参数方程

Area coordinates and general Duffycoordinates are employed to transform the singular integrals of the Time-Domain Electric Field Integral Equation into non-singular integrals, which can be accurately and efficiently evaluated by dividing the transformed domain of integration into sub-domains.

摘要该文首先利用参数坐标和广义Duffy坐标变换将时域电场积分方程的奇异性积分转换成非奇异性积分，然后根据时间基函数的特点将该积分转换成可以快速精确计算的分区域积分。

The results are as follows: 1 mean length and weight tend to increase while dominant length and weight groups are noted to be increasing from Oct. 2004 to Sep. 2007; 2 by using length-weight formula, calculated weight value at the same length is higher for track-data than that for background-data; 3 growth parameters of L∞, W∞ and K respectively increase from 140.5 mm, 36.5 g and 0.28 a-1 to 186.0 mm, 118.5 g and 0.36 a-1 after artificial reef deployment; 4 appreciable increases are noted in body length and weight growth rate after artificial reef deployment, and inflexion age of weight growth increases from 2.55 to 2.58 years after artificial reef deployment; 5 there is an increase in critical biomass age from 3.21 to 3.77 years after artificial reef deployment; 6 there is a decrease in total instantaneous population mortality from 1.065 to 0.75 per year after artificial reef deployment; and 7 the overall population biomass of small yellow croaker stands at 131.5 tons.

结果表明：投礁后小黄鱼的平均体长和体重均呈上升趋势，优势体长组和体重组均向高值移动；同等体长情况下由投礁后体长体重关系式估算的体重比用投礁前的体长体重关系式估算的值大；投礁后小黄鱼个体生长方程的参数 L∞、W∞、K 值分别从投礁前的140.5 mm、36.5 g和0.28 a-1增加到186.0 mm、118.5 g和0.36 a-1；投礁后体长与体重生长速度与投礁前相比有所增大，且体重生长的拐点年龄从投礁前2.55 a提高到2007年的2.58 a；小黄鱼种群生物量增长的临界年龄从投礁前的3.21 a提高到3.77 a；小黄鱼种群的总瞬时死亡率从投礁前的1.065 a-1减小到0.75 a-1；鱼礁区小黄鱼资源量约

Based on the basic theoryof non linear finite element, the author of the paper set up the double non linearfinite element equation based on the updated Lagrangefor mutations forthe 8-node degenerate shell element and considering the nonlinear of geometryand the nonlinear of materials.

本文根据非线性有限元的基本理论，采用基于修正的拉格朗日法描述的八节点超参数壳体单元，考虑几何非线性和材料非线性，推导建立了双重非线性有限元方程，结合混合强化本构关系，编制了非线性有限元计算程序。

Based on Reddy higher-order shear deformation plate theory and general von Kármán-type equations, the analytical solutions for free vibration and dynamic response of simply supported functionally graded plates with piezoelectric layers in thermal environments are described with double Fourier series, where temperature-dependent material properties are taken into account.

基于Reddy高阶剪切变形理论和广义Kármán 型方程，用双重Fourier级数展开法求得了热环境下带压电层的功能梯度复合材料混合层合板的自由振动及动力响应的解析解，分析中考虑了材料热物参数对温度变化的依赖性，讨论了环境温度和控制电压对固有频率及动力响应的影响。

Utilizing the terra-mechanics equation and parameters of the lunar topsoil (the following is abbreviated as lunar-soil), the drawbar clevis pulling force of wheel was predicted by calculation.

应用地面力学方程和月球表层土壤参数计算预测了车轮的挂钩牵引力。

In this paper, a uniform numerical solution of the elliptic equation singular perturbation problem with two directions of turning points is considered.

讨论具有双向转向点的椭圆型方程奇摄动问题的一致数值解法，证明带指数型拟合因子的差分格式关于小参数ε的一致收敛结果。

Elliptic curves discrete logarithm ; elliptic curve domain parameter ; point group ; base point ; quadratic remainder ; quadratic congruence equation

椭圆曲线离散对数；椭圆曲线域参数；点群；基点；平方剩余；二次同余方程

In order to solve parabolic equation of heat conduction with interval parameters, the regions of space are discretized by finite elements and the regions of time are discretized by finite difference. The interval finite element method based on the element is established via the combination of interval analysis and the traditional finite element method.

对具有区间参数的热传导抛物型方程的求解，在空间域上利用有限单元离散，在时间域上利用差分离散，将区间分析和常规的有限元法相结合，建立了求解不确定温度场的基于单元的区间有限元方法。

The vapour and plasma ignition times of the target are got based on the equation of heat conduction and cascade model. We suppose that the plasma is ignited when 210 generations of new electrons are born in vapour generation time. The influence of temperature on the thermodynamics and optics parameters of material also have been considered in the model. The resulting theory has good agreement with the experiment and overseas report. A blade method to measure the laser spot is given in this paper with validation and error analysis. The plasma threshold of metals in atmosphere and water ambients both are diagnosed with the light deflection and piezoelectric transducer. A Q-switched pulsed Nd:YAG laser operating at infrared (1064nm), visible(532nm) and ultraviolet (355nm) wavelengths has been used. Al、Fe、Cu are used as targets and get a similar results with both method. Theoretical and experimental analyses are applied on the influence of wavelength on the threshold have been done, both of which have shown that the plasma threshold of metals decrease as the laser wavelength increases; The plasma threshold of metals are higher in water than in air and the pressure of the shock wave in water is five times higher than in air.

从热传导方程和雪崩电离机制出发，假设当电子增值2~(10)倍时，考虑了温度对材料热力学和光学参数的影响时，得到了气化和等离子体点燃的时间，利用该模型进行计算得到的结果与国内外报道及自行通过实验测得的阈值基本一致；提出了利用刀刃法测量激光光斑面积的方法，并通过实验进行了验证和误差分析；利用光偏转装置和压电换能器分别对空气和水中金属等离子体点燃阈值进行了实验诊断，激光器均为调Q—YAG激光器(波长1064nm，532nm，355nm，脉宽10ns)，靶材分别为Al、Fe和Cu，两种测试方法得到的等离子体点燃阈值基本一致；本文从实验和理论计算两个方面讨论了波长对等离子体点燃阈值的影响，均得到了等离子体点燃阈值随着波长的增加而减小的结论；对空气中和水中不同环境下金属等离子体的点燃阈值进行了比较研究，得到了金属在水中的等离子体点燃阈值比空气中的大，且水中产生的冲击波的压强是空气中的5倍左右的结论。

Then with some special parameters selected, the equation of motion in the phase plane is obtained.

为了更深入研究系统的运动规律，寻找某些特殊参数以得到系统在相平面内运动方程的解析表达式。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。