Filters — Part I Grzegorz

Filters - Part I

Filters of a lattice, maximal filters (ultrafilters), operation to create a filter generating by an element or by a nonempty set of elements of the lattice are discussed. Besides, there are introduced implicative lattices such that for every two elements there is an element being pseudo-complement of them. Some facts concerning these concepts are presented too, i.e. for any proper filter there ...

Analysis of the selected optical parameters of filters protecting against hazardous infrared radiation

The paper analyses the selected optical parameters of protective optic filters used for protection of the eyes against hazardous radiation within the visible (VIS) and near infrared (NIR) spectrum range. The indexes characterizing transmission and reflection of optic radiation incident on the filter are compared. As it follows from the completed analysis, the newly developed interference filter...

$z^circ$-filters and related ideals in $C(X)$

In this article we introduce the concept of $z^circ$-filter on a topological space $X$. We study and investigate the behavior of $z^circ$-filters and compare them  with corresponding ideals, namely, $z^circ$-ideals of $C(X)$,  the ring of real-valued continuous functions on a completely regular Hausdorff space $X$. It is observed that $X$ is a compact space if and only if every $z^circ$-filter ...

Basic formulas and languages Part I. The theory

Grammars as Processes

In 1999 I met Grzegorz Rozenberg in Amsterdam, while I was attending the ETAPS conference and he was taking part in a meeting. The next day I was giving a talk with the title “Grammars as Processes”, and Grzegorz, who had seen it announced in the program, asked me about it. We had little time, and so I could barely sketch the contents. I think Grzegorz would have liked the talk, because it poin...