On a class of polynomial triangular macro-elements

Trivariate C Polynomial Macro-Elements

Trivariate C macro-elements defined in terms of polynomials of degree 8r + 1 on tetrahedra are analyzed. For r = 1, 2, these spaces reduce to well-known macro-element spaces used in data fitting and in the finite-element method. We determine the dimension of these spaces, and describe stable local minimal determining sets and nodal minimal determining sets. We also show that the spaces approxim...

Differential Polynomial Rings of Triangular Matrix Rings

On constant products of elements in skew polynomial rings

Let $R$ be a reversible ring which is $alpha$-compatible for an endomorphism $alpha$ of $R$ and $f(X)=a_0+a_1X+cdots+a_nX^n$ be a nonzero skew polynomial in $R[X;alpha]$. It is proved that if there exists a nonzero skew polynomial $g(X)=b_0+b_1X+cdots+b_mX^m$ in $R[X;alpha]$ such that $g(X)f(X)=c$ is a constant in $R$, then $b_0a_0=c$ and there exist nonzero elements $a$ and $r$ in $R$ such tha...

differential polynomial rings of triangular matrix rings

On a Certain Class of submeasures Based on Triangular Norms

In this paper we study a generalization of a submeasure notion which is related to a probabilistic concept, especially to Menger spaces where triangular norms play a crucial role. The resulting notion of a τT -submeasure is suitable for modeling those situations in which we have only probabilistic information about the measure of the set. We characterize a class of universal τT -submeasures (i....