白沙河平原区需水预测

白沙河平原区为青岛市蔬菜基地，农业为主要用水户，根据本区未来菜粮比例进一步提高、城乡生活水平不断提高、乡镇工业迅速发展、节水意识有所提高等特点．设计了包括工业、农业和生活需水的需水预测模型，预测结果表明，工业及生活用水比例将不断提高，农业用水仍占主要地位，但增幅不大。预测结果为管理模型设计提供了信息．     

时滞广义时变系统的渐近稳定与镇定

研究了时滞广义时变系统的渐近稳定和镇定问题。首先利用相关不等式,通过建立Lyapunov方程,给出了1个时滞广义时变系统无脉冲、渐近稳定性的充分条件。然后,基于这一工作,利用Riccati方程,进一步研究了时滞广义时变系统的镇定问题。最后,举例说明该结论的可行性。     

极坐标变换变边界模型及其应用

Ｊｏｈｎｓ变边界模型用于海湾海域风暴潮漫滩计算是，由于岸界变曲较大，而影响了计算的稳定性和精度，本文针对这个问题，导出了极坐标下的连续移动边界模型，从而改善了对岸界弯曲较大海域的风暴潮漫滩计算，通过对１９６９年黄河口沿岸一带水域风暴潮漫滩的模拟，证明这种极坐标变边界模型用于海湾海域的风暴潮漫滩计算，优于Ｊｏｈｎｓ变边界模型。     

Numerical Calculation for Nonlinear Waves in Water of Arbitrarily Varying Depth with Boussinesq Equations

Based on the high order nonlinear and dispersive wave equation with a dissipalive term, a numerical model for nonlinear waves is developed. It is suitable to calculate wave propagation in water areas with an arbitrarily varying bottom slope and a relative depth h/ L0≤ 1. By the application of the completely implicit slagger grid and central difference algorithm, discrete governing equations are obtained. Although the central difference algorithm of second-order accuracy both in time and space domains is used to yield the difference equations, the order of truncation error in the difference equation is the same as that of the third-order derivatives of the Boussinesq equation. In this paper, the correction to the first-order derivative is made, and the accuracy of the difference equation is improved. The verifications of accuracy show that the results of the numerical model are in good agreement with those of analytical solutions and physical models.     

关于矩阵方程A~TX+X~TA=B的极小范数解

作者讨论矩阵方程 ATX+ XTA=B。该方程在 Hamilton力学研究中有用。首先利用L yapunov方程证明了极小 Frobenius范数解的存在性和惟一性。然后用奇异值分解给出了求解最小范数解的一种方法。最后讨论极小范数解的向前扰动分析和最佳向后扰动分析     

Derivation of statistical properties of wave-induced offshore structural response by principal component technique

According to linear random wave theory, water particle kinematics at different nodes of an offshore structure form a set of correlated jointly Gaussian random variables. Thus, using principal component analysis, all the foregoing kinematics can be expressed as linear combinations of a few independent Gaussian random variables. This technique can be used to generate statistically independent hydrodynamic load and response values, as opposed to time simulation technique that leads to correlated response values. The sampling variability of the statistics generated from a set of independent data points is considerably smaller than that of a set (of the same size) of correlated values. Therefore, a much smaller number of simulated data points are necessary for accurate prediction of the statistical properties of response. Furthermore, simulating N data points by principal component technique (PCT) has proved to be at least two times faster than simulating the same number of data points by the time simulation technique (TST). As a result, PCT is considerably more efficient (about 25 times) than TST. The forgoing conclusions have been verified by applying both techniques to two test structures under different environmental conditions.     

An Explicit High Resolution Scheme for Nonlinear Shallow Water Equations

The present study develops a numerical model of the two-dimensional fully nonlinear shallow water equations （NSWE） for the wave run-up on a beach. The finite volume method （FVM） is used to solve the equations, and a second-order explicit scheme is developed to improve the computation efficiency. The numerical fluxes are obtained by the two dimensional Roe＇ s flux function to overcome the errors caused by the use of one dimensional fluxes in dimension splitting methods. The high-resolution Godunov-type TVD upwind scheme is employed and a second-order accuracy is achieved based on monotonic upstream schemes for conservation laws （MUSCL） variable extrapolation; a nonlinear limiter is applied to prevent unwanted spurious oscillation. A simple but efficient technique is adopted to deal with the moving shoreline boundary. The verification of the solution technique is carried out by comparing the model output with documented results and it shows that the solution technique is robust.     

The New Form of Time-Dependent Mild Slope Equation for Random Waves

The mild-slope equation derived by Berkhoff (1972), has widely been used in the numerical calculation of refraction and diffraction of regular waves. However, it is well known that the random sea waves has a significant effect in the refraction and diffraction problems. In this paper, a new form of time-dependent mild slope equation for irregular waves was derived with Fade approximation and Kubo's time series concept. The equation was simplified using WKB method, and simple and practical irregular mild slope equation was obtained. Results of numerical calculations are compared with those of laboratory experiments.     

Numerical Simulation of Freak Waves Based on the Four-Order Nonlinear Schroelinger Equation

A numerical wave model based on the modified four-order nonlinear Schoedinger （NKS） equation in deep water is developed to simulate freak waves. A standard split-step, pseudo-spectral method is used to solve NLS equation. The validation of the model is firstly verified, and then the simulation of freak waves is perforated by changing sideband condi- tions. Results show that freak waves entirely consistent with the definition in the evolution of wave trains are obtained. The possible occurrence mechanism of freak waves is discussed and the relevant characteristics are also analyzed.     

一族可积孤子方程的Darboux变换与类孤子解

本文利用新的等谱特征值问题 ,首先为 1类耦合的非线性演化方程建立了 1个具有多个参数的 N-波 Darboux变换。通过约化 ,得到了 1族可积孤子方程的 Darboux变换。作为应用 ,获得了该孤子方程的类孤子解 ,并借助 Mathematica软件画出了其中 1个新解的图形