Constructive Description of Hölder Classes on Some Multidimensional Compact Sets

Compact Description and Modeling of Multidimensional Information

We present a technique to compress data de ned as functions in high dimensional spaces. The objects in the spaces are represented by manifolds. Traditionally, data compression methods have been applied to functions de ned on simple manifolds such as the real line (e.g., audio), a rectangle (e.g., images), or a three{dimensional open{ended box (e.g., video). However, many conventional data compr...

Polynomial meshes on some classes of planar compact domains ∗

We construct low cardinality admissible meshes for polynomials on three classes of planar compact domains: cartesian graph domains, polar graph domains, and domains with piecewise C 2 boundary, that satisfy a Markov polynomial inequality. 1 Planar cartesian and polar graph domains Let K ⊂ R d be a polynomial determining compact domain (i.e., a polynomial vanishing there vanishes everywhere). We...

Probability of Mutually Commuting N-Tuples in Some Classes of Compact Groups

On Pre-θ-Open Sets and Two Classes of Functions

Some Compact Classes of Open Sets under Hausdorff Distance and Application to Shape Optimization

In this paper, we introduce three new classes of open sets in a general Euclidean space RN . It is shown that every class of open sets is compact under the Hausdorff distance. The result is then applied to a shape optimization problem of elliptic equation. The existence of the optimal solution is presented.