This paper introduces a new concept to the processing of graph structured information using self organising map framework. Previous approaches to this problem were limited to the processing of bounded graphs. The computational complexity of such methods grows rapidly with the level of connectivity, and are restricted to the processing of positional graphs. The concept proposed in this paper add...

A Platonic map is a regular map M on the sphere S. Following [CMo] we say that M has type {n,m} if it has n-gonal faces and the vertices have valency m; since these parameters determine a Platonic map uniquely, one can unambiguously write M = {n,m}. As one must have 0 ≤ (m − 2)(n − 2) < 4, there are precisely the possibilities M = {n, 2} (dihedron), M = {2,m} (hosohedron), M = {3, 3} (tetrahedr...

In this paper we deal with one of the fundamental problems for mobile robots, namely their ability to produce accurate representations of their environment. We propose an office mapping algorithm that iteratively alternates between a Kalman smoother based localization step and a map features recalculation step. Moreover, a hybrid algorithm with global localization capabilities is employed in th...

In this paper, we first introduce the concept of MT − K condition. Some best proximity point theorems for mappings satisfying MT − K condition instead of K-cyclic mappings are established in metric spaces. Our results generalize and improve some main results in [5] and references therein. Mathematics Subject Classification: 54H25

Recently, regular Cayley maps of cyclic groups and dihedral have been classified in [7] [20], respectively. A nature question is to classify elementary abelian p-groups Zpn. In this paper, a complete classification Zpn given moreover, the number these their genera are enumerated.

Abstract We classify $SU(2)$-cyclic and $SU(2)$-abelian 3-manifolds, for which every representation of the fundamental group into $SU(2)$ has cyclic or abelian image, respectively, among geometric 3-manifolds that are not hyperbolic. As an application, we give examples hyperbolic do admit degree-1 maps to any Seifert Fibered manifold other than $S^3$ a lens space. also produce infinitely many o...

A generalised Paley map is a Cayley map for the additive group of a finite field F , with a subgroup S = −S of the multiplicative group as generating set, cyclically ordered by powers of a generator of S. We characterise these as the orientably regular maps with orientation-preserving automorphism group acting primitively and faithfully on the vertices; allowing a non-faithful primitive action ...

We first consider a cyclic φ-contraction map on a reflexive Banach space X and provide a positive answer to a question raised by Al-Thagafi and Shahzad on the existence of best proximity points for cyclic φ-contraction maps in reflexive Banach spaces in one of their works 2009 . In the second part of the paper, we will discuss the existence of best proximity points in the framework of more gene...