微分的

The maximum principle of the optimal control for the stochastic systems described by Zakaj stochastic partial sifferential equationis proved by approximately minimum point theorem of E. Ekeland. The convexity and compactness of the set of control values is not assumed, and it is not necessary for the maximum principle about differentiability in control variables included in drift term of the stoch astic system and the integrand in index functional, and costate process satisfies the stochastic partial ...

在不假便定控制变量取值的集合是凸的和紧的，不要求随机系统的漂移项和指标泛函的被积函数关于控制变量具有可微性的情况下，用E，Ekeland的近似极小点定理证明了Zakai随机偏微分方程描述的随机系统的最优控制的最大值原理，和用很简洁的方法证明了协态过程满足一个随机偏微分方程。

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。

In order to testify our whether correction to Rossi's exchange term andthe potential of electron and nucleus is reasonable, we calculate 〓 moleculeelastic differential scattering cross section by electron impact on 100eV, ourresult is obviously better than Rossi's. Then we calculate elastic differentialscattering cross section at 150eV. In order to check the program thatcalculates molecule excitation cross section by electron impact, we calculatehydrogen excitation cross section from ground state to 〓 state at 20eVand 30eV, oxygen excitation cross section from ground state to 〓 state at15eV and 20eV. These calculations are in agreement with other theoreticresults, and experiment measure. Finally, we calculate sulfur moleculeexcitation〓 cross section by electron impact at5eV,7eV,9eV, 11eV, 13eV,15eV, and draw curve of excitation total crosssection corresponding to incident electron energy.

为了核对我们修改的计算激发态的程序是否正确，计算了电子与氢分子碰撞从基态激发到〓态入射能量分别为20eV和30eV时的微分截面以及电子与氧分子碰撞从基态激发到〓态入射能量分别为15eV和20eV时的微分截面，与别人的理论计算结果、实验的测量值基本一致，最后计算了电子与硫分子在5eV、7eV、9eV、11eV、13eV、15eV时的碰撞激发〓截面，作出了电子的入射能量与激发总截面的关系曲线，找出了总截面最大时对应的电子入射能量大约是11电子伏。

Integral of one variable functions, improper integral and its convergence properties.

本课程的主要内容包括：1 各种极限运算，其中包括数列极限、函数极限以及上、下极限；2 一元函数的微分学，包括微分和导数的运算法则、微分中值定理及其应用等；3 一元函数的积分和广义积分及其收敛性；4 级数及其收敛性，包括数值级数的收敛性和函数项级数的各种运算和性质；5 多元函数的微分学及其应用，其中很多方面与一元函数的微分学近似，需要注意它们之间的区别；6 多元函数的积分学，包括多重积分的性质与计算，多重积分的的应用等；7 曲线、曲面积分及其应用；8 含参变量积分的计算与性质；9 Fourier 级数及其应用，等等。

On the whole, we do as follows: Firstly, we list some conceptions and lemmas for later use. Secondly, we define δ-fine partitions for infinite interval and integral of vector-valued functions on infinite interval, and discuss the properties of integral, and characterize its primitives...

主要包括以下五部分内容：在第一部分中，我们介绍了本文所用到的基本概念和引理；在第二部分中，通过定义无穷区间上δ-精细的分法，我们给出了无穷区间上向量值函数的积分的定义，并讨论其性质，还给出了原函数的刻划；在本文的第三部分中，我们着重讨论了无穷区间上向量值函数积分的收敛定理；在本文的在第四部分中，我们首先应用无穷区间上向量值函数积分的收敛定理给出了常微分方程整体广义解的存在性定理，其次应用强积分对Banach空间常微分方程广义解进行了讨论；最后，在第五部分中，我们将模糊积分推广到无穷区间上并给出了其数值计算方法。

A important result is the one-order expression of AR Yt = DYt-1 + E, from paralleling a high-order differential equation transformation into a one-order differential equation system, the one-order expression exposes that the AR is only a certain more-multivariable power series processAnd, if a process is described as an AR, the sufficient and necessary condition is the spectrum norm A of the coefficient matrix D less than one.

作者用高阶微分方程化一阶微分方程组的方法，获得多元弱平稳序列p阶自回归模型的一步滑动平均表达式，证明了AR的是一个更高维的幂级数的线性过程，从而，说明了AR关于序列依概率成立的充要条件是：该模型更高维的幂级数的线性过程的表达式中系数矩阵D的谱范数λ＜1。

After the brief retrospect of spectral methods applied to get the numerical solutions of partial differential equations, the Walsh spectral methods are extensively studied. A new method of designing the "derivate operator" and a new Walsh spectral method based on quasi-Walsh order are proposed, which primarily prove the special uses of it.

回顾了数值求解偏微分方程的谱方法，比较深入地考察了数值求解偏微分方程的Walsh谱方法，提出了一种新的设计"求导算子"的方法，基于这样设计出来的"求导算子"，提出了一种新的基于类Walsh序的Walsh函数的Walsh谱方法，初步验证了这种序的特殊价值。

According the experiential formulas of headbox to design the stepped diffuser headbox's geometry parameters. Supposing Paper suspension flow as potential flow and basing on hydrokinetic and computational fluid dynamics theories, we can solve the elliptoid partial differential equations which are followed by the flow functions and the potential functions by finite element method and simulate the flow's speed distribution with pde toolbox of matlab software. The simulate results and the flow analysis have good precision.

按照流浆箱的经验设计公式，设计阶梯扩散式流浆箱的各组件几何参数，以流体动力学、计算流体力学等理论为基础，假定浆流的流动为势流，采用有限元法求解浆流流动时其流函数和速度势函数所符合的椭圆型偏微分方程，应用matlab软件的偏微分方程工具包pde toolbox，模拟出所设计的流浆箱各组件内的浆流的流场流速分布，模拟结果与数值计算流动分析结果吻合。

The nonlinear hyperbolic conservation laws of the transient flow of the media in gas pipeline are hard to he solved, so, the control conservation laws are constituted of mass, momentum arid energy conservation laws, TVD/Godunov hydrid algorithm is used to simulate the transient flow in gas pipeline, and the traditional splitting approach processing nonlinear convection in momentum equation is dismissed ,the convection tern; is directly processed, in the way, the stablization of the algorithm and emulating accuracy of the transient flow are greatly improved.

针对管道中介质瞬变流动的非线性偏微分方程组难以解析求解的问题，由质量、动量、能量三个偏微分方程构成的控制方程组，应用TVD/Godunov混合算法数值模拟天然气管道中气体的瞬变流动，摒弃了传统的差分方法时动量方程非线性时流项的线性化处理，而直接处理非线性对流项，从而大大提高了算法的稳定性和管道瞬变流动的仿真精度。

To reduce or remove size effect, the size classification elimination method, volume average method and normalization method based on volume were presented and the calibration and prediction results indicate that these three methods could reduce or remove the size effect effectively. The normalization method is more suit to in-line application and obtained better calibration and prediction results with the r of 0.789, 0.858 and 0.947, the RMSEC of 0.596, 0.499 and 0.313, and the RMSEP of 0.606, 0.686 and 0.413 than the results without normalization with the r of 0.716, 0.793 and 0.848, the RMSEC of 0.678, 0.592 and 0.515 and the RMSEP of 0.825, 0.764 and 0.714 for the original spectra, the first derivative spectra and the second derivative spectra with soluble solids content using partial least square method , respectively. 4. Owing to much thick skin of watermelon, contrast experiment was conducted in skin-peeled watermelon and intact watermelon to compare the influence of skin on spectra.

针对西瓜果型大且差异显著的特点，研究果型差异对可见／近红外光谱以及建模与预测结果的影响，并提出三种方法消除或减小这一影响因素，分别是分级消除法、体积平均法和基于体积的正则化方法，其中基于体积的正则化方法，更适合在线生产应用，该方法使果型大小差异明显样品的原始光谱、一阶微分光谱、二阶微分光谱在对可溶性固形物含量检测时，采用偏最小二乘法的建模与预测结果由原来的校正相关系数r分别为0.716、0.793、0.848提高到r分别为0.789、0.858、0.947，均方根校正标准偏差RMSEC由原来的0.678、0.592、0.515分别降为0.596、0.499、0.313，均方根预测标准偏差RMSEP由原来的0.825、0.764、0.714分别降为0.606、0.686、0.413； 4。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。