2-widths of the Hölder unit balls

Widths of l p balls

The Gelfand widths of ℓp-balls for 0<p≤1

We provide sharp lower and upper bounds for the Gelfand widths of lp-balls in the N -dimensional lNq -space for 0 < p ≤ 1 and p < q ≤ 2. Such estimates are highly relevant to the novel theory of compressive sensing, and our proofs rely on methods from this area.

Touching Graphs of Unit Balls

The touching graph of balls is a graph that admits a representation by non-intersecting balls in the space (of prescribed dimension), so that its edges correspond to touching pairs of balls. By a classical result of Koebe [?], the disc touching graphs are exactly the planar graphs. This paper deals with a recognition of unit-ball touching graphs. The 2– dimensional case was proved to be NP-hard...

Best approximation by closed unit balls

We obtain a sucint and nesessery theoreoms simple for compactness andweakly compactness of the best approximate sets by closed unit balls. Also weconsider relations Kadec-Klee property and shur property with this objects.These theorems are extend of papers mohebi and Narayana.

Lines Tangent to Four Unit Balls problem 2

The Golden Partition Conjecture is motivated by conjectures whose root is a famous sorting problem. Imagine that a finite set S with cardinality n has a hidden total order ≺ that we would like to uncover by making comparisons between pairs of elements from S. Comparing a pair u, v ∈ S means uncovering either u ≺ v or v ≺ u. How many comparisons are needed in the worst case? The classical answer...