本文即选用对称插值尺度函数作为解空间的基。
In this paper, we use the symmetric interpolating scaling function as the basis for the resolution space.
其次，证明了该尺度函数满足正交性﹑插值性﹑再生性。
Secondly, the scale function was proved satisfy orthonormal property interpolate property and reproducing property.
通过线性规划技术和采用尺度函数作为核函数来实现支持向量回归模型。
Using linear programming technique and scaling kernel function, the support vector regression model was obtained.
本文给出构造紧支撑三元不可分正交尺度函数和正交小波函数的新算法。
In this paper, we give a new algorithm of construction compactly supported trivariate orthogonal scaling function with dilation matrix 21, at the same time, the correspond wavelets are also given.
得出了不存在各分量满足反对称性的具有实用价值的2重尺度函数的结果。
Then it is proved the multi-scaling functions which are practically valuable and which components satisfy antisymmetry do not exist.
本文对已有的“协因子”算法进行了改进，并构造了二阶有限元双正交多尺度函数。
So, this method is modified in the article, and the finite element biorthogonal multiwavelets are constructed.
本文给出构造矩阵伸缩为2i的紧支撑二元正交尺度函数的一种算法，得到相应的小波函数。
In this paper, we give an algorithm of construction compact support bivariate orthogonal scaling function whose dilation matrix is 2i, the correspond wavelets are also offered.
结果表明，如果我们想从多尺度分析出发构造正交小波，那么该多尺度分析必须有正交尺度函数。
This result shows that if we want to construct orthonormal wavelets from a multireso- lotion, then that multiresolution must have an orthonormal scaling function.
立足于小波的构造，比较深入地探讨了尺度函数和小波函数的两尺度符号与小波构造的紧密关系。
Basing on the construction of wavelet, discuss the close relation between the scaling function and wavelet function's two scale symbol and wavelet construction.
构造的正交尺度函数和小波的两尺度方程中只包含4项，因而相应的分解和重构算法也只有4项。
There are only 4 terms in the corresponding refinement equations of the orthogonal scaling functions and the wavelets (and so do the decomposition and reconstruction algorithms).
并进一步构造了与尺度函数对称点一致、系数长度不超过8的所有对称（反对称） 小波滤波器组。
Moreover, all symmetric and antisymmetric wavelets, which have same symmetric point as the scaling function and the length of their filters are no more than 8, are also given.
基于多尺度函数面具的一种特定形式，提出构造一类具有正交、对称、紧支撑的多尺度函数的方法。
Based on a special form of matrix mask, a method of constructing symmetric orthogonal compactly support is presented.
然后利用正交多分辨率分析，给出由该尺度函数构造的一类频带有限的M进制正交小波函数的必要条件。
Next, by the orthogonal multiresolution analysis, the necessary conditions of a kind of M-band band-limited orthogonal wavelet function constructed by the scaling function are proposed.
通过研究MST的性质及与M带多尺度函数的逼近阶的关系，利用MST可以对M带多尺度函数的逼近阶进行提升。
MST has relation to approximation order. One can increase approximation of M-band multiscaling functions with help of MST.
谐波小波在频域具有良好的盒形谱特性，另外它比通常由二进尺度函数得到的小波还具如下优越性：存在确定的函数表达式；
The spectrum of harmonic wavelet is more box like than other wavelet, At the same time it has following advantages:existing certain function expression;
为了避免经验模式分解(EMD)过程中不同时间尺度函数间的模式混叠，采用基于高斯白噪声加入的经验模式分解方法，并将之应用于旋转机械故障诊断中。
The EMD added Gauss white noise is proposed to avoid mode mixing of different time-scale IMF, and is applied in fault diagnosis for rotating machine.
根据在不同尺度下的轮廓曲率乘积，建立了尺度积函数。
A scale product function is established derived from the curvature product of the contour at different scales.
提出的算法不用计算b -样条函数的显式值，而是利用B -样条的尺度关系计算采样点的值，具有一致且简单的编码。
New algorithm need not directly compute values of B-spline interpolatory function, the values were computed using B-spline scaling relation on sampling points, which had simple and uniform coding.
它是运用多尺度分析方法，构造出格点模型的演化方程的局部平衡分布函数。
The local equilibrium distribution function of lattice model evolution equation is constructed by use of multi scale analysis.
提出用离散曲率法提取特征点，曲率表达式包含了高斯核函数曲线，选用了合适的离散尺度因子。
The discrete curvature arithmetic was used to extract feature points, which the curvature expression contains Gaussian nuclear function and chooses appropriate discrete scale factor.
摘要在单涡模型的基础上，根据各向同性湍流的能谱函数，考虑不同尺度的旋涡对气液传质的影响，建立了气液自由界面传质系数模型。
A model of mass transfer coefficients in liquid phase near free gas-liquid interface is developed based on the energy spectrum functions of isotropic turbulence.
论文基于这一思想，从二维平滑函数出发，并根据尺度呈级数变化的特点，导出了一组多尺度小波滤波器。
According to the peculiarity that the scale exhibit progressional variety, this paper deduces a group of multiscale wavelet filter from two dimensions smooth function.
小波是表示具有点奇异性函数的最优基，它由于具有时-频局部化特点和多尺度特性，在图像处理领域得到了广泛应用。
Wavelet is the best base of functions, with point singularity, and it has wide application in image processing because of its time-frequency localization and multiscale features.
首先，用多尺度法导出弱非线性强迫激励系统的频率响应函数。
Firstly, by means of multiple scale method the frequency response function of weakly nonlinear vibration system is derived.
首先，给出了包含大气湍流内，外尺度效应的折射率功率谱密度函数。
Firstly, the power spectral density function of refractive index is given including the effects of inner and outer scale of the turbulence.
由于较粗尺度下目标函数呈现较强的凸性及较少的局部极值，很有利于收敛至优化解。
Objective function presents comparatively strong convexity and lesser local extreme values on wide scale which is favour of converging to optimized values.
在此基础上研究了利用等式约束与不等式约束的惩罚函数法对平面多杆机构进行尺度最优综合的有关问题。
Some problems of optimum synthesis of planar multi-bar linkages are studied by the penalty function method with equality and inequality constraints.
在此基础上研究了利用等式约束与不等式约束的惩罚函数法对平面多杆机构进行尺度最优综合的有关问题。
Some problems of optimum synthesis of planar multi-bar linkages are studied by the penalty function method with equality and inequality constraints.
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