Mass neutrino flavor evolution in spacetime with torsion

In the framework of the spacetime with torsion, we obtain the flavor evolution equation of the mass neutrino oscillation in vacuum. A comparison with the result of general relativity case, it shows that the flavor evolutionary equations in Riemann spacetime and Weitzenb\"ock spacetimes are equivalent in the spherical symmetric Schwarzschild spacetime, but turns out to be different in the case of the axial symmetry.Comment: 8 papes, no fiur

On the hydrostatic approximation of the Navier-Stokes equations in a thin strip

In this paper, we first prove the global well-posedness of a scaled anisotropic Navier-Stokes system and the hydrostatic Navier-Stokes system in a 2-D striped domain with small analytic data in the tangential variable. Then we justify the limit from the anisotropic Navier-Stokes system to the hydrostatic Navier-Stokes system with analytic data

Stereoisomer libraries: Total synthesis of all 16 stereoisomers of the pine sawfly sex pheromone by a fluorous mixture-synthesis approach

All 16 stereoisomers of the sex pheromone of pine sawfly (3,7,11-trimethylundecanol propanoate ester) have been synthesized on a 10- to 20-mg scale by a split-parallel fluorous mixture-synthesis approach. Spectral data obtained for all 32 compounds (16 alcohols and the corresponding propionates) matched well with published data, thereby validating the fluorous-tag encoding of diastereoisomers. This fluorous-tag encoding method is recommended for the efficient synthesis of multiple stereoisomers for spectroscopic studies, biological tests, or other structure-function relationships