The Cantor-Bernstein theorem was extended to $\sigma $-complete boolean algebras by Sikorski and Tarski. Chang’s MV-algebras are a nontrivial generalization of boolean algebras: they stand to the infinite-valued calculus of Łukasiewicz as boolean algebras stand to the classical two-valued calculus. In this paper we further generalize the Cantor-Bernstein theorem to $\sigma $-complete MV-algebras, and compare it to a related result proved by Jakubík for certain complete MV-algebras.
Meshless methods have become an effective tool for solving problems from engineering practice in last years. They have been successfully applied to problems in solid and fluid mechanics. One of their advantages is that they do not require any explicit mesh in computation. This is the reason why they are useful in the case of large deformations, crack propagations and so on. Reproducing kernel particle method (RKPM) is one of meshless methods. In this contribution we deal with some modifications of the RKPM. The construction of the methods considered is given together with simple examples of their applications to solving boundary value problems.