Külshammer, Olsson and Robinson conjectured that a certain set of numbers determined the invariant factors of the `-Cartan matrix for Sn (equivalently, the invariant factors of the Cartan matrix for the Iwahori-Hecke algebra Hn(q), where q is a primitive `th root of unity). We call these invariant factors Cartan invariants. In a previous paper, the second author calculated these Cartan invarian...

We provide a new approach to the Hutchinson-Barnsley theory for idempotent measures first presented in Mazurenko and Zarichnyi (2018) [24]. The main feature developed here is metrization of space using embedding fuzzy sets. metric obtained induces topology stronger than canonical pointwise convergence topology. A key result existence bijection between sets conjugation Markov operator an IFS on ...

In this paper, we develop three essential ingredients of an algebraic structure theory of nite block Hankel matrices. The development centers around a transformation of block Hankel matrices, rst introduced by Fischer and Frobenius for scalar Hankel matrices. We prove three results: First, Iohvidov's fundamental notion of the characteristic of a Hankel matrix is extended to the block matrix cas...

a projective parameter of a geodesic as solution of certain ode is defined to be a parameter which is invariant under projective change of metric. using projective parameter and poincaré metric, an intrinsic projectively invariant pseudo-distance can be constructed. in the present work, solutions of the above ode are characterized with respect to the sign of parallel ricci tensor on a finsler s...

In this paper, we propose a novel, effective and fast method to obtain a color illumination invariant and shadow-free image from a single outdoor image. Different from state-of-the-art methods for shadow-free image that either need shadow detection or statistical learning, we set up a linear equation set for each pixel value vector based on physically-based shadow invariants, deduce a pixel-wis...