Regional Difference and the Equalization Paths of Public Cultural Services: Based on Theil Index Measurement

Unequal provision of public cultural services in deferent regions of China is the significant factor of residential satisfaction degree in government offering public service. Through analyzing the related data of fiscal expenditure of public cultural service, this article proves the fact that there is a great difference between regions in public cultural service in China. From the relevant Theil index, we can find that there were large difference of public cultural expenditure among the eastern, western and middle regions in China, the difference between the eastern and western regions is larger than the one between the middle and the western regions, while the relative difference among regions is being narrowing. Overall cultural differences in public culture expenditure are mainly caused by differences within the region, and the regional difference is being reduced. Regional differences within the region mainly caused by the gap among the eastern provinces of China. According to results of the analysis are discussed in the short and long-term path, the article proposes paths on how to promote the equalization of public cultural service area

Snyder's Model -- de Sitter Special Relativity Duality and de Sitter Gravity

Between Snyder's quantized space-time model in de Sitter space of momenta and the \dS special relativity on \dS-spacetime of radius $R$ with Beltrami coordinates, there is a one-to-one dual correspondence supported by a minimum uncertainty-like argument. Together with Planck length $\ell_P$, $R\simeq (3/\Lambda)^{1/2}$ should be a fundamental constant. They lead to a dimensionless constant $g{\sim\ell_PR^{-1}}=(G\hbar c^{-3}\Lambda/3)^{1/2}\sim 10^{-61}$. These indicate that physics at these two scales should be dual to each other and there is in-between gravity of local \dS-invariance characterized by $g$. A simple model of \dS-gravity with a gauge-like action on umbilical manifolds may show these characters. It can pass the observation tests and support the duality.Comment: 32 page

Smoothing the Nonsmoothness

To tackle difficulties for theoretical studies in situations involving nonsmooth functions, we propose a sequence of infinitely differentiable functions to approximate the nonsmooth function under consideration. A rate of approximation is established and an illustration of its application is then provided