We describe under various conditions abelian subgroups of the automorphism group Aut(Tn) of the regular n-ary tree Tn, which are normalized by the n-ary adding machine τ = (e, . . . , e, τ)στ where στ is the n-cycle (0, 1, . . . , n− 1). As an application, for n = p a prime number, and for n = 4, we prove that every soluble subgroup of Aut(Tn), containing τ is an extension of a torsion-free met...

Breast cancer is currently one of the leading causes of death among women worldwide. This paper presents an approach for detecting in digital mammograms not only the detection and early stage of tumors can also detectable. In difficulty of image segmentation found misclassified pixels leads to ambiguity at correct detection of boundary. The effective classification is possible by NN Classifier....

The paper deals with the perfect 1-error correcting codes over a finite field with q elements (briefly q-ary 1-perfect codes). We show that the orthogonal code to the q-ary non-full-rank 1-perfect code of length n = (q − 1)/(q − 1) is a q-ary constant-weight code with Hamming weight equals to qm−1 where m is any natural number not less than two. We derive necessary and sufficient conditions for...

We present an explicit formula for the mask of odd points n-ary, for any odd n 3, interpolating subdivision schemes. This formula provides the mask of lower and higher arity schemes. The 3-point and 5-point a-ary schemes introduced by Lian, 2008, and 2m 1 -point a-ary schemes introduced by, Lian, 2009, are special cases of our explicit formula. Moreover, other well-known existing odd point n-ar...

We consider the classic problem of designing heaps. Standard binary heaps run faster in practice than Fibonacci heaps but have worse time guarantees. Here we present a new type of heap that runs faster in practice than both standard binary and Fibonacci heaps, but has asymptotic insert times arbitrarily better than O(logn), namely O((logn)) for arbitrary positive integer m. Our heap is defined ...

We propose in this paper a method to extract instances of n-ary relations in a text guided by an Ontological and Terminological Resource (OTR). An OTR is a resource composed of a conceptual component (the ontology) and a terminological component (the terminology) in which the terms are distinguished from the concepts they denote. The ontology allows n-ary relationships to be described between a...

The notion of n-ary algebras, that is vector spaces with a multiplication concerning n-arguments, n ≥ 3, became fundamental since the works of Nambu. Here we first present general notions concerning n-ary algebras and associative n-ary algebras. Then we will be interested in the notion of n-Lie algebras, initiated by Filippov, and which is attached to the Nambu algebras. We study the particular...

In this paper, we propose a construction of fullrank q-ary 1-perfect codes over finite fields. This construction is a generalization of the Etzion and Vardy construction of fullrank binary 1-perfect codes (1994). Properties of i-components of q-ary Hamming codes are investigated and the construction of full-rank q-ary 1-perfect codes is based on these properties. The switching construction of 1...