By adopting natural generalizations of relational frame and relational model we showed in [2] that the deontic law D, Dp -» Op, is not universally first-order definable. In effect, we showed there that for n > 2, there is no n-adic first-order sentence p such that for every n-ary frame F,F ^D iff F ^(3 in the first-order sense. The notion of n-ary frame and model employed there may be summarize...

The interconnection network considered in this paper is the k-ary n-cube that is an attractive variance of the well-known hypercube. Many interconnection networks, including the ring, the torus and the hypercube, that are attractive in both theoretical interests and practical systems can be regarded as the subclasses of the k-ary n-cubes. In this paper, we investigate the fault tolerant cycle e...

When n is odd, a cohomology of type Hochschild for n-ary partially associative algebras has been defined in Gnedbaye’s thesis. Unfortunately, the cohomology definition is not valid when n is even. This fact is found again in the computations of the n-ary partially associative free algebra. In this work, we define in a first time two approachs of an Hochschild cohomology for n-ary partially asso...

We count all latin cubes of order n ≤ 6 and latin hypercubes of order n ≤ 5 and dimension d ≤ 5. We classify these (hyper)cubes into isotopy classes and paratopy classes (main classes). For the same values of n and d we classify all d-ary quasigroups of order n into isomorphism classes and also count them according to the number of identity elements they possess (meaning we have counted the d-a...

This article describes an approach to solving distributed constraint optimization problems (DCOP) with n-ary constraints. A key instance of this problem is distributed resource-constrained task scheduling, in which limited resource capacities implicitly imply n-ary relations among the start-times of the tasks. We describe ADOPT-N, an extension of ADOPT [16], a recent successful algorithm for DC...

We introduce and study category of $(m, n)$-ary hypermodules as a generalization of the category of $(m, n)$-modules as well as the category of classical modules. Also, we study various kinds of morphisms. Especially, we characterize monomorphisms and epimorphisms in this category. We will proceed to study the fundamental relation on $(m, n)$-hypermodules, as an important tool in the study of a...

This paper deals with hypergroupoids obtained from n-ary relations. We give conditions for an n-ary relation such that the hypergroupoid associated with it is a hypergroup. First we analyze this construction using a ternary relation and then we generalize it for an n-ary relation.

The growing amount of data available in modern-day datasets makes the need to efficiently search and retrieve information. To make large-scale search feasible, Distance Estimation and Subset Indexing are the main approaches. Although binary coding has been popular for implementing both techniques, n-ary coding (known as Product Quantization) is also very effective for Distance Estimation. Howev...