We prove a q-analog of a classical binomial congruence due to Ljunggren which states that ap bp ! ≡ a b ! modulo p for primes p > 5. This congruence subsumes and builds on earlier congruences by Babbage, Wolstenholme and Glaisher for which we recall existing q-analogs. Our congruence generalizes an earlier result of Clark. Résumé. Nous démontrons un q-analogue d’une congruence binomiale classiq...

The definition of open bisimilarity on the χ-processes does not give rise to a sensible relation on the χ-processes with the mismatch operator. The paper proposes ground open congruence as a principal open congruence on the χ-processes with the mismatch operator. The algebraic properties of the ground congruence is studied. The paper also takes a close look at barbed congruence. This relation i...

In the last decade, algebraic methods have led to much progress in classifying the complexity of the non-uniform Constraint Satisfaction Problem (CSP). The programming language Datalog, whose origins lie in logic programming and database theory, has been playing an important role in classifying complexity of CSP since at least the classic paper of Feder and M. Vardi [10]. Feder and Vardi used D...

in this paper, we define the notions of fuzzy congruence relations and fuzzy convex subalgebras on a commutative residuated lattice and we obtain some related results. in particular, we will show that there exists a one to one correspondence between the set of all fuzzy congruence relations and the set of all fuzzy convex subalgebras on a commutative residuated lattice. then we study fuzzy...

This work presents an extension with cuts of Schwichtenberg’s multiary sequent calculus. We identify a set of permutative conversions on it, prove their termination and confluence and establish the permutability theorem. We present our sequent calculus as the typing system of the generalised multiary λ-calculus λJ, a new calculus introduced in this work. λJ corresponds to an extension of λ-calc...

The vectorial fundamental transformation for the Darboux equations is reduced to the symmetric case. This is combined with the orthogonal reduction of Lamé type to obtain those vectorial Ribaucour transformations which preserve the Egoroff reduction. We also show that a permutability property holds for all these transformations. Finally, as an example, we apply these transformations to the Cart...

A Cliiord algebra model for MM obius geometry is presented. The notion of Ribaucour pairs of orthogonal systems in arbitrary dimensions is introduced , and the structure equations for adapted frames are derived. These equations are discretized and the geometry of the occuring discrete nets and sphere congruences is discussed in a conformal setting. This way, the notions of \discrete Ribaucour c...

The relationship between phylogenetic accuracy and congruence between data partitions collected from the same taxa was explored for mitochondrial DNA sequences from two well-supported vertebrate phylogenies. An iterative procedure was adopted whereby accuracy, phylogenetic signal, and congruence were measured before and after modifying a simple reconstruction model, equally weighted parsimony. ...