L'anneau $$\mathbb{Z} [\sqrt {14} ]$$ et l'algorithme Euclidien
The aim of this note is to study the ring\(\mathbb{Z} [\sqrt {14} ]\) and in particular the question whether it is Euclidean or not. The following results are obtained: ::: ::: 1) ::: ::: The couples of elements of\(\mathbb{Z} [\sqrt {14} ]\) which are not Euclidean with respect to the absolute value of the norm are determined. ::: ::: ::: ::: ::: 2) ::: ::: An Euclidean algorithm for\(\mathbb{Z} [\sqrt {14} ]\) is constructed under suitable assumptions (Hypothese 4.1).
There are several formulations for the beam element in the large deformation and displacement problem. Recently, Absolute Nodal Coordinate Formulation (ANCF) is studied for such problems. In this formulation, the mass matrix and the stiffness matrix are described as simple equations, even in the case of the large deformation and displacement problem. However, degree of freedom of the beam element of ANCF increases from conventional finite element method, since the beam element is formulated by 8 absolute nodal coordinates. In this paper, the authors propose a formulation and an assembling method of the beam element formulated by 6 absolute nodal coordinates considering the calculation efficiency. In this method, the number of nodal coordinates of the assembling point of beam elements is same as nonlinear finite element method. The effect of the proposed method is verified by the numerical simulations.