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Abstract  

Weak atomic decompositions of B-valued martingales with two-parameters in weak Hardy spaces w pΣα and w p H α are established and the boundedness of sublinear operators on these spaces are proved. By using them, some characterizations of the smoothness of Banach spaces are obtained.

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Abstract  

Some characterizations of S-paracompact spaces are given. We introduce a class of S-expandable spaces and study topological properties of S-expandable spaces.

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Abstract

The phenomenon of all-elements-sleeping-beauties in science is revealed by four special cases. The ‘sleeping beauties’ prick their fingers on the ‘spindles’ so that they fall into sleep then are awakened by their ‘princes’. The authors speculate that the phenomenon could happen in scientific literatures with high quality.

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