Equivalence of generalized moduli of continuity

Moduli of Continuity

On the topological equivalence of some generalized metric spaces

‎The aim of this paper is to establish the equivalence between the concepts‎ ‎of an $S$-metric space and a cone $S$-metric space using some topological‎ ‎approaches‎. ‎We introduce a new notion of a $TVS$-cone $S$-metric space using‎ ‎some facts about topological vector spaces‎. ‎We see that the known results on‎ ‎cone $S$-metric spaces (or $N$-cone metric spaces) can be directly obtained‎ from...

Combinatorial Equivalence of Real Moduli Spaces

The Riemann moduli space Mg of surfaces of genus g with n marked points has become a central object in mathematical physics. Its importance was emphasized by Grothendieck in his famous Esquisse d’un programme. The special case M0 is a building block leading to higher genera, playing a crucial role in the theory of Gromov-Witten invariants, symplectic geometry, and quantum cohomology. There is a...

Quadrature Error Estimates Involving Moduli of Continuity of Derivatives

CLT for L moduli of continuity of Gaussian processes

Let G = {G(x), x ∈ R1} be a mean zero Gaussian processes with stationary increments and set σ2(|x − y|) = E(G(x) − G(y))2. Let f be a symmetric function with Ef(η) < ∞, where η = N(0, 1). When σ2(s) is concave or when σ2(s) = sr, 1 < r ≤ 3/2 lim h↓0 ∫ b a f ( G(x+h)−G(x) σ(h) ) dx− (b− a)Ef(η) √ Φ(h, σ(h), f, a, b) law = N(0, 1) where Φ(h, σ(h), f, a, b) is the variance of the numerator. This r...