We generalize geodesic finite elements to obtain spaces of higher approximation order. Our approach uses a Riemannian center of mass with a signed measure. We prove well-definedness of this new center of mass under suitable conditions. As a side product we can define geodesic finite elements for non-simplex reference elements such as cubes and prisms. We prove smoothness of the interpolation fu...

We study Kostant’s partial order on the elements of a semisimple Lie group in relations with the finite dimensional representations. In particular, we prove the converse statement of [3, Theorem 6.1] on hyperbolic elements. A matrix in GLn(C) is called elliptic (resp. hyperbolic) if it is diagonalizable with norm 1 (resp. real positive) eigenvalues. It is called unipotent if all its eigenvalues...

Let f(n) be the largest integer such that every poset on n elements has a 2-dimensional subposet on f(n) elements. What is the asymptotics of f(n)? It is easy to see that f(n) > n. We improve the best known upper bound and show f(n) = O(n). For higher dimensions, we show fd(n) = O ( n d d+1 ) , where fd(n) is the largest integer such that every poset on n elements has a d-dimensional subposet o...

Fractional-order circuits are finding applications in control systems, signal processing, and other allied fields. As a result, realizing fractional-order elements or fractance devices is an essential research topic. A unique device realized this study using continued fraction expansion (CFE) partial (PFE) formulas. Continued used to calculate the rational approximation. For simulation, fourth ...