A tessellation is a process that surrounds us every day. It is an old problem in mathematics and in computational geometry Preparata, 1985 . Several tessellations are known, although only some of them are interesting in the computational geometry. The main aim of the tessellation is to tile or divide the space of the interest into smaller parts tiles upon which other problems could be solved mo...

We parametrize the space of double cosets group GL(n,k) with respect to two subgroups T−, T+ block strictly triangular matrices. In appendix, we consider quasi-regular representation GL(n,C) in L2 on T−∖GL(n,C), observe that it admits an additional symmetries, find joint spectrum, and is multiplicity free.

Quasi-ideals were introduced by Otto Steinfeld [43] as those non-empty subsets Q of a semigroup T satisfying QTD TQ c Q. When T is regular they are precisely the subsets Q of T which satisfy QTQ = Q ([43, Theorem 9.3]). There are many examples of quasi-ideals in regular semigroup theory. We list below some of the most important: • Every subsemigroup of the form eSe (where e is an idempotent) is...

We study superpositions and direct integrals of quadratic Dirichlet forms. show that each quasi-regular space over a probability admits unique representation as integral irreducible spaces, for the same underlying topology. The holds strongly local metrizable Luzin, Radon measure space, admitting carr\'e du champ operator. In this case, is only projectively unique.

We present a topological characterization for fuzzy regular languages: we show that there is a bijective correspondence between fuzzy regular languages and the set of all clopen fuzzy subsets with finite image in the induced fuzzy topological space of Stone space (Profinite space), and then we give a representation of closed fuzzy subsets in the induced fuzzy topological space via fuzzy regular...

We describe a quasi-affine representation for algebras having a binary central term.