In this paper a guaranteed upper bound of the global discretization error in linear elastic finite element approximations is presented, based on a generalized Trefftz functional. Therefore, the general concept of complementary energy functionals and the corresponding approximation methods of Ritz, Trefftz, the method of orthogonal projection and the hypercircle method are briefly outlined. Furt...

martindale proved that under some conditions every multiplicative isomorphism between two rings is additive. in this paper, we extend this theorem to a larger class of mappings and conclude that every multiplicative $(alpha, beta)-$derivation is additive.

Strongly multiplicative linear secret sharing schemes (LSSS) have been a powerful tool for constructing secure multi-party computation protocols. However, it remains open whether or not there exist efficient constructions of strongly multiplicative LSSS from general LSSS. In this paper, we propose the new concept of 3-multiplicative LSSS, and establish its relationship with strongly multiplicat...

We prove that a stochastic flow of reflected Brownian motions in a smooth multidimensional domain is differentiable with respect to its initial position. The derivative is a linear map represented by a multiplicative functional for reflected Brownian motion. The method of proof is based on excursion theory and analysis of the deterministic Skorokhod equation.