In this paper, we introduce the notion of N -graphs and describe methods of their construction. We prove that the isomorphism between N -graphs is an equivalence relation (resp. partial order relation). We then introduce the concept of N -line graphs and discuss some of their fundamental properties.

The fundamental relation betwen the slopes of diffraction cone in single diffraction dissociation and elastic scattering has been derived. PACS numbers: 11.80.-m, 13.85.-t, 21.30.+y

In this paper, a construction of a congruence having a given filter is presented. Also as a generalization of an BE-algebra homomorphism, the notion of a relation on BE-algebra, called an BE-relation is introduced and some fundamental properties to BE-algebras are discussed. Mathematics Subject Classification: 06F35, 03G25, 08A30

We analyze a continuous and discrete symmetries of the maximum lifetime problem in two dimensional sensor networks. We show, how a symmetry of the network and invariance of the problem under a given transformation group G can be utilized to simplify its solution. We prove, that for a G-invariant maximum lifetime problem there exists a G-invariant solution. Constrains which follow from the G-inv...

We construct fundamental domains for arithmetic subgroups of Γ = GL2(Fq [t]). Given ∆ ⊇ Γ(a) we construct a contracted form T of the Bruhat-Tits tree T and a fundamental domain F of ∆ acting on T. We define a lift of F to F ⊂ T called the “bipartite” lift. We show that F is a fundamental domain of ∆ acting on T precisely when F is “∆-compressed.”

The relation between an object and its matter is fundamental to all physical sciences, and represented widely and diversely in scientific ontologies. An under-appreciated aspect of this relation is the emergence of voids at finer levels of physical granularity. In this paper we enhance the constitution relation to account for the presence of finer voids, and show how this helps delineate two fo...

In this paper we study the Casimir force for a piston configuration in R 3 with one dimension being slightly curved and the other two infinite. We work for two different cases with this setup. In the first, the piston is " free to move " along a transverse dimension to the curved one and in the other case the piston " moves " along the curved one. We find that the Casimir force has opposite sig...

Hyperbolic space groups are isometry groups, acting discontinuously on the hyperbolic 3-space with compact fundamental domain. One possibility to classify them is to look for fundamental domains of these groups. Here are considered supergroups for four series of groups with simplicial fundamental domains. Considered simplices, denoted in [9] by T19, T46, T59, belong to family F12, while T31 bel...