The study of languages of labelled birooted trees, that is, elements of the free inverse monoid enriched by a vertex labelling, has led to the notion of quasi-recognisability. It generalises the usual notion of recognisability by replacing homomorphisms by certain prehomomorphism into finite ordered monoids, called adequate, that only preserve some products: the so-called disjoint ones. In this...

‎ranking fuzzy numbers is generalization of the concepts of order, and class, and so have fundamental applications. moreover, deriving the final efficiency and powerful ranking are helpful to decision makers when solving fuzzy problems. selecting a good ranking method can apply to choosing a desired criterion in a fuzzy environment. there are numerous methods proposed for the ranking of fuzzy n...

The study of algebraic surfaces in Gr (1, p3), the Grassmann variety parametrising lines in projective three-space, was a popular one for algebraic geometers of the late nineteenth and early twentieth centuries. Calling them line congruences, researchers such as Kummer, Fano, Roth and many others published many papers on the topic, classifying congruences and studying their invariants. Since th...

We extend Howe’s method to prove that input-early strong and -delay contextual bisimulations are congruences for the Higher-order mobile embedded resources (Homer) calculus, a typed higher order process calculus with active mobile processes, nested locations and local names which conservatively extends the syntax and semantics of higher-order calculi such as Plain CHOCS and HOpi. We prove that ...

Applicative bisimilarity is a coinductive characterisation of observational equivalence in call-by-name lambda-calculus, introduced by Abramsky (1990). Howe (1996) gave direct proof that it congruence, and generalised the result to all languages complying with suitable format. We propose categorical framework for specifying operational semantics, which we prove (an abstract analogue of) applica...

We give a detailed description of the arithmetic Fuchsian group of the Bolza surface and the associated quaternion order. This description enables us to show that the corresponding principal congruence covers satisfy the bound sys(X) > 4 3 log g(X) on the systole, where g is the genus. We also exhibit the Bolza group as a congruence subgroup, and calculate out a few examples of “Bolza twins” (u...

We consider the congruence a P s i=1 b i h i mod I where h 1 ; : : : ; hs are given modulo a zero dimensional ideal I. We give two polynomial time algorithms for determining a Grr obner basis, relative to an arbitrary term order, of the module M of solutions of the congruence, and, in particular, for nding its minimal element. These are based on a generalization of an algorithm of Faug ere et a...

Algebraic properties and structures of intuitionistic $$L-$$ fuzzy multiset finite automata (ILFMA) are discussed through congruences on a semigroup in this paper. Firstly, we put forward the notion compatible relation, monoid associated with relation can be effectively constructed, construct two monoids different congruence relations given ILFMA, then prove that they isomorphic. Furthermore, u...