We prove the existence of (non compact) complex surfaces with a smooth rational curve embedded such that there does not exist any formal singular foliation along curve. In particular, at arbitrary small neighborhood curve, meromorphic function is constant. This implies Picard group countably generated.

Education is the foundation for renaissance of ethnic groups. As an important means to achieve educational equity and basic human rights, rational allocation education resources a necessary requirement address resource scarcity. Due various factors such as geography, economy, history, overall level development in areas Guizhou relatively low, with significant gaps compared Han national average....

The Top Trading Cycles mechanism emerges as a desirable solution in various market design applications. Yet recommendations are made without any rigorous foundation for the role priorities play in assignment. We explain that role by recursive individual rationality with respect to a priority structure. We show that a mechanism is Pareto efficient, strategy-proof and recursively individual ratio...

This paper tries to contribute to the understanding of the essence of rational systems design and verification. Information technologists and teachers and students of computer science may find the concepts presented here helpful to disentangle complex achievements of computer science and re-use their constituents in other contexts, but also to view their own activities in the light of other dis...