It is proved that a compact Kähler manifold whose Ricci tensor has two distinct constant non-negative eigenvalues is locally the product of two Kähler-Einstein manifolds. A stronger result is established for the case of Kähler surfaces. Irreducible Kähler manifolds with two distinct constant eigenvalues of the Ricci tensor are shown to exist in various situations: there are homogeneous examples...

Data Warehouses facilitate multi-dimensional analysis of data from various data sources. While the original data sources are often heterogeneous, current modeling and implementation techniques discard and, thus, cannot exploit these heterogeneities. In this paper we introduce Hetero-Homogeneous Hierarchies to model dimension hierarchies and cubes with inherent heterogeneities. Hetero-homogeneou...

It is shown that for every triple of integers (α, β, γ) such that α ≥ 1, β ≥ 1, and γ ≥ 2, there is a homogeneous, non-bihomogeneous continuum whose every point has a neighborhood homeomorphic the Cartesian product of Menger compacta μ ×μ × μ . In particular, there is a homogeneous, non-bihomogeneous, Peano continuum of covering dimension four.

The goal of this paper is to develop a coherent theory for inhomogeneous Diophantine approximation on curves in R akin to the well established homogeneous theory. More specifically, the measure theoretic results obtained generalize the fundamental homogeneous theorems of R.C. Baker (1978), Dodson, Dickinson (2000) and Beresnevich, Bernik, Kleinbock, Margulis (2002). In the case of planar curves...

In this paper the propagation of harmonic plane waves in a homogeneous anisotropic magneto-piezothermoelastic diffusive body with fractional order derivative is studied. The governing equations for a homogeneous transversely isotropic body in the context of the theory of thermoelasticity with diffusion given by Sherief et al. [1] are considered as a special case. It is found that three types of...

In this work we study the Hausdorff dimension of measures whose weight distribution satisfies a markov non-homogeneous property. In particular, we prove that the Hausdorff dimensions of this kind of measures coincide with their lower Rényi dimensions (entropy). Moreover, we show that the Tricot dimensions (packing dimension) equal upper Rényi dimensions. As an application we get a continuity pr...

Assume that M is close three dimensional manifold. We prove that M \ {p} is a complete homogeneous manifold. As a corollary, we give a new proof on the classical Poincaré’s conjecture. Homogénéité variété de dimension trois Résumé. Soit M est une variété de dimension 3, conexe, fermée. Alors, M \{p} est complet Homogénéité variété. Nous présentons une neuve preuve du la Conjecture sur une varié...