Let Th be a triangulation of a bounded polygonal domain Ω ⊂ R2 , Lh the space of the functions from C(Ω) linear on the triangles from Th and Πh the interpolation operator from C(Ω) to Lh. For a unit vector z and an inner vertex a of Th, we describe the set of vectors of coefficients such that the related linear combinations of the constant derivatives ∂Πh(u)/∂z on the triangles surrounding a are equal to ∂u/∂z(a) for all polynomials u of the total degree less than or equal to two. Then we prove that, generally, the values of the so-called recovery operators approximating the gradient ∇u(a) cannot be expressed as linear combinations of the constant gradients ∇Πh(u) on the triangles surrounding a.
Based on the fuzzy probability distribution and its properties, the paper defines the fuzzy reliability and its characteristics for the double-stage probability model of object. Two fuzzy reliability models are described that are based on the Weibull fuzzy distribution. The results can be applied to determining the reliabililty of real objects in cases where pre-failure times are of a vague numerical type. and Obsahuje seznam literatury