~(-1),ν_2(α_1)=2225.1347 cm~(-1),ν_3(α_1)=2233.7565 cm~(-1).这些结果与实验值较为相符.对H_2的基态使用优选出的cc-pV6Z基组、对AsH的基态使用优选出的cc-pV5Z基组进行平衡几何与谐振频率的计算并进行单点能扫描,且将扫描结果拟合成了Murrell-Sorbie函数.与实验数据及其他理论结果的比较表明,本文关于AsH(X~3∑~-)自由基光谱常数(D_0,D_e,R_e,ω_e,B_e,α_e和ω_eX_e)的计算结果达到了很高的精度并最为完整.采用多体项展式理论导出了AsH_2(C_(2v),X~2B_1)自由基的解析势能函数,其等值势能图准确再现了它的离解能和平衡结构特征.首次报导了AsH_2(C_(2v),X~2B_1)自由基对称伸缩振动等值势能图中存在的两个对称鞍点,对应于反应AsH+H→ABH_2,势垒高度约0.1512×4.184 kJ/mol.

Abstract：

The CCSD(T) theory in combination with the cc-pV5Z basis set is used to determine the equilibrium geometry, dissociation energy and vibrational frequencies of AsH_2 (C_(2v), X~2B_1) radical. By comparison, excellent agreement can be found between the present results and the experiments. The values obtained at present are of 0.1508 ran for the equilibrium bond length R_(As-H), 91.2231° for the bond angle ∠ HASH, 2. 8795 eV for the dissociation energy D_e (HAs-H) and 1013.3361 cm~(-1), 2225.1347 cm~(-1) and 2233.7565 cm~(-1) for the vibrational frequencies ν_1(α_1), ν_2(α_1) and ν_3(α_1), respectively. The equilibrium geometry,harmonic frequency and potential energy curve of the AsH(X~3∑~-) radical are calculated at the CCSD(T)/cc-pV5Z level of theory. The ab initio results are fitted to the Murrell-Sorbie function with the least-square method. The spectroscopic parameters are in excellent agreement with the experiments. The analytic potential energy function of the AsH_2 (C_(2v), X~2 B_1) radical is derived by using the many-body expansion theory. This function correctly describes the configuration and dissociation energy of the AsH_2 (C_(2v), X~2B_1) radical. Two symmetrical saddle points have been found at (0.160 nm,0.296 nm) and (0.296 nm,0.160 nm) ,respectively. And the barrier height is equal to 0.1512×4.184 kJ/mol.     

《纯粹数学与应用数学》稿约

1 该刊是经国家科委、新闻出版署批准公开发行的数学及其应用的综合性学术刊物,主要刊登数学学科中有创造性的研究论文和具有重要经济价值的应用性论文,以繁荣数学理论,推进应用数学研究．该刊2000年荣获《CAJ—CD规范》执行优秀奖,2004年入选全国中丈核心期刊．2006年获陕西省出版编辑良好奖．