定解问题的可视化教学设计探讨

通过对一维弦振动的定解问题的计算机动态仿真,比较了不同定解条件下弦振动的视觉效果,讨论了相应的课外仿真设计.教学设计中突出了将传统的理论推导与计算机编程技术结合起来的教学思路,注重培养学生发现、分析和解决问题的兴趣和能力.     

The quasi-reversibility method to solve the Cauchy problems for parabolic equations

In this paper, on the one hand, we take the conventional quasi-reversibility method to obtain the error estimates of approximate solutions of the Cauchy problems for parabolic equations in a sub-domain of QT with strong restrictions to the measured boundary data. On the other hand, weakening the conditions on the measured data, then combining the duality method in optimization with the quasi-reversibility method, we solve the Cauchy problems for parabolic equations in the presence of noisy data. Using this method, we can get the proper regularization parameter ε that we need in the quasi-reversibility method and obtain the convergence rate of approximate solutions as the noise of amplitude δ tends to zero.     

具分布时滞和阻尼项的偶阶半线性中立型微分方程的振动性

研究一类具分布时滞和阻尼项的偶阶半线性中立型微分方程解的振动性质,利用广义Riccati变换和积分平均技巧得到方程一切解均为振动的若干新的振动准则,推广、改进和统一了新近文献中的某些结果.     

一阶中立型时滞差分方程振动的充分必要条件

研究了一阶常系数中立型时滞差分方程A[x(n)-px(n-τ)]+qx(n-σ)=0的振动性.通过构造若干适当的函数,分别得到了在01两种情况下该方程的一切解振动的充分必要条件.     

食物受限人口模型中非线性延迟微分方程数值解的振动性

本文讨论食物受限人口模型中的一个非线性延迟微分方程数值解的振动性.通过应用两种θ-方法,即线性θ-方法和单腿θ-方法,构造指数θ-方法,得到数值解振动的条件,进一步考虑非振动解的渐近行为,最后给出两个数值算例.     

利用海洋环境噪声直接提取海底反射系数

提出了一种利用海洋环境噪声直接(非迭代)提取海底反射系数的方法,基于海洋环境噪声垂直相关函数与方向密度函数的相似性,结合海洋环境噪声射线理论,由两个垂直排列的水听器实现海底反射系数的被动获取.方法适应性的仿真分析说明较高海况下且近场无航船干扰的海洋环境噪声数据有利于方法的实现;对于两层海底,海洋环境噪声垂直相干函数经高...     

The pressure dependences of elastic and lattice dynamic properties of AlAs from ab initio calculations

Ab initio calculations,based on norm-conserving nonlocal pseudopotentials and density functional theory(DFT),are performed to investigate the structural,elastic,dielectric,and vibrational properties of aluminum arsenide(AlAs) with a zinc-blende(B3) structure and a nickel arsenide(B81) structure under hydrostatic pressure.Firstly,the path for the phase transition from B3 to B81 is confirmed by analyzing the energies of different structures,which is in good agreement with previous theoretical results.Secondly,we find that the elastic constants,bulk modulus,static dielectric constants,and the optical phonon frequencies vary in a nearly linear manner under hydrostatic pressure.What is more,the softening mode of the transversal acoustic mode at the X point supports the phase transition in AlAs.     

Analysis of atom detection via the magnetic optical effect

We demonstrated a new method of atom detection by means of the magnetic optical effect. The number density of the atom cloud was measured by detecting the rotation angle of the polarization plane of linearly polarized probe light when propagating inside the atomic cloud. Detuning, the magnetic field and light intensity dependencies of the rotation angle were studied theoretically and experimentally to find the best parameter for atom detection. In this way, we managed to achieve a rotation angle of 0.22 rad with a signal to noise ratio (SNR) of 75 and a contrast of 87.5%.     

Cubature Kalman filters: Derivation and extension

This paper focuses on the cubature Kalman filters （CKFs） for the nonlinear dynamic systems with additive process and measurement noise. As is well known, the heart of the CKF is the third-degree spherical–radial cubature rule which makes it possible to compute the integrals encountered in nonlinear filtering problems. However, the rule not only requires computing the integration over an n-dimensional spherical region, but also combines the spherical cubature rule with the radial rule, thereby making it difficult to construct higher-degree CKFs. Moreover, the cubature formula used to construct the CKF has some drawbacks in computation. To address these issues, we present a more general class of the CKFs, which completely abandons the spherical–radial cubature rule. It can be shown that the conventional CKF is a special case of the proposed algorithm. The paper also includes a fifth-degree extension of the CKF. Two target tracking problems are used to verify the proposed algorithm. The results of both experiments demonstrate that the higher-degree CKF outperforms the conventional nonlinear filters in terms of accuracy.