Let α = −2+ √ −1 be a root of the polynomial p(x) = x +4x+5. It is well-known that the pair (α, {0, 1, 2, 3, 4}) forms a canonical number system, i.e., that each γ ∈ Z[α] admits a finite representation of the shape γ = a0 + a1α+ · · ·+ alα with ai ∈ {0, 1, 2, 3, 4}. The set T of points with integer part 0 in this number system

This paper presents a static analysis of laminated composite doubly-curved shells using refined kinematic models with polynomial and non-polynomial functions recently introduced in the literature. To be specific, Maclaurin, trigonometric, exponential and zig-zag functions are employed. The employed refined models are based on the equivalent single layer theories. A simply supported shell is sub...

The application of a new mean value theorem to the fractional parts of polynomials 1. Introduction. The new mean value estimates provided by recent advances in Waring's problem (see, in particular, [9, 10, 11, 14]) may plainly be applied to improve current estimates for αn k , the distance from αn

Fuzzy Newton-Cotes method for integration of fuzzy functions that was proposed by Ahmady in [1]. In this paper we construct error estimate of fuzzy Newton-Cotes method such as fuzzy Trapezoidal rule and fuzzy Simpson rule by using Taylor's series. The corresponding error terms are proven by two theorems. We prove that the fuzzy Trapezoidal rule is accurate for fuzzy polynomial of degree one and...