This short note is devoted to an approach of the quasi-hereditary orderings of An-type algebras with exactly two generators. A necessary and sufficient condition for a quasi-hereditary ordering is obtained. Moreover, the numbers of quasi-hereditary orderings of such algebras are explicitly given.
In this paper, the properties of bianalytic functions w（z） = z^-Ф1（z） ＋Ф2（z） with zero arc at the pole z = 0 are discussed. Some conditions under which there exists an arc γ, an end of which is z = 0, such that w（z） =0 for arbitary z ∈γ／{0} are given. Secondly, that the limit set of w（z） is a circle or line as z → 0 is proved in this case. Finally, two numerical examples are given to illustrate our results.
