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In 1970, J.B. Kelly proved that $$\begin{array}{ll}0 \leq \sum\limits_{k=1}^n (-1)^{k+1} (n-k+1)|\sin(kx)| \quad{(n \in \mathbf{N}; \, x \in \mathbf{R})}.\end{array}$$ We generalize and complement this inequality. Moreover, we present sharp upper and lower bounds for the related sums $$\begin{array}{ll} & \sum\limits_{k=1}^{n} (-1)^{k+1}(n-k+1) | \cos(kx) | \quad {\rm and}\\ & \quad{\sum\limits_{k=1}^{n} (-1)^{k+1}(n-k+1)\bigl( | \sin(kx) | + | \cos(kx)| \bigr)}.\end{array}$$   相似文献
2.
This paper presents a new method for exact evaluation of a limit surface generated by stationary interpolatory subdivision schemes and its associated tangent vectors at arbitrary rational points. The algorithm is designed on the basis of the parametric m-ary expansion and construction of the associated matrix sequence. The evaluation stencil of the control points on the initial mesh is obtained, through computation, by multiplying the finite matrices in a sequence corresponding to the expansion sequence and eigendecomposition of the contractive matrix related to the period of rational numbers. The method proposed in this paper works for other non-polynomial subdivision schemes as well.  相似文献
3.
Image editing is a hot research topic in the image processing region, and one of the most basic problems in this field is the color transfer. It modifies the color style of the target image to match the color palette of the source while preserving the content of the target. Although there exist many algorithms to deal with this problem, none of existing methods can handle all kinds of images, especially complex landscape images. In this paper, we propose a Mass Transport based color transfer method in the CIELab color space, which can generate natural transfer results for different kinds of images including landscapes. Different from previous methods using the same transfer model for all the channels, we adopt different models for the luminance channel and color channels. For the luminance channel, a global transfer method is adopted for keeping the consistence in the visual perception. For the color channels, we construct a model based on histogram and Mass Transport, which perfectly transfers the colors of all the pixels from the source to the target and simultaneously preserves the content. What is more, experiments on real images demonstrate that our approach performs favorably against most of the existing methods.  相似文献
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