Suppose a, b, c are algebraic indeterminates. The mapping (a, b, c) → (bc, ca, ab) is an example of a second-degree involutory symbolic substitution (SISS) which maps the transfigured plane of a triangle to itself. The main result is a classification of SISSs as four individual mappings and two families of mappings. The SISS (a, b, c) → (bc, ca, ab) maps the circumcircle onto the Steiner ellips...

Extending the-calculus with either explicit substitution or generalised reduction has been the subject of extensive research recently which still has many open problems. Due to this reason, the properties of a calculus combining both generalised reduction and explicit substitutions have never been studied. This paper presents such a calculus sg and shows that it is a desirable extension of the-...

The disturbance rejection, defined as the problem of designing control laws that ensure, where possible, exogenous disturbances that do not affect the output of the perturbed system, has been resolved by means of algebraic and geometric techniques. This is a steady linear case by means of the static feedback state. Modifications of the Smith form through the SPR0 substitutions are presented whi...

This paper introduces a -calculus with explicit substitutions, corresponding to an S4 modal logic of constructive necessity. As well as being semantically well motivated, the calculus can be used (a) to develop abstract machines, and (b) as a framework for specifying and analysing computation stages in the context of functional languages. We prove several syntactic properties of this calculus,...

There are several notions of the ‘dual’ of a word/tile substitution. We show that the most common ones are equivalent for substitutions in dimension one, where we restrict ourselves to the case of two letters/tiles. Furthermore, we obtain necessary and sufficient arithmetic conditions for substitutions being selfdual in this case. Since many connections between the different notions of word/til...

Substitutions generate hierarchical colorings of the plane. Despite the non-locality of substitution rules, one can extend them by adding compatible local matching rules to obtain locally checkable colorings as the set of tilings of finite tileset. We show that the resulting tileset can furthermore be chosen strongly deterministic, a tile being uniquely determined by any two adjacent edges. A t...

Indexing techniques support the retrieval and maintenance of large sets of terms There is also an indexing method called substi tution tree indexing that e ciently handles sets of substitutions We present three advanced indexing operations for substitution trees The multi merge for the simultaneous uni cation of sets of substitutions the subsumption operation on two sets of substitutions and th...

Given an $$\omega $$ -automaton and a set of substitutions, we look at which accepted words can also be defined through these in particular if there is least one. We introduce method using desubstitution -automata to describe the structure preimages under arbitrary sequences homomorphisms: this takes form meta- -automaton. decide existence purely substitutive word, as well fixed point. In case ...

Background: There is limited information on the 3D prediction and modeling of the colistin resistance-associated proteins PmrA/B TCS in Acinetobacter baumannii. We aimed to evaluate the stereochemical structure and domain characterization of PmrA/B in an A. baumannii isolate resistant to high-level colistin, using bioinformatics tools. Methods: The species of the isolate and its susceptibility ...

Calculi of explicit substitutions have been introduced to give an account to the substitution process in lambda calculus. The idea is to introduce a notation for substitutions explicitely in the calculus. In other words one makes substitutions first class citizens whereas the classical lambda calculus leaves them in the meta-theory. Originally, the expression “explicit substitution” and the con...