坐标轴平移在多元函数积分计算中的应用

利用适当的坐标轴平移可将某些多元函数积分转换为便于计算的形式.     

基于推广的回归模型的风险管理方法

首先,利用Choquet积分将多元线性回归模型进行推广;然后,基于推广的非线性回归模型,将若干交互作用的风险因素抽象成一个数学模型,采用定量分析的方法,在给定风险损失和风险发生概率的历史数据的基础上,计算出各个风险在风险集合中的重要程度及其风险之间交互作用的大小,从而进行有效的风险管理.     

Surface integral analogy approaches for predicting noise from 3D high-lift low-noise wings

Three surface integral approaches of the acoustic analogies are studied to predict the noise from three concep- tual configurations of three-dimensional high-lift low-noise wings. The approaches refer to the Kirchhoff method, the Ffowcs Williams and Hawkings （FW-H） method of the permeable integral surface and the Curle method that is known as a special case of the FW-H method. The first two approaches are used to compute the noise generated by the core flow region where the energetic structures exist. The last approach is adopted to predict the noise specially from the pressure perturbation on the wall. A new way to con- struct the integral surface that encloses the core region is proposed for the first two methods. Considering the local properties of the flow around the complex object-the actual wing with high-lift devices-the integral surface based on the vorticity is constructed to follow the flow structures. The surface location is discussed for the Kirchhoff method and the FW-H method because a common surface is used for them. The noise from the core flow region is studied on the basis of the dependent integral quantities, which are indicated by the Kirchhoff formulation and by the FW-H formulation. The role of each wall component on noise contribution is analyzed using the Curle formulation. Effects of the volume integral terms of Lighthill＇s stress tensors on the noise pre-diction are then evaluated by comparing the results of the Curle method with the other two methods.     

几个由积分形成的数列的极限

围绕着若干个由积分定义的数列展开讨论，求出了这些数列的极限，并指出它们是一些已知的数列极限的推广。     

Stereoselective interactions of chiral dipeptides on amylose based chiral stationary phases

Dipeptides are stereo-specifically involved in several biological functions that are challenging to separate enantiomerically. Elution order of enantiomers is an important issue in chiral chromatography. Amylose tris-(3,5-dimethylphenylcarbamate) chiral stationary phase(CSP) is the best and most-widely-used CSP in chiral separations, but experimental data of enantiomeric separation of dipeptides on this CSP is lacking. Simulation studies were conducted to determine the order of elution and the chiral recognition mechanism of didpetides on this CSP. Results indicated that the docking energy of SR-enantiomers were higher than SS-antipodes. The range of docking energies for SR-enantiomers was -7.44 to -5.92 kcal/mol with CSP, but -7.15 to -5.87 kcal/mol for SS-stereoisomers. Therefore it is predicted that SS-enantiomer will elute first, followed by SR-antipode. Furthermore, hydrogen bondings, van der Waal’s interactions and electrostatic interactions were observed among SR- and SSenantiomers and chiral grooves of CSP. The number of hydrogen bonds was one in each enantiomer binding except S-Ala-R-Tyr, which contained two hydrogen bonds. No hydrogen bond was found in S-Ala-R-Trp, S-Leu-S-Trp, and S-Leu-S-Tyr dipeptides bindings. The chiral recognition mechanisms dictate different strengths of stereoselective bindings of the enantiomers on CSP.     

具有N-各向异性拉普拉斯算子的超线性问题的先验界

通过改进Brezis和Merle的方法,结合Moser-Trudinger不等式,移动平面方法及比较原理,得到了方程-Q_Nu=f(u),u∈W_0~(1,N)(Ω)的正解的先验界,其中Ω是R~N中的一个有界光滑区域,非线性项f至多具有指数型增长.     

一类弱奇性Volterra积分微分方程的级数展开数值解法

本文考察了一类弱奇性积分微分方程的级数展开数值解法,并给出了相应的收敛性分析.理论分析结果表明,若用已知函数的谱配置多项式逼近已知函数,那么方程的数值解以谱精度逼近方程的真解.数值实验数据也验证了这一理论分析结果.     

一类积分边值问题的再生核数值算法

研究了一类具有积分条件的边值问题.基于再生核理论,巧妙地构造了一个具有积分条件的再生核空间,并且给出了再生核函数表达式.应用泛函分析中的算子理论及逼近论思想,给出了方程的近似解,即再生核数值算法.通过实例验证了算法的可行性和有效性.     

Toader型平均的算术与调和平均界

给出了Toader型平均T[A(a,b),G(a,b)]关于调和平均H(a,b)与算术平均A(a,b)组合的精确界.作为应用,发现了几个关于第二类完全椭圆积分的精确不等式.     

具有蛋白酶抑制剂治疗的HIV病毒的传染病模型分析

建立了T细胞以胸腺和自身有丝分裂进行增殖且具有蛋白酶抑制剂治疗的HIV传染病模型.通过分析该传染病模型,得到蛋白酶抑制剂失效的临界阈值σ和平衡点存在的条件,证明了在不同参数范围内的稳定性.通过对模型的理论分析和数值模拟,发现当σσ,无病平衡点是全局渐近稳定的,即疾病消失.当σσ,正平衡点是全局渐近稳定的,即HIV病毒流行.且得到σ的值越低,基本再生数R_0的值也越低,即当蛋白酶抑制剂的有效率越高,使得艾滋病患者的免疫功能提高.降低被感染T细胞的死亡率,也使病毒的输入率降低,从而更有利的控制病毒的传播.