二次函数

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。

In this paper,we give the error expressions of piecewise linear Lagrange polynomial interpolation and piecewise cubic polynomial interpolation using the Taylor expansions.

中文摘要：本文利用Taylor展开得到三角形上线性Lagrange插值和三次Lagrange插值的导数余项公式，对这些余项公式进行分析，给出了两类能以四阶精度逼近被插函数在对称点的导数值的格式，一种是在均匀剖分时其分片线性插值的相邻单元的导数值的后处理格式，一种是在六片强正规剖分时的三次插值在对称点上的导数值的后处理格式，使得在已知原函数在各节点的值后，通过一个简单的线性计算就可得到原函数在对称点的导数的一个超逼近值，将以往提出的平均导数的二阶精度提高到四阶。

By introducing the NCP function, the KKT conditions of POPF system are transformed equivalently. Based on the transformed nonsmooth nonlinear algebraic equations, the FOSMM is used to determine the POPF model expressed by the numerical characteristic of variables. The model includes nonsmooth functions, so it can be solved by a semismooth L-M method based on the subdifferential.

将概率最优潮流表述为随机非线性规划问题后，利用非线性互补函数将该问题的KKT条件进行转化，基于转化后的非线性代数方程组，利用一次二阶矩法确定了以待求量的数字特征表示的概率最优潮流模型，由于该模型包含不光滑函数，因此采用基于次微分的半光滑L-M方法求解。

In the POPF model, wind farm is modeled by the probabilistic wind farm model considering the reactive power-slip characteristic, and the inequality constraints include not only the unit output constraints, the ratio constraints, the voltage constraints and the line current constraints but also the reactive compensation capacity constraints in wind farm and the system climbing capacity constraints per minute. By introducing the NCP function, the KKT conditions of POPF system are transformed equivalently. Based on the transformed nonsmooth nonlinear algebraic equations, the FOSMM is used to determine the POPF model expressed by the numerical characteristic of variables. The model includes nonsmooth functions, so it can be solved by a semismooth Newton-type method based on the subdifferential.

概率最优潮流模型中，风电场采用考虑无功功率—滑加热器差特性的风电概率模型，不等式约束中除了机组出力约束、有载调压变压器变比约束、电压约束和支路电流约束，也考虑了风电场无功补偿容量约束、系统的分钟级爬坡能力约束；使用非线性互补函数将概率最优潮流的KKT条件转化为一组包含有不光滑函数的非线性代数方程组，然后基于一次二阶矩法确定了以待求量的数字特征表示的POPF模型，由于该模型包含不光滑函数，因此采用基于次微分的半光滑牛顿型方加热器法求解。

Based on the Lyapunov stability theory and the linear matrix inequality approach, the sufficient condition and conformation approach of the guaranteed cost controller was given, which could make the closed-loop systems quadratic stable for all admissible uncertainties, as well as guarantying the cost was bounded in a limitation.

所设计的保性能控制器保证了对所有容许的不确定性，不仅使得相应的闭环系统达到二次稳定，同时保证闭环性能指标函数具有上界。

Adhibiting the nerve cell and qurdratic capability target, by the self-adapting self-studying consistent and better abiding of the nerve cell ,the thesis realizes the conforming of the parameter not depending the canal mathematics ,furthermore the parameter can self-adjust for the information of the canal.Combining the BP nets and the routine PID controller, and adhibiting the linear optimization target function, the thesis realizes the conforming of the parameter not depending the canal mathematics, furthermore the parameter can self-adjust for the information of the canal. Using the MATLAB the thesis simulates and acquires some significative effects.

在传统PID渠道控制中引入了神经元和二次型性能指标，利用神经元自适应、自学习、并行处理及较强的容错能力，实现了PID控制中参数的整定不依赖于渠道数学模型，且PID参数能根据渠道的适时信息在线调整以满足适时控制的要求将BP网络与常规PID控制结合，并引入了最优化目标函数，利用BP网络来实现PID控制器参数的在线整定，将其运用于渠系等体积控制，并利用MATLAB软件进行了数值模拟仿真，取得了一些有意义的成果和较为满意的结果。

First, It estimates the frequency-modulated coefficients by performing Radon transform to the ambiguity function result of the LFMs.

首先，通过对信号模糊函数进行Radon变换获得各分量的调频系数。然后用滤除单分量自项二次项的方法使信号成为普通的正弦信号。

Nine substances containing hydrocarbon, alcohol, ketone, ester, water and 18 systems of isothermal VLE date have been calculated and the results show that using the quadratic functional local composition mixing rule the precision of vapor composition and pressure calculation is better than by using temperature mixing rule.

结果表明，二次形局部组成混合规则优于温度函数混合规则，对于丙酮-水、乙醇-水、甲醇-水及苯-丙醇体系计算气相组成与压力精度均有明显提高。

Aiming at the thermal resistance and pressure drop as two objective functions,the multiobjective optimization model of the microchannel cooling heat sink was built.

以热阻和压降作为2个目标函数建立了微槽冷却热沉的多目标优化模型，采用序列二次规划方法对微槽的结构尺寸进行了优化设计。

Finally, based on the studies above, the characteristics of pantograph/catenary are analyzed and the active pantograph is modeled. By using the linear quadratic optimal control law, the design objective is to minimize the performance index, which is a function of the state variables representing the pantographs dynamic characteristic and the active control force. The control system is designed considering the complete state feedback.

最后，在此基础上，分析了受电弓／接触网系统的工作特点，建立了受电弓主动控制系统的数学模型，利用线性二次型最优控制策略，以给定性能指标为最小值为设计目标，性能指标为表征受电弓动力学特性的状态变量和主动控制力的函数，考虑了完全状态反馈的情况，进行了控制系统的设计。

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。