Abstract. Let M be an isoparametric hypersurface in CP n , and M the inverse image of M under the Hopf map. By using the relationship between the eigenvalues of the shape operators of M and M , we prove that M is homogeneous if and only if either g or l is constant, where g is the number of distinct principal curvatures of M and l is the number of non-horizontal eigenspaces of the shape operator on M .
The extraction of vanadium and chromium from high chromium content vanadium slag by salt roasting and water leaching process has been investigated, which uses mixed sodium salts (Na2CO3 and NaOH) as additive agent in roasting process. The mineralogical morphology was prospected by TG-DSC, XRD, SEM and EDS. The oxidation of slag and transversion of V/Cr-containing phase and sodium salts have been discussed. It has been demonstrated that the presence of NaOH contributes to decompose spinel and olivine phases, which is beneficial to reduce the roasting temperature and elevate V, Cr leaching ratio. The roasting parameters have been studied as a function of roasting temperature, roasting time and ratio of alkali, in which the roasting temperature is the most effective factor on the leaching rate of vanadium and chromium. Under the optimum condition, the leaching rates of V and Cr reached 95.8% and 97.6%, respectively.
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