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In this paper, we study the convergence rates for homogenization problems for solutions of partial differential equations with rapidly oscillating Neumann boundary data. Such a problem raised due to its importance for higher order approximation in homogenization theory. High order approximation gives rise to the so-called boundary layer phenomenon. As a consequence, we obtain the pointwise and W1,p convergence results. Our techniques are based on Fourier analysis.

-When AMSS (Affine Morphological Scale Space) operator is applied in image filtering, the scale parameter t has great impact on the filtering results. In order to determine the parameters more precisely, this paper analyzed affine invariance properties and classical invariance properties of AMSS operator using the affine transform theory And the numerical solution of AMSS equation is realized with the finite difference method . Based on the cross entropy theory, the forms of cross entropy under the two situations of standard image and nonstandard image were analyzed. The relationship between cross entropy and the scale parameter was explored in both cases, and the AMSS equation's iteration stopping time is determined based on this criterion. Experiment shows that the satisfactory smooth images can be achieved based on the method of cross entropy iteration stopping, under the circumstances of both standard and nonstandard images.

Abstract-As the electricity ladder-type price scheme implemented into the trail stage, studying on it has attracted more and more attention. The present study evaluated the efficiency in energy conservation and timeliness of this scheme based on utility function and time sequence. The results show that the scheme can save energy to certain extend, but it can not work well for long. Taking Beijing as an example, ladder-type scheme can only stabilize 80% of Beijing residents' electricity cost till 2014 and further regulations are required to adapt to the development of the society.

In this paper, we study the convergence of solutions for homogenization problems about the Poisson equation in a domain with double oscillating locally periodic boundary. Such a problem arises in the processing of devices with very small features. We utilize second-order Taylor expansion of boundary data in combination with boundary correctors to obtain the convergence rate in H1-norm. This work explores the domain with double oscillating boundary and also shows the influence of the amplitudes and periods of the oscillations to convergence rates of solutions.