43 research outputs found
On a multi-dimesional generalization of the notion of orthostochastic and unistochastic matrices
We introduce the notions of -orthostochastic, -unistochastic, and
-qustochastic matrices. These are the particular cases of -bistochastic
matrices where is real or complex numbers or quaternions. The concept is
motivated by mathematical physics. When , we recover the orthostochastic,
unistochastic, and qustochastic matrices respectively. This work exposes the
basic properties of -bistochastic matrices
Billiard Dynamics: An Updated Survey with the Emphasis on Open Problems
This is an updated and expanded version of our earlier survey article
\cite{Gut5}. Section introduces the subject matter. Sections expose the basic material following the paradigm of elliptic, hyperbolic and
parabolic billiard dynamics. In section we report on the recent work
pertaining to the problems and conjectures exposed in the survey \cite{Gut5}.
Besides, in section we formulate a few additional problems and
conjectures. The bibliography has been updated and considerably expanded