A distinguished variety is a variety that exits the bidisk through the distinguished boundary. We show that Andô’s inequality for commuting matrix contractions can be sharpened to looking at the maximum modulus on a distinguished variety, not the whole bidisk. We show that uniqueness sets for extremal Pick problems on the bidisk always contain a distinguished variety.

This research experimentally analyzes the issue of Sociopetaloid of architecture space. Sociopetal represents spaces where people come together or stay away from each other, and when they stay away from each other it is also called sociofugal. The research methodology was primarily compiled by presenting a pattern with a theoretical standpoint regarding the Sociopetaloid of space using hypot...

A general technique is given for constructing new Markov processes from existing ones. The new process and its state space are both projective limits of sequences built by an iterative scheme. The space at each stage in the scheme is obtained by taking disjoint copies of the space at the previous stage and quotienting to identify certain distinguished points. Away from the distinguished points,...