Let K and L be compact convex sets in Rn. The following two statements are shown to be equivalent: (i) For every polytope Q ⊆ K having at most n+ 1 vertices, L contains a translate of Q. (ii) L contains a translate of K. Let 1 ≤ d ≤ n − 1. It is also shown that the following two statements are equivalent: (i) For every polytope Q ⊆ K having at most d+ 1 vertices, L contains a translate of Q. (i...

Approximation properties of multivariate quasi-projection operators are studied in the paper. Wide classes such considered, including sampling and Kantorovich-Kotelnikov type generated by different band-limited functions.The rate convergence weighted $L_p$-spaces for these is investigated. The results allow to estimate error reconstruction signals (approximated functions) whose decay not enough...

in this paper, we investigate the relation between l-projections and conditional expectations on subalgebras of the fourier-stieltjes algebra b(g), and we will show that compactness of g plays an important role in this relation.

We show stability of the $L^2$-projection onto Lagrange finite element spaces with respect to (weighted) $L^p$ and $W^{1,p}$-norms for any polynomial degree space dimension under suitable conditions on mesh grading. This includes $W^{1,2}$-stability in two dimensions meshes generated by newest vertex bisection. Under realistic but conjectured assumptions grading three we all degrees. also propo...

The PROJECTION algorithm by Buhler and Tompa is one of the best existing methods for solving hard motif discovery problems for monad motifs of fixed length l. In this paper we introduce the AGGREGATION algorithm, which like PROJECTION projects all l-mers from the given input sequences into buckets, but uses a different scheme for selecting buckets for subsequent refinement search. This new neig...

For n ≥ 2 a construction is given for convex bodies K and L in R n such that the orthogonal projection Ku can be translated inside Lu for every direction u, while the volumes of K and L satisfy Vn(K) > Vn(L). A more general construction is then given for n-dimensional convex bodies K and L such that the orthogonal projection Kξ can be translated inside Lξ for every k-dimensional subspace ξ of R...