aim: to investigate the effect of emdogain gel (emd) in pulpotomized primary molars and its clinical and radiographic outcomes. methods and materials: in this   study, 18 lower second primary molars of nine children were treated by   pulpotomy. the teeth were randomly assigned to the emd (experimental) and formocresol (control) groups in each patient (split mouth). following removal of the coro...

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In this paper we prove Hopf’s boundary point lemma for the fractional Laplacian. With respect to the classical formulation, in the non-local framework the normal derivative of the involved function u at z ∈ ∂Ω is replaced with the limit of the ratio u(x)/(δR(x)) , where δR(x) = dist(x, ∂BR) and BR ⊂ Ω is a ball such that z ∈ ∂BR. More precisely, we show that lim inf B∋x→z u(x) (δR(x)) > 0 . Als...

In this article, we present inverse and implicit function theorems forH -differentiable functions and semismooth functions, thereby generalizing the classical inverse and implicit function theorems to certain classes of nonsmooth functions. The classical inverse function theorem [47] asserts that a continuously differentiable function f : R → R is locally invertible at a point with a continuous...

The charge-current density and two-photon operators consistent with a single-particle semi-relativistic Hamiltonian are derived within a suitable functional derivative formalism which preserves gauge invariance. An application to electron scattering is presented and results are compared with a fully relativistic case and the non-relativistic cases corrected through fourth order in M−1.

the present study aims at indicating the existence and uniqueness result of system in extended colombeaualgebra. the caputo fractional derivative is used for solving the system of odes. in addition, rieszfractional derivative of colombeau generalized algebra is considered. the purpose of introducing rieszfractional derivative is regularizing it in colombeau sense. we also give a solution to a n...