This study is concerned to check the validity and applicability of a five parameter viscoelastic model for harmonic wave propagating in the non-homogeneous viscoelastic rods of varying density. The constitutive relation for five parameter model is first developed and validity of these relations is checked. The non-homogeneous viscoelastic rods are assumed to be initially unstressed and at rest....

We construct a homogeneous subspace of 2ω whose complement is dense in 2ω and rigid. Using the same method, assuming Martin’s Axiom, we also construct a countable dense homogeneous subspace of 2ω whose complement is dense in 2ω and rigid.

It is well known that no infinite homogeneous space is both compact and extremally disconnected. (Since there are infinite compact homogeneous spaces and infinite extremally disconnected homogeneous spaces, it is the combination of compactness and extremal disconnectedness that brings about this result.) The following question then arises naturally: How “close to compact” can a homogeneous, ext...

Consider a closed manifold M immersed in Rm. Suppose that the trivial bundle M × Rm = TM ⊗ νM is equipped with an almost metric connection ∇̃ which almost preserves the decomposition of M × Rm into the tangent and the normal bundle. Assume moreover that the difference Γ = ∂ − ∇̃ with the usual derivative ∂ in Rm is almost ∇̃-parallel. Then M admits an extrinsically homogeneous immersion into Rm.

let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . in this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . as an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via the linear operator .

We prove that a connected, countable dense homogeneous space is n-homogeneous for every n, and strongly 2-homogeneous provided it is locally connected. We also present an example of a connected and countable dense homogeneous space which is not strongly 2-homogeneous. This answers in the negative Problem 136 of Watson in the Open Problems in Topology Book.

This paper is concerned with embeddings of homogeneous spaces into Euclidean spaces. We show that any homogeneous metric space can be embedded into a Hilbert space using an almost bi-Lipschitz mapping (biLipschitz to within logarithmic corrections). The image of this set is no longer homogeneous, but ‘almost homogeneous’. We therefore study the problem of embedding an almost homogeneous subset ...