计算中近似法

In this paper, on the base of paraxial approximations, we present a set of absorbing boundary conditions of 3D elastic wave equations and apply to the 3D elastic wave numerical modeling in isotropic medium.

本文基於傍轴近似法提出了计算三维弹性波方程的吸收边界条件公式，表示了各边界面、边棱和角点处波场所满足的单程波方程，并在三维弹性波数值模拟中进行了应用。

The formula can be used in approximate calculation of instable critical load of high pier in the design and construction.

本文利用能量原理的Ritz法，在对截面惯性矩变化作线性假定后，推导出变截面空心薄壁高墩失稳临界荷载近似计算公式，可用于设计施工中对高墩失稳临界荷载的近似计算。1中心压杆稳定理论及能量原理中心压杆的失稳问题是稳定问题中的一个最基本的问题。

Among used machine learning methods, the gradient descent method is widely used to train various classifiers, such as Back-propagation neural network and linear text classifier. However, the gradient descent method is easily trapped into a local minimum and slowly converges. Thus, this study presents a gradient forecasting search method based on prediction methods to enhance the performance of the gradient descent method in order to develop a more efficient and precise machine learning method for Web mining.However, a prediction method with few sample data items and precise forecasting ability is a key issue to the gradient forecasting search method. Applying statistic-based prediction methods to implement GFSM is unsuitable because they require a large number of data items to model a prediction model. In the contrast with statistic-based prediction methods, GM(1,1) grey prediction model does not need a large number of data items to build a prediction model, and it has low computational load. However, the original GM(1,1) grey prediction model uses a mathematical hypothesis and approximation to transform a continuous differential equation into a discrete difference equation in order to model a forecasting model.

其中梯度法是一个最常被使用来实现机器学习的方法之一，然而梯度法具有学习速度慢以及容易陷入局部最佳解的缺点，因此，本研究提出一个梯度预测搜寻法则(gradient forecasting search method， GFSM)来改善传统梯度法的缺点，用来提升一些以梯度学习法则为基础的分类器在资讯探勘上的效率与正确性；而一个所需资料量少、计算复杂度低且精确的预测模型是梯度预测搜寻法能否有效进行最佳解搜寻之关键因素，传统统计为基础之预测方法的缺点是需要较大量的数据进行预测，因此计算复杂度高，灰色预测模型具有建模资料少且计算复杂度低等优点，然而灰色预测理论以连续之微分方程式为基础，并且透过一些数学上的假设与近似，将连续之微分方程式转换成离散之差分方程式来对离散型资料进行建模及预测，这样的作法不尽合理，且缺乏数学理论上的完备性，因为在转换过程中已经造成建模上的误差，且建模过程仅考虑相邻的两个资料点关系，无法正确反应数列未来的变化趋势。

Results show that radial basis function and point interpolation methods possess Kronecker Delta function property, but the robustness is poor in some cases; the MLS approximation function does not possess Kronecker Delta function property, but it has good robustness. Differences among the three discretization schemes of meshless method are as follows:the collocation method requires no numerical integration and very little computational time while its robustness is poor; Galerkin method is not a truly meshless method due to the background meshes required for integration; the Petrov-Galerkin method is a truly meshless method and need numerical integration in each sub-domain, so it needs more computational time.

分析结果显示：径向基函数和点插值法均具有d 函数属性，但计算稳定性差；移动最小二乘近似函数不具有d 函数属性，但计算比较稳定；无网格方法中的3种离散方法不同之处在于：配点法不需要积分，计算量小，计算稳定性差；Galerkin方法需要借助背景网格进行积分，它不是真正的无网格方法；Petrov-Galerkin方法，是一种真正的无网格方法，它需要对每个子域进行积分，计算工作量较大。

On the basis of introducing the fixed point of Banach theorem, this paper firstly elaborates the important application of the existence of the solution of the linear algebraic equation and the ordinary differential equation, then it narrates the important application of obtaining the leading Newton repetitive process and the natural number the inferior square root and the equation root in the approximate calculation.

本文在介绍Banach不动点定理的基础上，首先阐述了其在线形代数方程、常微分方程解的存在性中的重要应用；然后讲述了其在求导Newton迭代法、求自然数的次平方根、求方程根的近似计算中的重要应用；最后，介绍了其在求一类递推数列极限中的应用。

The NIEL induced by low energy proton in Si and GaAs have been calculated using analytical method and Monte-Carlo code. Thin_target approximation was used when calculating NIEL by SRIM code and the result compared with that of other authors'. The results show that thin_target approximation is reasonable and NIEL scaling is feasible. The NIEL values become lower after taking into account the screening effect.

为此，本文采用解析法和基于Monte-Carlo方法的SRIM程序计算了考虑库仑屏蔽效应后低能质子在半导体材料Si，GaAs中的NIEL，SRIM程序在计算过程中采用薄靶近似法，并与其他作者的计算数据和实验数据进行了比较。

In this paper, the stray light and ghost image caused by multi-reflection in high power infrared optical systems are analyzed and discussed, and the comprehensive method incorporating paraxial approximation and real ray trace is presented; the data structure of binary tree is used in the storage of interdata so that the storage problem of huge-size data is resolved.

本文主要研究了大功率红外光学系统中光学表面多重反射而形成的杂散光及其数学模型与计算方法，提出了将近轴近似法和有限光线追迹法相结合的综合分析方法；同时在数据存储方式上采用二叉树这种数据结构，巧妙地解决了鬼像分析中海量的中间数据存储的问题。

The polynomial function bases are used to form the approximately matching function. Moreover, the discrete values of grey image is transformed to polinomial function that are exact fit at the considered pixel locations. As a result, The mathematical operations performed such as derivation, integration, and gradient evaluation also give out the polynomial functions, therefore, the system of undetermined coefficient equations is derived to be a system of linear algebraic equations.

我们把立体匹配过程看作泛函的极小化过程，因此选用变分问题近似解法的Ritz法构造数值算法，以多项式函数为基构作匹配函数的近似解，进而又利用多项式过样值点的拟合将离散的灰度图象变换为多项式函数，因此计算中所需的求导，积分，及梯度运算的结果仍然是多项式函数，最终将待定系数方程组化为线性代数方程组。

In a 1997 interview, Plass told me,"all sorts of things came together" that placed him at the scientific forefront: new detailed laboratory measurements of the absorption bands of water vapor, carbon dioxide and ozone; theoretical developments involving the influence of temperature and pressure on infrared absorption; new information about the carbon cycle and industrial emissions; and access to a new high-speed electronic computer to facilitate complex calculations of radiative transfer that replaced the older, graphical approximations.

在1997年的一次采访中，普拉斯告诉我：&所有的事情都赶在一块儿&，把他推到了研究的最前沿：测量水蒸气、二氧化碳和臭氧的吸收光谱带有了新的实验方法；温度和压强对红外吸收的影响理论有了新的发展；碳循环和工业废气排放有了新的资料；新的高速电子计算机代替了老式的图解近似法，让辐射传热的复杂计算变得简单了。

Simultaneously, the exports of ionization rate and nonionzed concentration are set up as a powerful tool for studying thoroughly the freeze-out effect. dN〓/dp and dN〓/dn are neglected in the linearized equation system of the iteration methods of Newton and Gummel, due to having lower 15 orders or more than dN〓/dn and dN〓/dp, thus the computing effort is cut down with no effect on precision. A new cut-off technique is adopted to accelerate the convergence speed, about twice reduced for Newton iteration method and six times or so for Gummel iteration method. The approximate formulae of Fermi-Dirac statistics are also put forward with simpler form and higher precision. 3. A term dependent on time is added to the electron and hole current succession equations respectively. It is only this model that conservation of charge in transient analysis and alternating small-signal analysis at low temperature can be kept by. 4. The performance of SE-PISCES is explained by the simulation example of PISCES-2B, diode.

研究了低温半导体器件模拟的数值方法：对载流子浓度进行了新的归一化；编制了不考虑掺杂所引进的内建电场时的电离率计算程序；由于低温杂质电离率随偏压状态而变化，为此编制了每次求解迭代时的电离浓度计算程序，并将其插入到求解迭代程序中；同时，设置了杂质电离率和未电离杂质浓度的出口点，为更深入地研究冻析效应提供了有力工具；在Newton迭代法和Gummel迭代法的线性化方程组中忽略了dN〓/dp、dN〓/dn，是因为它们比dN〓/dn、dN〓/dp低15个数量级以上，这样减小了计算量又不影响模拟精度；对Newton迭代法和Gummel迭代法采取了新的截断技术，提高了收敛速度，Newton法迭代法和两次左右，Gummel法减少六次左右；给出了表达式更简单而精度更高的Fermi-Dirac积分近似计算公式。

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。