9 citations · 12 across the 7 of their papers we have counts for
7 papers
Multivariate tile B-splines
Tatyana Zaitseva
Tile B-splines in are defined as autoconvolutions of the indicators of tiles, which are special self-similar compact sets whose integer translates tile the space $\m…
Canonical formulation of embedding gravity in a form of General Relativity with dark matter
S. A. Paston, T. I. Zaitseva
We study embedding gravity, a modified theory of gravity, in which our space-time is assumed to be a four-dimensional surface in flat ten-dimensional space. Based on a simple geome…
Nontrivial isometric embeddings for flat spaces
S. A. Paston, T. I. Zaitseva
Nontrivial isometric embeddings for flat metrics (i.e., those which are not just planes in the ambient space) can serve as useful tools in the description of gravity in the embeddi…
Tiling of polyhedral sets
Vladimir Yu. Protasov, Tatyana Zaitseva
A self-affine tiling of a compact set G of positive Lebesgue measure is its partition to parallel shifts of a compact set which is affinely similar to G. We find all polyhedral set…
Recovery of regular ridge functions on the ball
Tatyana Zaitseva, Yuri Malykhin, Konstantin Ryutin
We consider the problem of the uniform (in ) recovery of ridge functions , , using noisy evaluations $y_1\approx f(x^1),\ldots,y_N…
Simple tiles and attractors
Tatyana Zaitseva
We study self-similar attractors in the space , i.e., self-similar compact sets defined by several affine operators with the same linear part. The special case of att…
Self-affine 2-attractors and tiles
Vladimir Yu. Protasov, Tatyana Zaitseva
We study two-digit attractors (2-attractors) in which are self-affine compact sets defined by two contraction affine mappings with the same linear part. They are wid…