Abstract Cantor sets are constructed from iteratively removing sections of intervals. This process yields a cumulative distribution function (CDF), the invariant Borel probability measure associated with their iterated systems. Under appropriate assumptions, we identify sampling schemes such CDFs, meaning that underlying set can be reconstructed sufficiently many samples its CDF. To this end, p...

The representation plays an important role in recognition and understanding of human action from video sequences. A view-invariant representation of action consisting of dynamic instants and intervals, which is computed using spatiotemporal curvature of a trajectory, is presented. In order to validate our representation, we report experiments on several different actions performed by different ...

In this survey paper, some of the basic properties of multiwavelets are reviewed. Particular emphasis is given to approximation-theoretic issues and sampling on compact intervals. In addition, a translation invariant multiwavelet transform is discussed and the regularity and approximation order of the associated correlation matrices, which satisfy a particular matrix-valued refinement equation,...

We consider words coding exchange of three intervals with permutation (3,2,1), here called 3iet words. Recently, a characterization of substitution invariant 3iet words was provided. We study the opposite question: what are the morphisms fixing a 3iet word? We reveal a narrow connection of such morphisms and morphisms fixing Sturmian words using the new notion of amicability.

We extend the notions of conditioned and controlled invariant spaces to linear dynamical systems over the max-plus or tropical semiring. We establish a duality theorem relating both notions, which we use to construct dynamic observers. These are useful in situations in which some of the system coefficients may vary within certain intervals. The results are illustrated by an application to a man...

‎this contribution mainly focuses on some aspects of lipschitz groups‎, ‎i.e.‎, ‎metrizable groups with lipschitz multiplication and inversion map‎. ‎in the main result it is proved that metric groups‎, ‎with a translation-invariant metric‎, ‎may be characterized as particular group objects in the category of metric spaces and lipschitz maps‎. ‎moreover‎, ‎up to an adjustment of the metric‎, ‎a...

a module is said to be $pi$-extending provided that every projection invariant submodule is essential in a direct summand of the module. in this paper, we focus on direct summands and indecomposable decompositions of $pi$-extending modules. to this end, we provide several counter examples including the tangent bundles of complex spheres of dimensions bigger than or equal to 5 and certain hyper ...

Let T : 0;1] ! 0;1] be an expanding piecewise monotonic map, and consider the set R of all points, whose orbits omit a certain nite union of open intervals. It is shown that the Hausdorr dimension HD (R) depends continuously on small perturbations of the endpoints of these open intervals. A similar result for the topological pressure is also obtained. Furthermore it is shown that for every t 2 ...

Let T : [0, 1] → [0, 1] be an expanding piecewise monotonic map, and consider the set R of all points, whose orbits omit a certain finite union of open intervals. It is shown that the Hausdorff dimension HD (R) depends continuously on small perturbations of the endpoints of these open intervals. A similar result for the topological pressure is also obtained. Furthermore it is shown that for eve...