A logarithmic type modulus of continuity is established for weak solutions to a two-phase Stefan problem, up the parabolic boundary cylindrical space-time domain. For Dirichlet we merely assume that spatial domain satisfies measure density property, and datum has continuity. Neumann lateral smooth, bounded. The proofs are theoretical in nature, exploiting De Giorgi's iteration refining DiBenede...

Let {L x t ; (x, t) ∈ R 1 × R 1 + } denote the local time of Brownian motion, and α t := ∞ −∞ (L x t) 2 dx. Let η = N(0, 1) be independent of α t. For each fixed t, ∞ −∞ (L x+h t − L x t) 2 dx − 4ht h 3/2 L → 64 3 1/2 √ α t η as h → 0. Equivalently, ∞ −∞ (L x+1 t − L x t) 2 dx − 4t t 3/4 L → 64 3 1/2 √ α 1 η as t → ∞. 1. Introduction. In [10] almost sure limits are obtained for the L p moduli o...

partial replacement of formaldehyde with furfural in the urea-formaldehyde resin on the formaldehydeemission, physical and mechanical properties of particleboard was investigated. the modulus ofrupture (mor), modulus of elasticity (moe), internal bond (ib), water absorption (wa), thicknessswelling (ts) and formaldehyde emission (fe) of poplar particleboards made with the modifiedresins were mea...

Bǎrbosu and Muraru (2015) introduced the bivariate generalization of the q -Bernstein–Schurer–Stancu operators and constructed a GBS operator of q -Bernstein–Schurer–Stancu type. The concern of this paper is to obtain the rate of convergence in terms of the partial and complete modulus of continuity and the degree of approximation by means of Lipschitz-type class for the bivariate operators. In...