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A meshless method with ridge basis functions for solving the 2D two-flow domain model problem is proposed in this paper, which is using ridge basis functions to construct the approximate functions, and using collocation method to discretize the governing equation. The existence and uniqueness of the solution to the mothod is analyzed. Compared with the traditional finite difference method, the new method reduces the calculation error. Numerical results show that the proposed method is convergent and can improve the error precision.

In order to improve image fusion quality, a novel image fusion method based on the local neighborhood feature and NSCT is proposed. Firstly, the NSCT is performed on the source image to obtain the low frequency subband and the high frequency subbands in each direction; Secondly, a weighted fusion strategy based on the gray mean deviation is adopted for the low frequency subband, and a weighted fusion strategy based on the local region energy is used for the high frequency subbands; Finally, the fused image is obtained by NSCT inverse transform. The simulation results show that the method we proposed has good fusion effect on multi-focus images, medical images and infrared and visible light images.

The decomposition of multiple source images using bidimensional empirical mode decomposition (BEMD) often produces mismatched bidimensional intrinsic mode functions, either by their number or their frequency, making image fusion difficult. A solution to this problem is proposed using a fixed number of iterations and a union operation in the sifting process. By combining the local regional features of the images, an image fusion method has been developed. First, the source images are decomposed using the proposed BEMD to produce the first intrinsic mode function (IMF) and residue component. Second, for the IMF component, a selection and weighted average strategy based on local area energy is used to obtain a high-frequency fusion component. Third, for the residue component, a selection and weighted average strategy based on local average gray difference is used to obtain a low-frequency fusion component. Finally, the fused image is obtained by applying the inverse BEMD transform. Experimental results show that the proposed algorithm provides superior performance over methods based on wavelet transform, line and column-based EMD, and complex empirical mode decomposition, both in terms of visual quality and objective evaluation criteria.

The main purpose of this paper is using the estimation of the character sums to study the 2k-th power mean of L-functions with the weight of a character sums, and give an interesting asymptotic formula for it.Keywords: Hybrid mean value, L-functions, character sums, asymptotic formulaQuaestiones Mathematicae 37(2014), 563-570

The configuration matrix obtained through the global radial basis function collocation method is usually an asymmetry full matrix and highly ill-conditioned for parabolic equations. To overcome the deficiencies, a radial basis meshless domain decomposition algorithm is proposed. It has the advantages of both the radial basis collocation method and the domain decomposition method. The new method can transform the solution to a large-scale problem into the solutions to several small sub-area ones. It effectively reduce the condition numbers of the collocation matrix. It is shown by numerical example that this method improves the stability and accelerates convergence of the numerical solution to parabolic equations.