A transform method for linear evolution PDEs on a finite interval

We study initial boundary value problems for linear scalar evolutionpartial differential equations, with spatial derivatives ofarbitrary order, posed on the domain {t > 0, 0 < x <L}. We show that the solution can be expressed as an integralin the complex k-plane. This integral is defined in terms ofan x-transform of the initial condition and a t-transform ofthe boundary conditions. The derivation of this integral representationrelies on the analysis of the global relation, which is an algebraicrelation defined in the complex k-plane coupling all boundaryvalues of the solution. For particular cases, such as the case of periodic boundaryconditions, or the case of boundary value problems for even-orderPDEs, it is possible to obtain directly from the global relationan alternative representation for the solution, in the formof an infinite series. We stress, however, that there existinitial boundary value problems for which the only representationis an integral which cannot be written as an infinite series.An example of such a problem is provided by the linearized versionof the KdV equation. Similarly, in general the solution of odd-orderlinear initial boundary value problems on a finite intervalcannot be expressed in terms of an infinite series.     

A novel method for automated grid generation of ice shapes for local‐flow analysis

Modelling a complex geometry, such as ice roughness, plays a key role for the computational flow analysis over rough surfaces. This paper presents two enhancement ideas in modelling roughness geometry for local flow analysis over an aerodynamic surface. The first enhancement is use of the leading‐edge region of an airfoil as a perturbation to the parabola surface. The reasons for using a parabola as the base geometry are: it resembles the airfoil leading edge in the vicinity of its apex and it allows the use of a lower apparent Reynolds number. The second enhancement makes use of the Fourier analysis for modelling complex ice roughness on the leading edge of airfoils. This method of modelling provides an analytical expression, which describes the roughness geometry and the corresponding derivatives. The factors affecting the performance of the Fourier analysis were also investigated. It was shown that the number of sine–cosine terms and the number of control points are of importance. Finally, these enhancements are incorporated into an automated grid generation method over the airfoil ice accretion surface. The validations for both enhancements demonstrate that they can improve the current capability of grid generation and computational flow field analysis around airfoils with ice roughness. Copyright © 2004 John Wiley & Sons, Ltd.     

Application of Discrete Wavelet Transform in the Analysis of Nonlinear Chemical System

Oscillations of species concentration are phenomena accompanying several types of electrochemical and purely chemical processes. Importance of analyzing of such processes results from both scientific and practical reasons. In the paper the authors deal with investigation of time dependent spectra of various stages of Belousov-Zhabotinsky type chemical oscillations. As the analytical tool the discrete wavelet transform is proposed.     

Study Hankel Transforms and Properties of Bessel Function via Entangled State Representation Transformation in Quantum Mechanics

In Phys. Lett. A 313 (2003) 343 we have found that the self-reciprocal Hankel transformation (HT) is embodied in quantum mechanics by a transform between two entangled state representations of continuum variables. In this work we study Hankel transforms and properties of Bessel function via entangled state representations' transformation in quantum mechanics.     

A Bregman-Split-Based Compressive Sensing Method for Dynamic Harmonic Estimation

In order to overcome the spectral interference of the conventional Fourier transform in the International Electrotechnical Commission framework, this paper introduces a Bregman-split-based compressive sensing (BSCS) method to estimate the Taylor–Fourier coefficients in a multi-frequency dynamic phasor model. Considering the DDC component estimation, this paper transforms the phasor problem into a compressive sensing model based on the regularity and sparsity of the dynamic harmonic signal distribution. It then derives an optimized hybrid regularization algorithm with the Bregman split method to reconstruct the dynamic phasor estimation. The accuracy of the model was verified by using the cross entropy to measure the distribution differences of values. Composite tests derived from the dynamic phasor test conditions were then used to verify the potentialities of the BSCS method. Simulation results show that the algorithm can alleviate the impact of dynamic signals on phasor estimation and significantly improve the estimation accuracy, which provides a theoretical basis for P-class phasor measurement units (PMUs).     

Lossless Medical Image Compression by Using Difference Transform

This paper introduces a new method of compressing digital images by using the Difference Transform applied in medical imaging. The Difference Transform algorithm performs the decorrelation process of image data, and in this way improves the encoding process, achieving a file with a smaller size than the original. The proposed method proves to be competitive and in many cases better than the standards used for medical images such as TIFF or PNG. In addition, the Difference Transform can replace other transforms like Cosine or Wavelet.     

关于有消失矩的函数的Hilbert变换的加权范数不等式

为刻划一类权函数W,使具有N阶消失矩的函数f的Hilbert变换f满足带权L~P强型不等式Adams给出了一个充要条件。利用A_P权的性质,本文进一步完善了这个结果。     

关于分布函数极大值位置的讨论

将关于某个变量的连续分布函数进行变数变换,除非新老变数为线性关系,否则变换前后的分布函数的极大值之间的关系一般会不同于新老变数之间的关系。     

基于二代curvelet变换的图像融合研究

曲波(Curvelet)作为一种新的多尺度分析方法比小波更加适合分析二维图像中的曲线或直线状边缘特征,而且具有更高的逼近精度和更好的稀疏表达能力.将curvelet变换引入图像融合,能够更好地提取原始图像的特征,为融合图像提供更多的信息.第二代curvelet理论的提出也使得其理论更易理解和实现.因此,提出了一种基于第二代curvelet变换的图像融合方法,首先将图像进行curvelet变换,然后在相应尺度上利用融合规则将curvelet系数融合,最后进行重构得到融合结果.对多聚焦图像进行了实验,采用均方误差、偏差指数和相关系数对融合结果进行了客观评价,并与基于小波变换的融合进行了比较,实验结果表明该方法除分解2层时与小波性能相当,取其他分解层数时均获得更好的融合效果.     

Study of a high-dimensional chaotic attractor

The nature of a very high-dimensional chaotic attractor in an infinite-dimensional phase space is examined for the purpose of studying the relationships between the physical processes occurring in the real space and the characteristics of high-dimensional attractor in the phase space. We introduce two complementary bases from which the attractor is observed, one the Lyapunov basis composed of the Lyapunov vectors and the another the Fourier basis composed of the Fourier modes. We introduce the exterior subspaces on the basis of the Lyapunov vectors and observe the chaotic motion projected onto these exteriors. It is shown that a certain statistical property of the projected motion changes markedly as the exterior subspace goes out of the attractor. The origin of such a phenomenon is attributed to more fundamental features of our attractor, which become manifest when the attractor is observed from the Lyapunov basis. A counterpart of the phenomenon can be observed also on the Fourier basis because there is a statistical one-to-one correspondence between the Lyapunov vectors and the Fourier modes. In particular, a statistical property of the high-pass filtered time series reflects clearly the difference between the interior and the exterior of the attractor.