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In this note we generalize two theorems of Klee [9] and a result of Bair-Jongmans [7] about the true separation of two convex cones; afterwards, we introduce the notion of true separation for$n(n≧2)$convex sets and we extend our three first statements for$n$convex cones.

So-called exceptional isomorphisms of low-dimensional spinor groups are directly worked out for the terminal two cases of rank five and six (in the sense of quadratic modules) at the level of special Clifford groups with norm characters as group schemes over a ring. Explicit formulas of identifications are available on big cells, restrictions to which being justified by scheme theory.

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Let X be a compact Khler manifold and X a subvariety of X with higher co-dimension. The aim is to study complete constant scalar curvature Khler metrics on non-compact Khler manifold X with Poincar--Mok--Yau asymptotic property (see Definition\ref {def}). In this paper, the methods of Calabi's ansatz and the moment construction are used to provide some special examples of such metrics.