From a stock culture of Cylindrotheca sp., non-motile colony-forming cells were observed and isolated.Colony-forming cells produced both single cells and colony-forming cells in liquid medla.the rate of single cell pr...From a stock culture of Cylindrotheca sp., non-motile colony-forming cells were observed and isolated.Colony-forming cells produced both single cells and colony-forming cells in liquid medla.the rate of single cell production varied among clones.展开更多
Quillen proved that if a Hermitian bihomogeneous polynomial is strictly positive on the unit sphere, then repeated multiplication of the standard sesquilinear form to this polynomial eventually results in a sum of Her...Quillen proved that if a Hermitian bihomogeneous polynomial is strictly positive on the unit sphere, then repeated multiplication of the standard sesquilinear form to this polynomial eventually results in a sum of Hermitian squares. Catlin-D'Angelo and Varolin deduced this positivstellensatz of Quillen from the eventual positive-definiteness of an associated integral operator. Their arguments involve asymptotic expansions of the Bergman kernel. The goal of this article is to give an elementary proof of the positive-definiteness of this integral operator.展开更多
文摘From a stock culture of Cylindrotheca sp., non-motile colony-forming cells were observed and isolated.Colony-forming cells produced both single cells and colony-forming cells in liquid medla.the rate of single cell production varied among clones.
文摘Quillen proved that if a Hermitian bihomogeneous polynomial is strictly positive on the unit sphere, then repeated multiplication of the standard sesquilinear form to this polynomial eventually results in a sum of Hermitian squares. Catlin-D'Angelo and Varolin deduced this positivstellensatz of Quillen from the eventual positive-definiteness of an associated integral operator. Their arguments involve asymptotic expansions of the Bergman kernel. The goal of this article is to give an elementary proof of the positive-definiteness of this integral operator.
