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Maximal regularity of second-order evolution equations with infinite delay in Banach spaces

100%
Fu X., Li M.
Studia Mathematica
|
2014
|
tom 224
|
nr 3
199-219
EN
By using Fourier multiplier theorems we characterize the existence and uniqueness of periodic solutions for a class of second-order differential equations with infinite delay. We also establish maximal regularity results for the equations in various spaces. An example is provided to illustrate the applications of the results obtained.
2
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On von Kármán spectrum from a view of fractal

100%
Li M., Leng J.
Waves, Wavelets and Fractals
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2015
|
tom 1
|
nr 1
EN
Von Kármán originally deduced his spectrum of wind speed fluctuation based on the Stockes-Navier equation. That derivation, however, is insufficient to exhibit the fractal information of time series, such as wind velocity fluctuation. This paper gives a novel derivation of the von Kármán spectrum based on fractional Langevin equation, aiming at establishing the relationship between the conventional von Kármán spectrum and fractal dimension. Thus, the present results imply that a time series that follows the von Kármán spectrum can be taken as a specifically fractional Ornstein-Uhlenbeck process with the fractal dimension 5/3, providing a new view of the famous spectrum of von Kármán’s from the point of view of fractals. More importantly, that also implies a novel relationship between two famous spectra in fluid mechanics, namely, the Kolmogorov’s spectrum and the von Kármán’s. Consequently, the paper may yet be useful in practice, such as ocean engineering and shipbuilding.
3
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Fast and Robust Orientation of Cryo-Electron Microscopy Images

81%
Xu G., Wang X., Li M., Jing Z.
Molecular Based Mathematical Biology
|
2015
|
tom 3
|
nr 1
EN
We present an efficient and reliable algorithm for determining the orientations of noisy images obtained fromprojections of a three-dimensional object. Based on the linear relationship among the common line vectors in one image plane, we construct a sparse matrix, and show that the coordinates of the common line vectors are the eigenvectors of the matrix with respect to the eigenvalue 1. The projection directions and in-plane rotation angles can be determined fromthese coordinates. A robust computation method of common lines in the real space using aweighted cross-correlation function is proposed to increase the robustness of the algorithm against the noise. A small number of good leading images, which have the maximal dissimilarity, are used to increase the reliability of orientations and improve the efficiency for determining the orientations of all the images. Numerical experiments show that the proposed algorithm is effective and efficient.
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