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.

We have pointed out the possibilities of quantum Hall effect (QHE) and Shubnikov-de Haas (SdH) oscillation in transportation strongly magnetized degenerate quark matter- expected inside highly dense compact star, such as neutron star. The anisotropic pattern electrical conductivity resistivity tensor is explored classical to cases by considering Landau quantization quarks presence a finite magn...

Let g be a semisimple complex Lie algebra and k ⊂ g be any algebraic subalgebra reductive in g. For any simple finite dimensional k-module V , we construct simple (g, k)-modules M with finite dimensional k-isotypic components such that V is a k-submodule of M and the Vogan norm of any simple k-submodule V ′ ⊂ M, V ′ 6≃ V , is greater than the Vogan norm of V . The (g, k)-modules M are subquotie...

A combination of crystallography, biochemistry, and gene expression analysis identifies the coactivator subcomplex Med8C/18/20 as a functionally distinct submodule of the Mediator head module. Med8C forms a conserved alpha-helix that tethers Med18/20 to the Mediator. Deletion of Med8C in vivo results in dissociation of Med18/20 from Mediator and in loss of transcription activity of extracts. De...

The Hardy space on the unit ball in C provides examples of a quasi-free, finite rank Hilbert module which contains a pure submodule isometrically isomorphic to the module itself. For n = 1 the submodule has finite codimension. In this note we show that this phenomenon can only occur for modules over domains in C and for finitely-connected domains only for Hardy-like spaces, the bundle shifts. M...

‎‎‎in this paper‎, ‎the‎ notion of injectivity with respect to order dense embeddings in ‎‎the category of $s$-posets‎, ‎posets with a monotone action of a‎ pomonoid $s$ on them‎, ‎is studied‎. ‎we give a criterion‎, ‎like the baer condition for injectivity of modules‎, ‎or skornjakov criterion for injectivity of $s$-sets‎, ‎for the order dense injectivity‎. ‎also‎, ‎we consider such injectivit...

In this paper, we introduce the concept of a quasi-radical semi prime submodule. Throughout work, assume that is commutative ring with identity and left unitary R- module. A proper submodule called (for short Q-rad-semiprime), if for , ,and then . Where intersection all submodules

a module m is called epi-retractable if every submodule of m is a homomorphic image of m. dually, a module m is called co-epi-retractable if it contains a copy of each of its factor modules. in special case, a ring r is called co-pli (resp. co-pri) if rr (resp. rr) is co-epi-retractable. it is proved that if r is a left principal right duo ring, then every left ideal of r is an epi-retractable ...