查询词典 linear operator

The main objective of this paper is to extend and complete the Sims limit-point, limit-circle classification on second order linear differential equations with a complex coefficient , and to study its Weyl function and Weyl solution , then we obtain some new results.

本文的主要目的是推广和完善Sims关于复系数二阶微分方程的极限点和极限圆理论，并且研究了它的Weyl函数和Weyl解，得到了一些新的结论。

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。

It is well known that the method of separation of variables is an efficient way to solve linear partial differential equation.

众所周知，分离变量的方法是研究线性偏微分方程的最实用、最有效的工具之一。

In the case of two kinds of chaotic observes, one is constructed by differential form, the other is constructed by linear and nonlinear feedback synchronization.

混沌观测器的设计有两种类型，一类基于微分形式构造；一类是塞于耦合系统线性与非线性反馈同步实现的。

A linear-quadratic differential game model based on the theory of differential games in military field is constructed,and then,a solution for its open-loop equilibrium strategy is given and an application of the solution in an arms race is given.

以微分对策在军事领域中的应用为背景，建立一类线性二次型微分对策模型，讨论其开环均衡策略解法，将其运用到一个具体的两国军备竞赛的模型中。

The result that will help to solve the linear system of differential equation and limited element method.

结论对于求解差分方法、有限元方法及科学计算中产生的线性方程组提供理论支持。

This course is suitable of students who have mastered infinitesimal calculus, linear algebra, set topology, differential geometry of curves and surfaces.

微分流形己成为现代数学研究的基本对象，是联系经典数学和当代数学文献的桥梁。

A simple linear model for the fixed diffraction angle was set up by numerical calculation and parameter fitting.

针对卫星光通信中衍射角固定的应用情况，通过数值求解和参量拟合，建立了一个基于平面方程的简单控制模型。

A fundamental solution for the linear case of the complex diffusion equation is developed.

一个复杂的线性情况下根本的解决办法扩散方程的发展。

Circuit principles, analogue circuit, digit circuit which laid me a solid foundation of circuit for the study of communication; the study of electronic circuit of communication provided me with the working principles of analog communication system; the study on communication theory made me grasp the working methods of digital communication; the study on electromagnetic field, electromagnetic wave and aerial let me know that how signals travel through signal paths and how to apply signal and linear system, random signal and system to the research of noise's impact on signals

学习了电路原理、模拟电路、数字电路打下了学习通信的电路基础；学习了通信电子线路掌握了模拟通信系统的工作原理；学习了通信原理掌握了数字通信的工作方法；学习了电磁场与电磁波、微波与天线了解了信号如何在信道中传输；学习了信号与线性系统和随机信号与系统来研究噪声对信号的影响。

In the days of sailing vessels the crew were afraid they would be becalmed on the ocean.

在使用帆船的时代，船员们担心他们会因为无风而无法在海洋上航行。

As long as foreign donors pay the PA's salary bill, few expect a new intifada.

只要外国继续为巴权力机构的薪水买单，希望发动新暴动的人便寥寥无几。