We investigate the rewrite relation over graphs induced by constructor-based weakly orthogonal graph rewriting systems. It is well known that this relation is not confluent in general whereas it is confluent in the case of weakly orthogonal term rewriting systems. We show, however, that the considered relation is always confluent, as well as confluent modulo bisimilarity, for a large class of g...

We start in this work the study of relation between theory regularity structures and paracontrolled calculus. give a representation reconstruction operator provide natural parametrization space admissible models.

Let α be an arbitrary Σ1-admissible ordinal. For each n, there is a formula φn(~x, ~y) such that for any relation R on a finite set F with n elements, there are α-degrees ~ p such that the relation defined by φn(~x, ~ p) is isomorphic to R. Consequently, the theory of α-degrees

We study the computable structure theory of linear orders of size א1 within the framework of admissible computability theory. In particular, we study degree spectra and the successor relation.

Partial types allow the reasoning about partial functions in type theory. The partial functions of main interest are recursively computed functions, which are commonly assigned types using xpoint induction. However, xpoint induction is valid only on admissible types. Previous work has shown many types to be admissible, but has not shown any dependent products to be admissible. Disallowing recur...

In this paper, we consider the unilateral contact problem between elastic bodies. We propose an error estimator based on the concept of error in the constitutive relation in order to evaluate the ®nite element approximation involving matching and non-matching meshes on the contact zone. The determination of the a posteriori error estimate is linked to the building of kinematically-admissible st...

We prove a conjecture of K. Monks 4] on the relation between the admissible basis and the Milnor basis of the mod 2 Steenrod algebra A 2 , and generalise the result to the mod p Steenrod algebra A p where p is prime. This establishes a necessary and suucient condition for the Milnor basis element P(r 1 ; r 2 ; : : : ; r k) and the admissible basis element P t 1 P t 2 : : : P t k to coincide. Th...

A coupled cell system is a network of dynamical systems, or ‘cells’, coupled together. Such systems are represented schematically by a directed graph whose nodes correspond to cells and whose edges represent couplings. Symmetry of coupled cell systems can lead to synchronized cells. We show that symmetry is not the only mechanism that can create such states in a coupled cell system. The first m...

The existence of admissible vectors for a locally compact group is closely related to the group's profile. In the compact groups, according to Peter-weyl theorem, every irreducible representation has admissible vector. In this paper, the conditions under which the inverse of this case is being investigated has been investigated. Conditions such as views that are admissible and stable will get c...

A coupled cell system is a network of dynamical systems, or ‘cells’, coupled together. Such systems can be represented schematically by a directed graph whose nodes correspond to cells and whose edges represent couplings. A symmetry of a coupled cell system is a permutation of the cells that preserves all internal dynamics and all couplings. Symmetry can lead to patterns of synchronized cells, ...