We show that the Kähler-Ricci flow on an algebraic manifold of positive Kodaira dimension and semi-ample canonical line bundle converges to a unique canonical metric on its canonical model. It is also shown that there exists a canonical measure of analytic Zariski decomposition on an algebraic manifold of positive Kodaira dimension. Such a canonical measure is unique and invariant under biratio...

We report the first enantioselective organocatalyzed domino synthesis of azepane moieties. This temporary-bridge strategy is based on a conceptually original annulation of ambident electrophilic and 1,4-bis-nucleophilic α-ketoamides with 1,3-bis-electrophilic enals. The obtained oxygen-bridged azepanes can be selectively transformed into optically active azepanone, azepanol or azepanedione deri...

Division planes in Escherichia coli, usually restricted to one dimension of the rod-shaped cell, were induced at all possible planes by transforming the cells to spheroids with mecillinam (inactivating PbpA). Such cells displayed many nucleoids and arcs of FtsZ, genetically tagged to green fluorescent protein, that developed to rings at constriction sites all around their surface. These observa...

let r be an associative ring with unity. an element a in r is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von neumann) element in r. if every element of r is r-clean, then r is called an r-clean ring. in this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. further we prove that if 0 and 1 are the only idempotents...

let r be an associative ring with unity. an element a in r is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von neumann) element in r. if every element of r is r-clean, then r is called an r-clean ring. in this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. further we prove that if 0 and 1 are the only idempotents...