近似法

Combining the definition of CWT and the derivative property of convolution, we constructed a general method to calculate the approximate derivative of signal through CWT by using the first and second derivative of Gaussian function, Haar, and the first derivative of three-order-Spline function as wavelets. As compared with the other approaches of calculating derivative, which include the numerical differentiation, polynomial filters, Fourier transform, and the recently proposed DWT method, fast calculation and simple mathematical operation were remarkable advantages of CWT method. For the signal corrupted by severe noise (Signal-toNoise Ratio=5), the satisfactory results could also obtained via CWT method through appropriately adiusting the dilations.

在此基础上，(1)结合连续小波变换的特点和卷积的微分性质，提出了使用Gaussian函数的一阶和二阶导数，Haar和三次样条函数的一阶导数作为小波函数的连续小波变换计算信号近似导数的一般性方法，与其他导数计算方法(包括数字微分法，多项式滤波法，Fourier变换法和离散小波变换法)相比，本法简单便捷，计算速度快，对于噪声含量较高的信号(S/N为5)，只要适当调节尺度即可获得比较满意的结果。

According to the definition of the minimum zone method, the mathematical model is presented for evaluating flatness error and establishing datum plane equation.

分析了常用的近似评定法(三点法、对角线法、最小二乘法等)存在的局限性，根据最小区域法的定义，给出了基准平面方程及平面度误差评定目标函数数学模型的建立方法，并举例说明了采用Matlab进行平面度误差的计算。

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。

Based on chapter two, In chapter three, the method of multiple scales is introduced to the study of the multiple-dimensional nonlinear stochastic systems under random external excitation. Using method of multiple scales, we strictly deduce the equation of modulation of amplitude and phase. The effects of random excitations are analyzed; numerical simulations verify the results. Theoretical and numerical simulations show that when the intensity of the random excitation increases, the nontrivial steady state solution may be changed from a limit cycle to a diffused limit cycle.

在第二章基础上，第三章将多尺度法引入到相应的随机系统的研究中；严格推导了系统的约简方程，用矩方法求出稳态解应满足的方程，获得一些结果；并且数值模拟结果与理论推导的结果是一致的；并注意到，与其对应的确定性系统相比较，系统响应从周期解变为近似周期解，系统的相轨线从极限环变为扩大的近似极限环；随着激励带宽的增大，此扩大的近似极限环的宽度将增大。

Secondly, point out that meshless method is different from finite element method in handling boundary condition and numerical integral because the approximation function of meshless method is not inserted function, it have itself special methods. Deduces meshless Galerkin essential equation of parabolic partial differential equation with the method ofweighted residuals------Galerkin. Furthermore, discusses the main factors which may effectthe calculation precision and give some suggestion with which can get the best result.

其次，由于无网格法的近似函数不是插值函数，所以无网格Galerkin法在处理边界条件和对区域积分时是不同于有限元的，它有其独特的处理方法，从加权残量法——Galerkin出发，推导出抛物型偏微分方程无网格Galerkin法的基本方程，并对影响无网格Galerkin法的主要因素进行探讨，给出了取得最佳效果的相应建议。

A program based on four kinds of methods in thermal analysis is designed for finding out the mechanism of decomposition reaction of explosives and calculating their kinetic parameters. Compared with the Kissinger's method, the program here adopted has the advantage of exploring the reaction mechanism besieds a calculation of the kinetic parameters. Mechanism of decomposition of the explosive PYX was determined applying this program. The kinetic parameters of PYX calculated by non-isothermal integral meth...

以热分析理论为依据，摒弃了以往仅用一种热分析法进行反应动力学研究和近似假设─—炸药的热分解反应机理f＝（1—α）n所带来的弊病，采取4种热分析方法（等温积分法、等温微分法、非等温微分法、非等温积分法）相结合的方法，编制了计算程序，首先判断反应机理，然后求取动力学参数，用所编程序对PYX炸药的反应动力学进行了研究，用非等温法判断了PYX炸药的反应机理，并求得动力学参数，所求参数与Kissinger法求得的结果十分接近。

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。

Maximum likelihood detector is the optimal detector and has the best performance. The challenge of MLD is the high computational complexity. K-Best decoding algorithm has been proposed to reduce the computational complexity. K-Best decoder algorithm computes Partial Euclidean Distance and only keeps the best K nodes that have the smallest accumulated PEDs. After completing breadth-first tree search, we will have K leaves with the smallest PEDs.

最大相似度侦测法是公认最佳化的演算法，有著最好的侦测效能，但运算复杂度将会随著调变群集和传送天线数目大小而呈指数型增加。K-Best球型解码演算法因而被提出来，得到近似最大相似度侦测法的结果，解决最大相似度侦测法运算复杂度过高的问题。K-Best球型解码演算法在计算完部份欧几里德距离后，需要取最小K个值做为候选点，再往下层去找候选点。

A simple radiation model was used to calculate daily changes of the aerosol radiative heating rates and cooling rates in different months. Two-stream approximation, hemispheric constant method, adding method and doubling method were applied in the computation.

摘 要：采用两流近似辐射模式，应用半球常数法近似，采用累加法和倍加法，计算了不同月份大气气溶胶的辐射加热率和减温率的日变化。

This paper reviews and summarizes the progress in this field as follows: the mathematical model and the difficulty of the analytical solutions is introduced; discusses the latest progress of the numerical solutions is discussed; the finite difference method, the Godunov method, the Boltzmann method, and the KFVS method of one-dimensional dam-break problem are introduced; the TVD method, the discontinuous finite element method, the finite volume method and characteristic method of two-dimensional dam-break problem are discussed; the applicability, the advantage and the disadvantage of each method are analyzed; and the progress in the numerical calculations of flow of fluid with free surface are presented.

回顾和总结了国内外对溃坝水流演进问题的研究进展：介绍了溃坝水流的数学模型及解析解法存在的困难，进而讨论了数值解法的最新进展；论述了求解溃坝水流一维问题的有限差分法、近似黎曼解的Godunov格式法、Boltzmann法、KFVS法和二维问题的TVD格式法、间断有限元法、有限体积法、特征线法，并分析了各种方法的适用范围和优缺点，及讨论了限制函数的使用；介绍了利用自由水面追踪方法计算溃坝水流的研究进展，并根据目前存在的不足和实际工程的需要，提出了进一步研究的方向和发展趋势。

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。