离散数学

The book is divided into 14 chapters, including Introduction, continuous control system theory, process and discrete sampling, Z transform, sampled-data systems, discrete approximation of continuous system the equivalent, based on mathematical transform the classical design method, based on state space pole placement design methodology, multi-variable system of quadratic optimal control, quantitative effects, the choice of sampling period, the digital control system modeling, digital control system for a variety of design methods, variables quadratic optimal control systems, sampling cycle of selection, non-linear control of the problem, as well as digital control system, a typical application - Disk drive servo control design.

全书共分14章，内容包括概论、连续控制系统理论、采样过程和离散化、Z变换、采样数据系统、连续系统的近似离散等效、基于数学变换的经典设计方法、基于状态空间的极点配置设计方法、多变量系统的二次型最优控制、量化效应、采样周期的选择、数字控制系统的建模问题、数字控制系统的各种设计方法、变量系统的二次型最优控制、采样周期的选择、非线性控制的有关问题，以及数字控制系统的一个典型应用——磁盘驱动器的伺服控制设计等。

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。

For the dynamic system of discrete coupled and nonlinear three phase voltage source PWM rectifier, the cycle switch average operator is introduced to transform the discrete system into continuous and the small signal perturbation method is used to transform the nonlinear system into linear, the small signal dynamic mathematical models are set up.

中文摘要：针对三相电压型PWM整流器这个离散的、耦合的、非线性的动态系统，引入开关周期平均算子将离散的系统变换为连续的系统，应用小信号扰动法将非线性的系统化解为线性的系统，进而分析系统的小信号动态数学模型。

Discrete calculus , discrete probability distribution s, discrete Fourier transform s, discrete geometry , discrete logarithm s, discrete differential geometry , discrete exterior calculus , discrete Morse theory , difference equation s, and discrete dynamical system s.

在应用数学中，离散模型连续模型的离散近似。在离散模型中，离散方程are fit to 数据。使用递推关系是这种建模方式的一般方法。时标微积分是差分方程理论与微分方程理论的统一，应用在需要建立离散和连续同步数据模型的领域。

The mathematical model is dispersed by finite-volume method and the dispersed equations are solved by SIMPLER algorithm. This is the first time to solve a problem of drilling fluid mechanics with the numerical method of Newtonian fluid mechanics.

5首次将牛顿流体力学经常采用的数值方法用于钻井流体力学的研究中：用有限体积法离散钻井液流动和传热的数学模型，用Simpler算法求解该数学模型的离散化方程。

On the basis of the relation, we will prove some useful properties of the discrete Zak transform which lay the foundation for the computation of discrete Gabor transform.

利用连续Zak变换和离散Zak变换的关系，证明了离散Zak变换的一些性质。为进一步研究离散Gabor变换建立了数学基础。

Moreover on-line forum etc. shuttering cake of the website also contributes to the interest that the student strengthens to study long-lost mathematics.

另外网站的在线论坛等模块也有助于学生增强学习离散数学的兴趣。

At first, setting up the arith relation between the signal input and the signal output of the generalized multi-carrier system of the Discrete Fourier Test spread-spectrum; then setting equilibria parameters of the frequency field equilibria subcarrier of the generalized multi-carrier system of the DFT spread-spectrum according to channel frequency response, channel noise variance and equilibria method; then calculating average power of useful signal, interferential average power between signals as well as noise variance of the generalized multi-carrier system receiving terminal of the DFT spread-spectrum according to the arith relation as well as the frequency field equilibria parameter, and recomputing available signal information noise ratio, so as to calculate the available signal information noise ratio of the generalized multi-carrier transmission system accurately, the method for estimating the available signal information noise ratio can be used for link self-adapting transmission solution of the generalized multi-carrier system based on Discrete Fourier Test spread-spectrum and radio material management.

一种DFT扩频的广义多载波系统的SINR估计方法，其通过首先建立所述离散傅立叶变换扩频的广义多载波传输系统的信号输入输出之间的数学关系，然后根据信道频率响应、信道噪声方差和均衡方法，设定所述DFT扩频的广义多载波传输系统的频域均衡子载波的均衡系数，再根据所述数学关系及所述频域均衡系数分别计算所述DFT扩频的广义多载波传输系统接收端有用信号的平均功率、信号间干扰的平均功率以及噪声方差，再计算有效信干噪比，如此以实现对广义多载波传输系统的有效信干噪比的准确计算，该有效信干噪比估计方法可用于基于离散傅立叶变换扩频的广义多载波传输系统的链路自适应传输方案和无线资源管理方面。

It effectively solves the problem of contact mechanics between burden granules. The dynamic data structure that is a linked list is built to save and delete the varying data in simulation calculation process. Therefore, the distinct element method simulation model of charging bell-less top blast furnace is established in view of the distinct element method model of blast furnace burden granular.

本文首先对离散单元法的基本原理和数值计算方法进行了系统研究，针对高炉炉料颗粒介质特点，对离散单元法进行了相应改进，建立了高炉炉料颗粒运动的离散单元法基本数学模型，推导出了相应的高炉炉料颗粒离散单元法数值计算基本参数的计算公式，例如阻尼、刚度、时步等，并确定了合理的数值模拟参数值。

The article that is based on theoretical knowledge of the discrete math and the computer technique provide numeric stimulate pattern of the flat-faced follower eccentric circle institution, which is applied to resolve the wearing problem of flat-faced follower eccentric circle institution.

本文基于离散数学理论和计算机技术提出了平底从动件偏心圆机构系统磨损的数值仿真模型，可用于解决平底从动件偏心圆机构系统的磨损问题。

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。