In our preceding paper we have introduced the notion of an s-homogeneous triple. this use technique to study connected algebras with two relations. For such algebras, describe all possible pairs (A,M), where A is s-Veronese ring and M (s,1)-Veronese bimodule dual algebra. each a pair classify corresponding or give necessary sufficient conditions for algebra under consideration correspond given ...

In this paper we extract the geometric characteristics from an antipodally symmetric spherical function (ASSF), which can be described equivalently in the spherical harmonic (SH) basis, in the symmetric tensor (ST) basis constrained to the sphere, and in the homogeneous polynomial (HP) basis constrained to the sphere. All three bases span the same vector space and are bijective when the rank of...

We show that in tilting perfect fluid cosmological models with an ultra-radiative equation of state, generically the tilt becomes extreme at late times and, as the tilt instability sets in, observers moving with the tilting fluid will experience singular behaviour in which infinite expansion is reached within a finite proper time, similar to that of phantom cosmology (but without the need for e...

what we mean by alliteration of homogeneous words is that such alliteration is based on two or more lexical basis that is conspicuously coordinative and homogeneous with each other. they are homogeneous in that their form, structure, and tone, are similar. we can name two homogeneous words, two bases of homonym. it is evident that such words, though homogeneous from one hand, should necessarily...

Countable homogeneous graphs have been classified by Alistair Lachlan and Robert Woodrow [5,11]. There is a countable bipartite graph called the universal 'homogeneous' bipartite graph. However, this graph does not occur in Lachlan and Woodrow's list, because it is not homogeneous as a graph but only as a graph with a fixed bipartition (Cameron [1]). In this paper, I describe a graph which is a...