Testing Lack-of-fit for a Polynomial Errors-in-variables Model

When a regression model is applied as an approximation of underlying model of data, the model checking is important and relevant. In this paper, we investigate the lack-of-fit test for a polynomial error-in-variables model. As the ordinary residuals are biased when there exist measurement errors in covariables,we correct them and then construct a residual-based test of score type. The constructed test is asymptotically chi-squared under null hypotheses. Simulation study shows that the test can maintain the significance level well.The choice of weight functions involved in the test statistic and the related power study are also investigated.The application to two examples is illustrated. The approach can be readily extended to handle more general models.     

非均匀变厚度梁的动力响应的一般解

在本文中提出一个新方法——阶梯折算法来研究在任意载荷下任意非均匀和任意变厚度伯努利-欧拉梁的动力响应问题.研究了自由振动和强迫振动.新方法需要将区间离散为一定数目的元素,每个元素可看作是均匀和等厚度的.因此均匀、等厚度梁的一般解可在每个元素上应用.然后用初参数表示的整个梁的一般解使之满足相邻二元素间的物理和几何连续条件,这样就可以得到解析形式的自由振动的频率方程和解析形式的强迫振动的最终解,它化为求解二元线性代数方程,与离散元素的数目无关.现在的方法可推广应用至任意非均匀及任意变厚度有粘滞性和其他种类的梁以及其他结构元件问题上去.     

免疫鹅血清中和抗体消长的数学模型

本文通过变量转换，对种母鹅注射小鹅瘟疫苗后血清中和抗体含量免疫后时间的变化建立了二次多项式回归模型，该模型的准确度Ｒ~２＝０．７６９０．应用该模型估计了血清中和抗体达到要求含量（滴度为１：１６或高于１：１６，即滴度倒数ｈ≥１６的免疫期间为第８天至第１９６天．并得出了整个产蛋期只需对种母鹅免疫注射一次的结论．     

一类基于变量分离的稳定化混合有限元方法

Based on a seperated model for saddle-point problems, we develop a new sta-bilized mixed finite element method. Such a model consists of two subproblems with respect to the primal and the dual variables, respectively. We show that the new method is coercive and that optimal error bounds hold. As an application,the nearly incompressible elastic problem is analyzed with our method.     

对流扩散方程的一种新型差分格式

对流扩散方程可以描述众多的物理化学现象，因而对其寻求稳定的，实用的数值解法有着重要的现实意义。本文针对形式较一般的一维非定常对流扩散方程，构造了对角元严格占优的Crank-Nicholson差分格式，然后对其分别用分离变量的方法以及能量估计的方法作了稳定性的分析，最后给出了数值试验的结果，数值结果表明本文构造的格式能够较好的处理经典的Crank-Nicholson格式所不能处理的对流项系数较大的对流扩散方程，并具有较好的精度。     

Birkhoff系统的Poincare—Cartan积分不变量

基于现代微分几何学，分析了作为保守系统和非保守系统的推广－Birkhoff系统的辛结构。构造Birkhoff系统的Poincare-Cartan积分不变量。最后，将一维阻尼振动作为示例，求出其Poincare积分不变量。     

具有第二次多选择服务的M[X]/G/1排队系统

本文研究成批到达的具有第二次多选择服务的单服务员排队系统．顾客的到达形成一广义泊松过程，不同批的顾客按先到先服务的规则，而同一批的顾客按随机次序接受服务．两次服务的服务时间都是一般分布且相互独立．本文采用补充变量法，求得在瞬态和稳态情况下系统队长的概率母函数，然后又计算出顾客的平均队长和平均等待时间．     

碲基掺铒光纤放大器对于渐变输入信号的瞬态响应

为了抑制输出信号功率的瞬态波动,提出了调理脉冲信号边沿变化方式的思想.通过有限差分法数值模拟四能级模型下的粒子数速率-光功率传输方程组,理论研究了宽带碲基掺铒光纤放大器(Erbium-doped Tellurite-based Fiber Amplifier,EDTFA)对于低频脉冲输入信号的瞬态响应.研究表明,相比具有阶跃上升沿的方波脉冲,选择一个合适的渐变上升沿脉冲信号可以有效地抑制EDTFA输出端信号功率的瞬时上冲幅度.在多信道系统中,选择渐变的信道功率上传和下载方式,可以延缓其余信道输出功率的瞬态响应速度,从而为后续增益箍制技术的实施提供了便利.     

Controlling optical responses through local dielectric resonance in nanometre metallic clusters

Optical responses in dilute composites are controlled through the local dielectric resonance of metallic clusters. We consider two located metallic clusters close to each other with admittances \varepsilon₁ and \varepsilon₂. Through varying the difference admittance ratio \eta [ = (\varepsilon₂- \varepsilon ₀) / (\varepsilon₁- \varepsilon₀)], we find that their optical responses are determined by the local resonance. There is a blueshift of absorption peaks with the increase of \eta. Simultaneously, it is known that the absorption peaks will be redshifted by enlarging the cluster size. By adjusting the nano-metallic cluster geometry, size and admittances, we can control the positions and intensities of absorption peaks effectively. We have also deduced the effective linear optical responses of three-component composites \varepsilon_e= \varepsilon₀ \bigl(1 + \sum_n=1^{n_s} [(\gamma_n2+ \eta \gamma_n2)/({\varepsilon₀(s - s_n))]} \bigr), and the sum rule of cross sections: \sum_n=1^{n_s} {(\gamma_n2+ \eta \gamma_n2 ) = N_h1+ N_h2, where N_h1and N_h2 are the numbers of \varepsilon₁ and \varepsilon₂ bonds along the electric field, respectively. These results may be beneficial to the study of surface plasmon resonances on a nanometre scale.     

结构动力学方程数值积分的三参数算法

本文提出计算结构动力响应的三参数单步数值积分法,它具有无条件稳定性质,并具有合适的算法阻尼.通过分析及与其他数值积分法比较,说明本文算法的精度有所提高.