扰动KdV方程孤子的同伦映射解

利用同伦映射方法研究了一类非线性KdV(Korteweg de Vries)方程. 首先引入一个同伦变换,使相应的方程求孤子解问题转化为映射变换问题.然后利用映射特性得到了原方程孤子的近似解. 关键词： 孤子 扰动 同伦映射     

基于小波核偏最小二乘回归方法的混沌系统建模研究

基于核学习的强大非线性映射能力,结合用于回归建模的线性偏最小二乘(PLS)算法,提出一种小波核偏最小二乘(WKPLS)回归方法. 该方法基于支持向量机使用的经典核函数技巧,将输入映射到高维非线性的特征空间,在特征空间中,构造线性的PLS回归模型. PLS方法利用输入与输出变量之间的协方差信息提取潜在特征,而可允许的小波核函数具有近似正交以及适用于信号局部分析的特性. 因此,结合它们优点的WKPLS方法显示了更好的非线性建模性能. 将WKPLS方法应用在非线性混沌动力系统建模上,并与基于高斯核的核偏最小二乘 关键词： 小波核 偏最小二乘回归 混沌系统 建模     

一类扰动Burgers方程的孤子同伦映射解

研究一类扰动非线性Burgers方程求解问题,利用同伦映射方法和理论,得到原方程孤子的任意次精度的近似解.     

反常氧化碲声光偏转器控制理论研究

根据晶体的声光特性以及反常布喇格衍射的Dixon方程,得出了氧化碲声光偏转器在反常布拉格衍射条件下的参量矢量关系.分析了超声波方向、入射光角度、衍射光角度与声波频率之间的关系.针对卫星光通信中衍射角固定的应用情况,通过数值求解和参量拟合,建立了一个基于平面方程的简单控制模型.利用该模型可以很快得到超声控制频率,使衍射角固定不变.     

反常氧化碲声光偏转器控制理论研究

根据晶体的声光特性以及反常布喇格衍射的Dixon方程,得出了氧化碲声光偏转器在反常布拉格衍射条件下的参量矢量关系.分析了超声波方向、入射光角度、衍射光角度与声波频率之间的关系.针对卫星光通信中衍射角固定的应用情况,通过数值求解和参量拟合,建立了一个基于平面方程的简单控制模型.利用该模型可以很快得到超声控制频率,使衍射角固定不变.     

GaN和GaN2分子基态的结构和解析势能函数

本文利用密度泛函方法,优化了CaN2基态(X2B2)的几何平衡结构,其对称性属于C2v,它的键角、平衡核间距和离解能分别为26.428°,0.2526 nm和9.574 eV.基于量子化学计算得出GaN和GaN2基电子态及其离解极限之后,利用计算数据和最小二乘法得到了GaN的M-S解析势能函数,并计算出各态的谐振频率、力常数和光谱数据.利用多体项展式理论首次得到了GaN2基态的解析势能函数,它准确表达了GaN2的平衡几何结构,在此基础上讨论了Ga N2和N GaN反应系统的反应动力学.     

重金属钋化物分子MPo(2∏),(M=Cu,Ag,Au)的结构和势能函数

利用相对论小核赝势研究了重金属钋化物分子MPo(X2∏),(M=Cu,Ag,Au).用群论方法结合原子分子反应静力学原理导出了分子的基电子状态和相应的离解极限,并在各种电子相关理论水平上计算了它们的平衡几何和振动频率.在此基础上用Murrell-Sorbie函数形式拟和势能曲线,得到了总的解析势能函数,并计算出了光谱数据和力常数.     

一类大气浅水波方程的近似解

研究了一类非线性浅水波方程，利用同论映射理论和方法，得到了相应系统的近似解. 关键词： 浅水波 非线性 同伦映射 近似解     

基于高斯核主成分分析的多通道拉曼光谱重建

针对多通道拉曼成像系统常会受荧光背景、噪声等非线性因素的影响而导致拉曼光谱重建结果一般的问题,提出了一种基于高斯核主成分分析的拉曼光谱重建算法.首先利用相似度因子对标定样本数据集进行预处理,其次通过高斯核函数将标定样本以非线性形式映射至高维特征空间,接着在特征空间中对映射后的数据集提取基函数并通过伪逆法求得与之对应的基函数系数.使用聚甲基丙烯酸甲酯作为测试样本,并引入均方根误差来评估拉曼光谱重建结果的准确性.实验结果表明,相比传统的伪逆法与维纳估计法,该算法具有更高的重建精度及抗噪能力,且能有效降低标定样本中不良数据和成像系统中非线性因素对拉曼光谱重建的影响.因此,该算法可以为多通道拉曼快速成像提供一种有效的拉曼光谱重建算法.     

地-气耦合动力系统的近似解析解

本文研究了一类地-气耦合系统的非线性模式.利用同伦映射方法，将问题转化为线性问题求解.最后得到了原非线性问题的近似表示式. 关键词： 非线性 地-气耦合 动力系统 同伦映射     

基于P范数的核最小对数绝对差自适应滤波算法

为了进一步提高在a稳定分布噪声背景下非线性自适应滤波算法的收敛速度,本文提出了一种新的基于p范数的核最小对数绝对差自适应滤波算法(kernel least logarithm absolute difference algorithm based on p-norm, P-KLLAD).该算法结合核最小对数绝对差算法和p范数,一方面利用最小对数绝对差准则保证了算法在a稳定分布噪声环境下良好的鲁棒性,另一方面在误差的绝对值上添加p范数,通过p范数和一个正常数a来控制算法的陡峭程度,从而提高该算法的收敛速度.在非线性系统辨识和Mackey-Glass混沌时间序列预测的仿真结果表明,本文算法在保证鲁棒性能的同时提高了收敛速度,并且在收敛速度和鲁棒性方面优于核最小均方误差算法、核分式低次幂算法、核最小对数绝对差算法和核最小平均p范数算法.     

Threshold orientation transition in nematic liquid crystals under ultrasonic action

The adequacy of the new theoretical model based on the ideas of nonequilibrium thermodynamics and nonlinear hydrodynamics of liquid crystals for describing the mechanism of threshold reorientation of molecules in a homeotropically oriented layer of a nematic liquid crystal under the effect of a cross-homogeneous ultrasonic wave is experimentally substantiated. It is demonstrated that (i) the critical particle velocity is inversely proportional to the layer thickness, (ii) its relation to the frequency of oscillations is ambiguous and depends on the relation between the ultrasonic frequency and the inverse relaxation time of the orientation order parameter, and (iii) the stationary distortion of microstructure is homogeneous along the layer.     

核覆盖算法在光谱分类问题中的研究

针对光谱分类,提出了一种基于核技巧的覆盖算法——核覆盖算法。该算法将核技巧与覆盖算法相结合,并在特征空间中抽取支持向量。实验表明核覆盖算法在光谱分类中的精度与SVM相差不大,但是它只涉及距离的计算,不必象SVM那样求解二次规划问题,对于核宽的选择也不象SVM那样非常敏感。核覆盖算法与覆盖算法相比分类性能相当,它的优势在于引入的非线性映射Φ改变了样本集在特征空间中之间的距离关系,使得核覆盖算法得到的支持向量个数大大少于覆盖算法。     

Theoretical examination of ultrasonic pole figures via comparison with the results analyzed by finite element polycrystal model

The ultrasonic wave velocities in a polycrystalline aggregate are sensitively influenced by texture development due to plastic deformation. According to Sayer's model, it is possible to construct ultrasonic pole figures via the crystallite orientation distribution function (CODF), which can be calculated by using ultrasonic wave velocities. In the previous papers, the theoretical modeling to simulate ultrasonic wave velocities propagating in solid materials under plastic deformation has been proposed by the authors and proved to be a good agreement with experimental results. Generally, wave velocities are dependent upon the propagating wave frequency; hence to evaluate texture development via ultrasonic pole figures it is necessary to examine an influence of frequency dependence on the ultrasonic wave velocities. In the present paper, the proposed theoretical modeling is applied to the texture characterization in polycrystalline aggregates of FCC metals under various plastic strain histories via ultrasonic pole figures, and also the frequency dependence is examined by using Granato-Lücke's dislocation strings model. Then the simulated ultrasonic pole figures are compared with the pole figures analyzed by the finite element polycrystal model (FEPM). The good qualitative agreement between both results suggests the sufficient accuracy of our proposed theoretical modeling.     

Linear and nonlinear waves in crystals with charged dislocations

Based on the principle, a set of equations describing ultrasonic wave propagation in a dielectric crystal with charged dislocations has been derived. The linear dispersion relation has been derived, and the ultrasonic wave velocity and absorbance have been determined. In the case of the nonlinear ultrasonic wave, equations for its amplitude damping and phase variation have been obtained.     

Haar basis and nonlinear modeling of complex systems

In this work we introduce a technique to perform nonlinear modeling of chaotic time series using the kernel method. The basic idea behind this method is to map the data into a high dimensional space via nonlinear mapping and do a linear regression in this space. Here we use a Haar wavelet-like kernel to achieve the task. This strategy, in contrast to Support Vector Machines technique, shows the conceptual simplicity of least mean square algoritm for linear regression but allows local nonlinear aproximation of the system evolution, with low computational cost.     

高功率超声脉冲激励下金属板的非线性振动现象研究

对高功率超声脉冲作用下金属板中的超谐波、次谐波、准次谐波以及混沌等非线性振动现象进行了实验和理论研究.在实验中,高功率超声换能器产生脉冲调制的高频振动激励金属板产生非线性振动,利用激光测振技术测量不同尺寸和不同固定方式下金属板复杂的非线性振动情况,并对其进行了时序分析、频谱分析以及相空间分析.根据实验条件,提出包含非线性接触阻尼的振动-碰撞动力学模型,用以研究强超声振动-碰撞作用下的板非线性振动机制,并进行了相应的理论计算.计算结果表明,超声换能器的变幅杆与金属板之间的间歇性高频碰撞作用是金属板强非线性振 关键词： 非线性板振动 强超声脉冲激发 振动-碰撞动力学     

Kernel representation-based nearest neighbor classifier

An improvement to the nearest neighbor classifier (INNC) has shown its excellent classification performance on some classification tasks. However, it is not very clearly known why INNC is able to obtain good performance and what the underlying classification mechanism is. Moreover, INNC cannot classify low-dimensional data well and some high-dimensional data in which sample vectors belonging to different class distribution but have the same vector direction. In order to solve these problems, this paper proposes a novel classification method, named kernel representation-based nearest neighbor classifier (KRNNC), which can not only remedy the drawback of INNC on low-dimensional data, but also obtain competitive classification results on high-dimensional data. We reveal the underlying classification mechanism of KRNNC in details, which can also be regarded as a theoretical supplement of INNC. We first implicitly map all samples into a kernel feature space by using a nonlinear mapping associated with a kernel function. Then, we represent a test sample as a linear combination of all training samples and use the representation ability to perform classification. From the way of classifying test samples, KRNNC can be regarded as the nonlinear extension of INNC. Extensive experimental studies on benchmark datasets and face image databases show the effectiveness of KRNNC.     

Global behavior of gear system using mixed cell mapping

In some mechanical nonlinear systems, the transient motion will be undergoing a very long process and the attractor-basin boundaries are so complicated that some difficulties occur in analyzing the system global behavior. To solve this problem a mixed cell mapping method based on the point mapping and the principle of simple cell mapping is developed. The algorithm of the mixed cell mapping is studied. A dynamic model of a gear pair is established with the backlash, damping, transmission error and the time-varying stiffness taken into consideration. The global behaviors of this system are analyzed. The coexistence of the system attractors and the respective attractor-basin of each attractor with different parameters are obtained, thus laying a theoretical basis for improvement of the dynamic behaviors of gear system.