We complete the proof of a theorem we announced and partly proved in [Math. Nachr. 271 (2004), 69-90, math.AG/0111299]. The concerns family curves on surfaces. It has two parts. first was that paper. describes natural cycle enumerates with precisely $r$ ordinary nodes. second part is here. asserts that, for $r\le 8$, class this given by computable universal polynomial pushdowns to parameter spa...

The following article presents the elaboration and results obtained from a 3D finite element, of 8-node hexahedron type with 6 degrees freedom (DOF) per node (48 DOF element) based on third degree Hermitian polynomials, 2-node structural (12 element), polynomials theory Timoshenko for beams. This has two purposes; first one is formulation element capable capturing bending effects, second to ver...

According to the Göttsche conjecture (now a theorem), the degree N of the Severi variety of plane curves of degree d with δ nodes is given by a polynomial in d, provided d is large enough. These “node polynomials” Nδ(d) were determined by Vainsencher and Kleiman–Piene for δ ≤ 6 and δ ≤ 8, respectively. Building on ideas of Fomin and Mikhalkin, we develop an explicit algorithm for computing all ...

We generalize the recent work of S. Fomin and G. Mikhalkin on polynomial formulas for Severi degrees. The degree of the Severi variety of plane curves of degree d and δ nodes is given by a polynomial in d , provided δ is fixed and d is large enough. We extend this result to generalized Severi varieties parametrizing plane curves that, in addition, satisfy tangency conditions of given orders wit...

in this paper we demonstrate the existence of a set of polynomials pi , 1 i  n , which arepositive semi-definite on an interval [a , b] and satisfy, partially, the conditions of polynomials found in thelagrange interpolation process. in other words, if a  a1  an  b is a given finite sequence of realnumbers, then pi (a j )  ij (ij is the kronecker delta symbol ) ; moreover, the sum of ...