The-calculus is a-calculus with a control-like operator whose reduction rules are closely related to normalisation procedures in classical logic. We introduce exp, an explicit substitution calculus for , and study its properties. In particular, we show that exp preserves strong normalisation, which provides us with the rst example {moreover a very natural one indeed{ of explicit substitution ca...

Particular and rare examples of aromatic nucleophilic substitution are described as tele-substitution. Usually strong nucleophiles are involved and the entering group is introduced at a position distant from the expected leaving group. Examples of tele-substitution in various heteroaromatic systems are presented.

This paper presents an algebra of idempotent substitutions whose operations have many properties. We provide an algorithm to compute these operations and we show how they are related to the standard composition. The theory of Logic Programming can be rewritten in terms of these new operations. The advantages are that both the operational and the declarative semantics of Horn Clause Logic can be...

By introducing the notion of mirror substitution, we show that, given a substitutive sequence over two letters, it is palindromic (that is, it contains arbitrarily long palindromes) if and only if its language is mirror-invariant (that is, it is closed under the mirror image map). Then we solve a question of Hof, Knill and Simon in the 2-letter case, and also, by constructing a counterexample, ...

The word substitutions are binary word operations which can be basically interpreted as a deletion followed by insertion, with some restrictions applied. Besides being itself an interesting topic in formal language theory, they have been naturally applied to modelling noisy channels. We introduce the concept of substitution on trajectories which generalizes a class of substitution operations. W...

= zu2(i + k) for all i E I,. If I = Z we call w a Z-word or a bi-infinite word. If I is finite we call x finite and its length Ixl is defined as The usual notation for a finite word of length n is x = xi ... zn where all xi E {a, &}. We write {a, b}* for the collection of finite words and {a, b~+ for the nonempty finite words. (The empty word will be denoted throughout by e). The concatena...

We introduce a type of substitution operation inspired by errors occurring in biologically encoded information. We derive the closure properties of language families in the Chomsky hierarchy under these substitution operations. Moreover, we consider some language equations involving these operations and investigate decidability of the existence of solutions to such equations.

We present a dependent-type system for a λ-calculus with explicit substitutions. In this system, meta-variables, as well as substitutions, are first-class objects. We show that the system enjoys properties like type uniqueness, subject reduction, soundness, confluence and weak normalization.

Metallothionein (MT) is important because it binds tightly to heavy metals to decrease their toxicity. DNA was isolated from 30 toxic metal exposed and 30 toxic metal unexposed Zebu cows. The amplified metallothionein isoform-2 (MT-2) PCR product (489 bp) was further used for PCR-RFLP and DNA sequencing. MT-2 TaqI PCR-RFLP revealed homozygous genotype (AA) except for the E23 animal (AB). The ge...

Dimension groups are complete invariants of strong orbit equivalence for minimal Cantor systems. This paper studies a natural family systems having finitely generated dimension group, namely the primitive unimodular proper $${\mathcal {S}}$$ S -adic subshifts. They by iterating sequences substitutions. Proper substitutions such that images letters start with same letter, and similarly end lette...