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In this note, we construct families of functionals of the type of F-functional and W-functional of Perelman. We prove that these new functionals are nondecreasing under the Ricci flow. As applications, we give a proof of the theorem that compact steady Ricci breathers must be Ricci-flat. Using these new functionals, we also give a new proof of Perelman's no… (More)
A novel serine protease inhibitor (serpin) gene designated as Spi1C was cloned via the sequenced-based screening of a metagenomic library from uncultured marine microorganisms. The gene had an open reading frame of 642 base pairs, and encoded a 214-amino acid polypeptide with a predicted molecular mass of about 28.7 kDa. The deduced amino acid sequence… (More)
Elevator group control scheduling is to dispatch every elevator to serve call requests from different floors based on some certain goal. It's a kind of typical combinatorial optimization problems. Ant colony algorithm is good at solving the discrete combinatorial optimization, its well global optimization ability and quick convergence velocity are both… (More)
In this short notes, we discuss monotonicity formulas under various rescaled versions of Ricci flow. The main result is Theorem 2.1.
A newly designed PE-supported arsine has been developed as an excellent catalyst for catalytic Wittig-type olefination. Simple ketones, in particular inactive ketones prove to be suitable substrates for the first time. This reaction provides an easy access to di-, tri-, and tetra-substituted olefins in high yield.