Schnorr showed that a real X is Martin-Löf random if and only if K(X ↾n) ≥ n − c for some constant c and all n, where K denotes the prefix-free complexity function. Fortnow (unpublished) and Nies, Stephan and Terwijn [NST05] observed that the condition K(X ↾n) ≥ n− c can be replaced with K(X ↾rn ) ≥ rn − c, for any fixed increasing computable sequence (rn), in this characterization. The purpose...

The reconstruction number rn(G) of graph G is the minimum number of vertex-deleted subgraphs of G required in order to identify G up to isomporphism. Myrvold and Molina have shown that if G is disconnected and not all components are isomorphic then rn(G) = 3, whereas, if all components are isomorphic and have c vertices each, then rn(G) can be as large as c + 2. In this paper we propose and ini...

which is the Bochner-Riesz operator (see [8]). Let E be the space E = {h : ‖h‖ = supr>0 |h(r)| <∞}, then, for each fixed x ∈ Rn, Bδ r ( f )(x) may be viewed as a mapping from [0,+∞) to E, and it is clear that Bδ ∗( f )(x) = ‖Bδ r ( f )(x)‖ and B ∗,b( f )(x) = ‖b(x)Bδ r ( f )(x)−Bδ r (b f )(x)‖. As well known, a classical result of Coifman et al. [4] proved that the commutator [b,T] generated by...

In this paper we prove the Lipschitz regularity for local minimizers of convex variational integrals form F(v,Ω)=∫ΩF(x,Dv(x))dx,where, n≥2 and N≥1, Ω is a bounded open set in Rn, u∈W1,1(Ω,RN) energy density F:Ω×RN×n→R satisfies so called variable growth conditions. The main novelty here that assume an almost critical Orlicz Sobolev setting as function x variable.

In this paper, we consider the degenerate numbers Rn(λ) and polynomials Rn(x, λ) related to the Stirling numbers and the Bell polynomials. We also obtain some explicit formulas for degenerate numbers Rn(λ) and polynomials Rn(x, λ). AMS subject classification: 11B68, 11S40, 11S80.

The q-rook monoid Rn(q) is a semisimple C(q)-algebra that specializes when q → 1 to C[Rn], where Rn is the monoid of n × n matrices with entries from {0, 1} and at most one nonzero entry in each row and column. We use a Schur-Weyl duality between Rn(q) and the quantum general linear group Uqgl(r ) to compute a Frobenius formula, in the ring of symmetric functions, for the irreducible characters...