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双语推荐：R变换

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利用函数变换与辅助方程相结合的方法,研究了构造广义Camassa-Holm(CH-r)方程的无穷序列类孤子新解问题,获得了新结果.首先,通过一些函数变换,把CH-r方程化为可求解的常微分方程;其次,利用可求解的常微分方程的新解和B?cklund变换,构造了CH-r方程的无穷序列类孤子新解.
The method of combining function transformations with auxiliary equation is presented to search for new infinite sequence soliton-like solutions of Camassa-Holm-r (CH-r) equation. And many new conclusions are obtained. Step one,according to some function transformations, CH-r equation is changed into the solvable ordinary differential equation. Step two, new infinite sequence soliton-like solutions of CH-r equation are constructed by applying new solutions and B?cklund transformation of the solvable ordinary differential equation.

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利用代数方法给出了三维内积空间中正交变换的特征向量的几何意义,研究了三维内积空间R3中的旋转变换（正交变换）的特征向量只有一个实的特征向量,以及研究了空间中关于经过原点的平面的对称变换（正交变换）的特征向量就是该平面的法矢量和该平面上自原点出发的任意矢量,并且它们是互相垂直的.
The geometric meaning of feature vector of orthogonal transformation is given in three di-mensional inner product spaces by using algebra method,that is,the rotation transform in three dimen-sional inner product spaces R3 is only a real feature vector.The feature vector plane reflection transfor-mation origin in space is the normal vector of the plane,and for any vector of the plane,they are per-pendicular to each other.

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电力系统分析中，经常将三相坐标系通过坐标变换到两相旋转坐标系以此来简化复杂的电力问题，这种变换可简称为3s/2r变换。详细介绍了3s/2r坐标变换及其逆变换的思想，从数学角度分析了三相坐标系交流变量的变化对两相坐标系分量的影响，同时也分析了逆变换时两相坐标系分量的变化对三相坐标系交流变量的影响。用MATLAB进行仿真，仿真结果验证了此分析的正确性。
In power system analysis ,the transformation called 3s/2r which converses three-phase coordinate system into two phase rotating coordinate system will simplify the complex problems of electricity .This paper introduces the 3s/2r transformation and its inverse transformation in details .From the view of mathematics ,the influence of the change of AC variable on two-phase coordinate component is analyzed ,and also the influence in the inverse transformation .MATLAB simulation is carried out ,and the results show the analysis method is correct .

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Hilbert-Huang变换(HHT)是一种新型的处理非线性、非平稳信号的时频分析方法。它已经被应用在金融、生物、通信等多个领域。该文讨论了Hilbert-Huang变换的基本原理及实现方法,并基于R开源环境实现Hilbert-Huang变换,最后采用金融高频数据进行实验并给出结果。
Hilbert-Huang Transform (HHT) is a new deal with the nonlinear, non-stationary time-frequency analysis method. It has been used in finance, biotechnology, telecommunications and other fields. This article discusses the Hilbert-Huang trans-form the basic principles and methods, and the open source environment to achieve based on R Hilbert-Huang transform, the fi-nal use of financial high-frequency data for the experiment and results are given.

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将R3中的经典的 Bianchi 变换推广到高维 Minkowski 空间R2 n -11中。
The classical Bianchi transformation to the high-dimensional Minkowski space R 2 n - 1 1 was generalized .

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文中通过多次量子Fourier变换和变量代换,给出了一个ZN上离散对数量子计算算法,刻画了元素的阶r与算法成功率的关系,当r为素数时,算法成功的概率接近于1,新算法所需基本量子门数的规模为O(L3),且不需要执行函数|f(x1,x2)〉的量子Fourier变换的反演变换,优于已有的ZN上离散对数量子计算算法,其中L=[log N]+1.
By applying multiple Fourier transform and variable transform,a quantum algorithmfor discrete logarithm problem over ZN is presented.The relationship between order r and successprobability is quantitatively characterized,where r is the order of the selective element.Particularly,when r is a prime number,the success probability is close to 1 and the scale of elementary quantumgates is O(L3),where L=[logN]+1.The new algorithm doesn’t need to perform inverse quantumFourier transform on|f(X1,X2)〉,which is superior to the existing algorithm.

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通过对土壤电导率和光谱测定，分析了南方丘陵稻田土壤电阻率特征、原始光谱数据及重采样光谱数据特征。在光谱重采样基础上进一步构建光谱包络线去除变换、光谱反射率倒数（1／R）、对数[ ln（1／R）]、平方根（ R0．5）、一阶微分等单一或复合变换模型。通过横向、纵向综合比较分析不同模型的反射率与电阻率相关性分析的曲线差异，着重探讨了基于一阶微分的数据变换模型间土壤电阻率与光谱反射率间相关性强弱，结果表明：（1）基于一阶微分变换的模型可以对重叠混合光谱进行分解以便识别，扩大样品之间的光谱特征差异，发掘敏感波段的光谱吸收、反射特征；（2）综合反射率的平方根的一阶微分变换、反射率的倒数的对数及反射率对数的一阶微分等模型得出，在波段为382 nm处，土壤电阻率与光谱反射率间相关系数最高达0．788，在波段为555～560 nm，多个微分变换模型相关性系数在0．7以上，可为后续反演因子的确定及土壤电阻率高光谱估测回归模型的建立提供参考。
This study used soil conductivity and spectra mensuration to analyse the characteristics of pad?dy soil resistivity,original spectral data and resample spectra data of Southern China hilly paddy fields. Single or comprehensive models of spectra continued removed data, the reciprocal value, logarithm, square root and first ore differential value of soil spectra reflectivity were built based on the spectra resample method.According to the transverse and longitudinal analysis of the correlation curve of different models,the correlation between soil conductivity and spectra reflectivity was probed attentively based on the first order differential data trans?formation model.The result showed that:(1) the mode based on the first order differential could discompose and identify overlapping spectra,amplify the spectra characteristics between samples,explore the spectra ab?sorption and reflectance characteristics of sensitive bands;( 2 ) the models of the first order differential of s

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小麦硬度是评价小麦品质的一项重要指标。对小麦籽粒碰撞发声装置发出的声信号进行频域分析研究,结合使用小波变换与离散余弦变换算法对小麦声音信号进行分析处理,利用小波变换的多分辨率特性及离散余弦变换的能量压缩和解相关能力,提取一些有用的特征参数,分别采用一元和多元线性回归的方法构建不同小麦硬度的声学检测模型。研究结果表明:建立的回归模型的线性相关系数r2可达到0.957。
wheat hardness is an important index for wheat quality evaluation .In this paper , the wheat grain collision ob-jects produce audio test signal analysis , combined with wavelet transform and discrete cosine transform algorithm for wheat audio test signal processing , using the multiresolution feature of wavelet transform and discrete cosine transform energy compression and related ability , extract useful characteristic parameters of linear regression analysis method is adopted to establish the regression model based on these feature parameters .Experiments show that the built model of the linear cor-relation coefficient can reach 0 .957 3 .

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平面目标识别中的几何形变可用射影变换群描述.与紧致李群SO(n,R)不同,正则化的射影变换群,即非紧致李群SL(n,R)上由黎曼度量决定的黎曼指数映射不同于由单参数子群决定的李群指数映射.基于黎曼流形优化算法得到取值于特殊线性群SL(3,R)的样本的内蕴均值和协方差矩阵,并依此构建李群正态分布.利用此先验知识,根据贝叶斯定理进行简单背景下的平面目标的识别实验.结果表明,利用射影变换群的统计特性可有效提高平面目标识别的成功率.
The geometric warps between planar objects can be represented by projective Lie groups. Compared with the compact Lie group SO(n, R), the Riemannian exponential map on the noncompact Lie group SL(n, R) determined by a Riemannian metric is usually different from the Lie group exponential map determined by one-parameter subgroups. We compute the samples'' intrinsic means on the special linear group SL(3, R) based on the Riemannian manifold optimum algorithm and propose the Lie group norm distribution. The test results of the planar object recognition in the simple background, which is based on the full Bayes statistical rule, have shown that the proposed algorithm with the intrinsic statistical property of the projective group may improve the rate of recognition effectively.

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本文以MIT-BIH心电数据库作为研究对象,简要介绍了使用小波变换进行心电信号检测的原理和小波提升算法的机制,阐述了采用提升小波变换的方法分解ECG信号并对R波进行定位的流程。给出了matlab示例代码。
We used the MIT-BIH database in our research, introduced the theary of ECG detection using wavelet transform and the mechanism of the Lifting Scheme, we explained how to decompose ECG signal by Lifting Scheme, and how to locate the position of R-Wave. We also give the example code of matlab.

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