近似连续

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。

ABSTRACT The main content of this dissertation is focused on formal Verification of Hybrid Systems with complex continuous dynamics. The research pivot is to solve the difficulties of Discrete model Approximation of Complex Continuous dynamics .

本文所有论述均围绕着解决具有复杂连续动态混合系统的形式验证这个主题而展开，以解决验证中复杂连续动态的离散近似所存在的困难为研究重点。

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。

And the effects of length of data N to the approximate entropy of chaotic system isalso analyzed.All these are accomplished by examining several time series produced by a surperposition of white noise and noise-free data.It uses the discrete system logistic map and continuous system Lorenz attractoras the examples.

以Logistic方程描述的离散系统和Lorenz方程描述的连续系统为例，采用白噪声和无噪声信号以不同的信噪比混迭而成数据的方法，分析了相同数据长度N，不同信噪比下，混沌系统近似熵的变化；相同信噪比，不同数据长度对系统近似熵的影响。

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。

The discrete 0-1 programming problem is translated into continuous nonlinear optimization problem by polish function, and the nonlinear optimization problem is solved by contraction algorithm.

3利用过滤函数近似处理连续体拓扑优化问题，使用缩并解法实现了对连续体拓扑优化问题的求解。

Dependent on the past research in seaice, in Bohai Sea, in 2003-2004 winter and 2004-2005 winter with level ice for the target we open the field experiments to study the essential spectrum characteristic of ice, removing by testing means various nonessential factor for sea water in the fixing big ice plate, building up 170 growth conditions to look like under the natural condition, the growth expect different sample series; in 2004-2005 winter and 2005-2006 winter continue two pass to break thorough Bohai Sea in the ship to collect 59 sea ice sample that have the non-essential ice factors in winter, open the influence research that the field hangs sand to contribute to the spectrum of the ice body; in 2005-2006 winter, fast ice to open the field spectrum curves to coast and analytical research.

总结前人的研究成果和开展一系列的室内实验，在渤海—北半球纬度最低的结冰海域，于2003/2004、2004/2005 连续两个冬季以单层平整冰为目标开展实验研究一年生海冰的冰体本质光谱特征，在固定冰盘上以实验手段摒除各种光谱干扰因素，在自然条件下建立170 个生长条件近似、生长期不同的样本系列；于 2004/2005、2005/2006 连续两个冬季通过破冰船深入渤海采集59 个具有非冰体本质因素的海冰样本，开展悬沙对冰体反射光谱的影响研究；于2005/2006 冬季，针对沿岸固定冰开展光谱测量和分析研究。

However, the solutions of the Cauchy problem of the nonlinear hyperbolic system generally develop singularities in finite time even if the initial data are small and smooth.For this reason, solutions must be found in the space of discontinuous functions. Therefore, one can not directly use the classical analytic techniques that predominate in the theory of partial differential equations of other types. Instead, we construct approximate solutions via the singular perturbation methods. By using the compactness of the approximate solutions, we can obtain the existence of the solutions of original system.

然而一般而言，即使是在初值很小且光滑的情况下，非线性双曲型守恒律的Cauchy问题的解在有限时间内也会出现奇异性，为此，我们必须在不连续函数空间中寻找上述问题的解，因此对这类问题的研究，我们也不可能直接利用在其它类型的偏微分方程中占主导地位的解析方法来解决问题，而是通过奇异扰动法构造近似解，由近似解的紧性得到原问题解的存在性。

However, there are always dispersed particles of capsulation structure in PBT/ E-MA-GMA/nano-CaCO3 when mixed directly with E-MA-GMA and nano-CaCO3 together or mixed nano-CaCO3 capsulated by E-MA-GMA.

SEM分析发现，在高的PC用量时，PC分散相在PBT/PC/E-MA-GMA体系中不再呈近似球形的颗粒分布，而是呈现出极不规则的近似条状或片状的结构形态，且局部区域有形成连续相结构的趋势。

Continuation--Optimization method is proposed for approximate synthesis of linkages The synthesis of planar four-bar and six-bar linkages are studied using this method and several solutions are obtained. Thus, selection of the optimum solution for approximate synthesis of linkages is realized.

提出了机构近似综合的连续---优化法，并应用该方法研究了平面铰链四杆及六杆机构的函数综合，得到了多组机构尺寸方案，实现了机构近似综合的多方案优选。

Objective To investigate the effects of interleukin-1 β converting enzyme gene on the biologic characteristics of ovarian cancer cells.

目的 探讨白细胞介素-1 β转换酶的表达，对卵巢癌细胞生物学特性的影响。

Campylobacter: This illness is the most commonly identified cause of diarrheal illness in the world.

弯曲：这种病是最常见的原因查明腹泻病，在世界上。