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This function is a kind of orthonormal function, and it can approximate almost any curve in quadratic continuous integral space, thus it enhances the generalization ability of the SVM.

该核函数不仅具有平移正交性，而且可以以其正交性逼近二次可积空间上的任意曲线，从而提升了支持向量机的泛化性能。

It is also pointed out that the fuzzy controller implemented through this way can approximate any continuous real function.

摘要基于对模糊集基本特性的分析，提出了一种模糊集合的距离度量方法，与传统方法不同的是它不但与模糊集的质心有关，而且与模糊集的基数有关；其次讨论了如何基于这种距离的定义来实现模糊控制，并指出基于这种方法实现的模糊控制器可以逼近任意连续函数。

Computer simulation results show that a continuous surface obtained from a group of discrete data of a reference defect can be used to determine the approximate shape of an unknown defect.

求解正问题的各种方法不仅可用于研究影响红外探测精度的各种因素，而且它们在求解反问题及处理噪声的过程中也是必不可少的。

The results show that the frequency characteristic corresponds with vortex structures; the detail and approximate characteristics of signal are reflected by wavelet coefficient at different scales; the coefficient map of continuous wavelet transformation reveals the self-similarity of the signal.

采用傅里叶变换和小波变换技术，实现了混合层密度脉动信号的频谱与多分辨率分析，结果表明：信号的频域特性与流场的涡结构相对应，不同层面的离散小波系数反映了不同尺度下信号与图像的细节和平滑近似特征，连续小波变换系数图定性的反映了信号的自相似特征。

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。

Firstly, we prove that if we select nodes properly, and let the distance between these nodes sufficiently small, cubic polynomial spline can approximate a continuously differentiable function, which with continuous derivatives of second order and discontinuity of the first kind in the derivatives of fourth order, to any desirable accuracy. This result lays a theoretical foundation for representing trajectories by splines and double orthogonal basis.

一是证明了适当选取节点并使节点距充分小时，三次多项式样条可以逼近具有二次连续导数的分段四次连续可微函数到足够的精度，这一结论为用样条和双正交基表示弹道打下了理论基础。

The stream data have the features of realtime, continuousness, orderliness and infinity, whose duplicates are detected generally by approximate methods which omission often exists.

流数据具有实时、连续、有序及无限等特点，一般使用近似方法检测重复，从而存在漏检等缺点。

In addition, a group of conditions which guarantees the approximate controllability of the system is found out.

三、首次建立并研究具有年龄分布和相互作用的两种群系统的控制策略。

In section 2, we prove the approximate controllability of the linearized system by means of a cost function.

第二节我们用传统的变分方法证明了系统(1.1)线性化以后的逼近能控性。

Because of the problem of convergence, the key techniques to complete the one step simulation were explored thoroughly. The geometry mapping method based on finite element model and inverse deformation was developed to get the approximate initial blank for one step simulation. The effective selection of convergence factor in Newton-Raphson method was studied. The divergence criterion in iterative process for one step simulation was put forward. Also the countermeasure to ill equations coefficient matrix was studied.

由于存在收敛性的问题，本文重点研究了一步模拟方法计算机实现的关键技术：提出了基于有限元模型的几何映射方法和反向变形方法来确定初始毛坯的近似解，研究了带收敛因子的Newton-Raphson方法中如何高效地选取收敛因子，提出了一步模拟迭代求解过程中的发散准则，并研究了病态方程组系数矩阵的修正方法。

There are different types of personal loans available.

有许多不同类型的个人贷款优惠。

The above mentioned teaching model of spiral rising can be used to avoid rigidness in teaching.

上述螺旋式上升的教学模式，可以避免教学形成模式後的僵化现象。