We generalize the notion of quasi-closed element to fuzzy posets in two stages: First, crisp style which each a given universe either is or not. Second, graded by defining degrees an quasi-closed. discuss different possible definitions and comparing them with other. Finally, we show that most general one has good properties be used when have complete lattice as frame.

We present a new proof of Banaschewski's theorem stating that the completion lift of a uniform surjection is a surjection. The new procedure allows to extend the fact (and, similarly, the related theorem on closed uniform sublocales of complete uniform frames) to quasi-uniformities ("not necessarily symmetric uniformities"). Further, we show how a (regular) Cauchy point on a closed uniform subl...

We classify all sub-cartesian closed categories of the category of separable Scott domains. The classification employs a notion of coherence degree determined by the possible inconsistency patterns of sets of finite elements of a domain. Using the classification, we determine all sub-cartesian closed categories of the category of separable Scott domains that contain a universal object. The sepa...

Recently, an interaction between the mathematical discipline of combinatorics on words and musical scale theory has led to various interesting results. So far, the focus was mainly on scales generated by a single interval. The paper proposes an extension of word scale theory to tone systems of higher dimensions, i.e. generated by more than one interval. It is shown that the number of specific v...

Many applications use sequences of n consecutive symbols (n-grams). We review n-gram hashing and prove that recursive hash families are pairwise independent at best. We prove that hashing by irreducible polynomials is pairwise independent whereas hashing by cyclic polynomials is quasi-pairwise independent: we make it pairwise independent by discarding n− 1 bits. One application of hashing is to...

Given a closed polygonal contour with N+3 vertices in IR q (q 2) there is a one to one correspondence between the zeros of r and minimal surfaces spanned by ?, where () := inf v2X() D(v) (2 T IR N) denotes Shiiman's function for the polygon ? and D denotes Dirichlet's Integral. We derive an explicit expression for r h , where h () := inf v2X h () D(v) with suitable nite element spaces X h (). F...

When equipped with the natural topology first defined by Chabauty, the closed subgroups of a locally compact group G form a compact space C(G). We analyse the structure of C(G) for some low-dimensional Lie groups, concentrating mostly on the 3-dimensional Heisenberg group H. We prove that C(H) is a 6-dimensional space that is path–connected but not locally connected. The lattices in H form a de...