2,044 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
Topological entropy and blocking cost for geodesics in riemannian manifolds
For a pair of points in a compact, riemannian manifold let
(resp. ) be the number of geodesic segments with length
joining these points (resp. the minimal number of point obstacles
needed to block them). We study relationships between the growth rates of
and as . We derive lower bounds on
in terms of the topological entropy and its fundamental group. This
strengthens the results of Burns-Gutkin \cite{BG06} and Lafont-Schmidt
\cite{LS}. For instance, by \cite{BG06,LS}, implies that is
unbounded; we show that grows exponentially, with the rate at least
.Comment: 13 page
Geometry, topology and dynamics of geodesic flows on noncompact polygonal surfaces
We establish the background for the study of geodesics on noncompact
polygonal surfaces. For illustration, we study the recurrence of geodesics on
-periodic polygonal surfaces. We prove, in particular, that almost all
geodesics on a topologically typical -periodic surface with boundary are
recurrent.Comment: 34 pages, 13 figures. To be published in V. V. Kozlov's Festschrif
Wedge disclination in the field theory of elastoplasticity
In this paper we study the wedge disclination within the elastoplastic defect
theory. Using the stress function method we found exact analytical solutions
for all characteristic fields of a straight wedge disclination in a cylinder.
The elastic stress, elastic strain, elastic bend-twist, displacement and
rotation have no singularities at the disclination line. We found a modified
stress function for the wedge disclination.Comment: 11 pages, 3 figure
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