Power-law solutions for f (G) gravity coupled with perfect fluid have been studied for spatially flat universe. It is shown that despite the matter dominated and accelerating power-law solutions, the power-law solution exists for an special form of f (G) when this universe enters a Phantom phase.

We revisit the classical and quantum cosmology of a universe in which a self interacting scalar field is coupled to gravity with a flat FRW type metric undergoing continuous signature transition. We arrange for quantum cosmologically allowed discontinuity in the classical solutions at the signature changing hypersurface, provided these solutions be dual in some respects. This may be of some importance in the study of early universe within the signature changing scenarios.

In this paper, molecular dynamics simulations were performed to study desalination performance of armchair carbon nanotubes (CNTs). The studied systems included the (7, 7) and (8, 8) CNTs embedded in a silicon nitride membrane immersed in an aqueous ionic solution. For desalinating water, an external electrical field was applied to the systems along the axis of nanotubes. The results indicated that the (7, 7) and (8, 8) CNTs were exclusively selective to ions. The (7, 7) CNT selectively separated sodium ions from aqueous solution. In contrast, the (8, 8) CNT selectively separated chlorine ions. CNTs ion selectivity is justified by calculating the potential of mean force for each ion in the related system. Also, the results were confirmed using the following simulated properties: ion current, retention time of ions, transport rate for water molecules, the average density of water inside the CNTs, and the radial distribution functions of ions-water. Based on the findings of this study, the studied systems can be recommended as a model for the desalination of water.

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We study the quantum cosmology of an empty (4+1)-dimensional Kaluza-Klein cosmology with a negative cosmological constant and a FRW type metric with two scale factors, one for 4-D universe and the other for one compact extra dimension. By assuming the noncommutativity in the corresponding mini-superspace we suggest a solution for the Hierarchy problem, at the level of Wheeler-DeWitt equation. PACS: 98.80.Qc