Regular homomorphisms of oriented maps essentially arise from a factorization by a subgroup of automorphisms. This kind of map homomorphism is studied in detail, and generalized to the case when the induced homomorphism of the underlying graphs is not valency preserving. Reconstruction is treated by means of voltage assignments on angles, a natural extension of the common assignments on darts. ...

Since the article [3] on polynomial maps of spheres appeared about 25 years ago, there have been a number of papers on the theory of rational maps of real varieties (see the references in [2], for example) which have many interesting things to say about the representation of homotopy classes by algebraic maps. As far as I know, however, the problem of representing elements in the homotopy group...

Understanding how the brain stores and processes information is central to mathematical neuroscience. Neural data is often represented as a neural code: a set of binary firing patterns C ⊂ {0, 1}n. We have previously introduced the neural ring, an algebraic object which encodes combinatorial information, in order to analyze the structure of neural codes. We now relate maps between neural codes ...

the notions of quasi-prime submodules and developed  zariski topology was introduced by the present authors in cite{ah10}. in this paper we use these notions to define a scheme. for an $r$-module $m$, let $x:={qin qspec(m) mid (q:_r m)inspec(r)}$. it is proved that $(x, mathcal{o}_x)$ is a locally ringed space. we study the morphism of locally ringed spaces induced by $r$-homomorphism $mrightar...

In this note we recall some well-known results about covering and k-covering of graphs. Then, we introduce a new notion of spanning tree which we call the p-spanning tree. This notion allows us to reduce the upper bound for the minimum integer k for which a connected graph G has no nontrivial k-covering. This note deals with the notion of covering of graphs and more precisely with the notion of...

The quadratic Veronese embedding ρ maps the point set P of PG(n, F ) into the point set of PG( (n+2 2 ) − 1, F ) (F a commutative field) and has the following well-known property: If M ⊂ P, then the intersection of all quadrics containing M is the inverse image of the linear closure of Mρ. In other words, ρ transforms the closure from quadratic into linear. In this paper we use this property to...

Let Kn = {x ∈ Rn | xi ≥ 0, 1 ≤ i ≤ n} and suppose that f : Kn → Kn is nonexpansive with respect to the l1-norm, ‖x‖1 = ∑n i=1 |xi|, and satisfies f(0) = 0. Let P3(n) denote the (finite) set of positive integers p such that there exists f as above and a periodic point ξ ∈ Kn of f of minimal period p. For each n ≥ 1 we use the concept of “admissible arrays on n symbols” to define a set of positiv...

We study a hierarchy of five classes of bijections between the edge sets of two graphs: weak maps, strong maps, cyclic maps, orientable cyclic maps, and chromatic maps. Each of these classes contains the next one and is a natural class of mappings for some family of matroids. For example, f: E(G) --t E(H) is cyclic if every cycle (eulerian subgraph) of G is mapped onto a cycle of H. This class ...

In this article, the notion of $n-$derivation is introduced for all integers $ngeq 2$. Although all derivations are $n-$derivations,  in general these notions are not equivalent. Some properties of ordinary derivations are  investigated for $n-$derivations. Also, we show that under certain mild condition  $n-$derivations are derivations.