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...

In this research paper, an improved Chebyshev-Gauss-Lobatto pseudospectral approximation of nonlinear Burger-Huxley and Fitzhugh- Nagumo equations have been presented. The method employs chebyshev Gauss-Labatto points in time and space to obtain spectral accuracy. The mapping has introduced and transformed the initial-boundary value non-homogeneous problem to homogeneous problem. The main probl...

A (generalized) weak solenoid is an inverse limit space over manifolds with bonding maps that are covering maps. If the covering maps are regular, then we call the inverse limit space a strong solenoid. By a theorem of M.C. McCord, strong solenoids are homogeneous. We show conversely that homogeneous weak solenoids are topologically equivalent to strong solenoids. We also give an example of a w...

It tries to distribute the curvature evenly around a manifold. In doing so, the Ricci flow preserves the symmetries of the space, and, in the limit, can increase the symmetries of the space. It has been extensively studied in [Ham82], [Pera], [Perc], and [Perb] and it was applied most famously to solve the Poincare conjecture. In general, the Ricci flow is a PDE, however on a homogeneous space ...

The following theorem is proved. THEOREM. Let X be a homogeneous continuum such that Hl(X) ^ 0. Ij'$/ is the collection of maximal terminal proper subcontinua of X, then (1) The collection ff is a monotone, continuous, terminal decomposition ofX, (2) The nondegenerate elements of%? are mutually homeomorphic, indecomposable, cell-like, terminal, homogeneous continua of the same dimension as X, (...

We determine all homogeneous pseudo-embeddings of the affine space AG(n, 4) and the projective space PG(n, 4). We give a classification of all pseudo-hyperplanes of AG(n, 4). We also prove that the two homogeneous pseudo-embeddings of the generalized quadrangle Q(4, 3) are induced by the two homogeneous pseudo-embeddings of AG(4, 4) into which Q(4, 3) is fully embeddable.

The consistency of the constraint with the evolution equations for spatially inhomogeneous and irrotational silent (SIIS) models of Petrov type I, demands that the former are preserved along the timelike congruence represented by the velocity of the dust fluid, leading to new non-trivial constraints. This fact has been used to conjecture that the resulting models correspond to the spatially hom...

• In Section 4, we define locally homogeneous singularities. A space with locally homogeneous singularities (SLHS) is an analytic space X such that for all x ∈ X , the x-completion of a local ring OxX is isomorphic to an x-completion of associated graded ring (OxX)gr. We show that a complex variety is SLHS if and only if the underlying real analytic variety is SLHS. This allows us to define inv...