Reflection matrices for the Uq[sl(r∣2m)(2)]U_{q}[sl(r|2m)^{(2)}] vertex model

The graded reflection equation is investigated for the $U_{q}[sl(r|2m)^{(2)}]$ vertex model. We have found four classes of diagonal solutions and twelve classes of non-diagonal ones. The number of free parameters for some solutions depends on the number of bosonic and fermionic degrees of freedom considered.Comment: 30 page

An exterior for the G\"{o}del spacetime

We match the vacuum, stationary, cylindrically symmetric solution of Einstein's field equations with $\Lambda$, in a form recently given by Santos, as an exterior to an infinite cylinder of dust cut out of a G\"{o}del universe. There are three cases, depending on the radius of the cylinder. Closed timelike curves are present in the exteriors of some of the solutions. There is a considerable similarity between the spacetimes investigated here and those of van Stockum referring to an infinite cylinder of rotating dust matched to vacuum, with $\Lambda=0$.Comment: 11 pages, LaTeX 2.09, no figures. Submitted to Classical and Quantum Gravit

G\"{o}del-type universes in f(R) gravity

The $f(R)$ gravity theories provide an alternative way to explain the current cosmic acceleration without a dark energy matter component. If gravity is governed by a $f(R)$ theory a number of issues should be reexamined in this framework, including the violation of causality problem on nonlocal scale. We examine the question as to whether the $f(R)$ gravity theories permit space-times in which the causality is violated. We show that the field equations of these $f(R)$ gravity theories do not exclude solutions with breakdown of causality for a physically well-motivated perfect-fluid matter content. We demonstrate that every perfect-fluid G\"{o}del-type solution of a generic $f(R)$ gravity satisfying the condition $df/dR > 0$ is necessarily isometric to the G\"odel geometry, and therefore presents violation of causality. This result extends a theorem on G\"{o}del-type models, which has been established in the context of general relativity. We also derive an expression for the critical radius $r_c$ (beyond which the causality is violated) for an arbitrary $f(R)$ theory, making apparent that the violation of causality depends on both the $f(R)$ gravity theory and the matter content. As an illustration, we concretely take a recent $f(R)$ gravity theory that is free from singularities of the Ricci scalar and is cosmologically viable, and show that this theory accommodates noncausal as well as causal G\"odel-type solutions.Comment: 7 pages, V3: Version to appear in Phys. Rev. D (2009), typos corrected, the generality of our main results is emphasized. The illustrative character of a particular theory is also made explici

Combining pot, atom and step economy (PASE) in organic synthesis. Synthesis of tetrahydropyran-4-ones

The combination of pot, atom and step economy (PASE) in the synthesis of organic molecules of medium complexity can lead to a significant 'greening' of a synthetic route. This is demonstrated by the synthesis of highly substituted tetrahydropyran-4-ones and is quantified by a series of recognised metrics, which demonstrate the efficiency of combining PASE over conventional synthetic strategies

Area Quantization in Quasi-Extreme Black Holes

We consider quasi-extreme Kerr and quasi-extreme Schwarzschild-de Sitter black holes. From the known analytical expressions obtained for their quasi-normal modes frequencies, we suggest an area quantization prescription for those objects.Comment: Final version to appear in Mod. Phys. Lett.

Knizhnik-Zamolodchikov-Bernard equations connected with the eight-vertex model

Using quasiclassical limit of Baxter's 8 - vertex R - matrix, an elliptic generalization of the Knizhnik-Zamolodchikov equation is constructed. Via Off-Shell Bethe ansatz an integrable representation for this equation is obtained. It is shown that there exists a gauge transformation connecting this equation with Knizhnik-Zamolodchikov-Bernard equation for SU(2)-WZNW model on torus.Comment: 20 pages latex, macro: tcilate

Interface States in Carbon Nanotube Junctions: Rolling up graphene

We study the origin of interface states in carbon nanotube intramolecular junctions between achiral tubes. By applying the Born-von Karman boundary condition to an interface between armchair- and zigzag-terminated graphene layers, we are able to explain their number and energies. We show that these interface states, costumarily attributed to the presence of topological defects, are actually related to zigzag edge states, as those of graphene zigzag nanoribbons. Spatial localization of interface states is seen to vary greatly, and may extend appreciably into either side of the junction. Our results give an alternative explanation to the unusual decay length measured for interface states of semiconductor nanotube junctions, and could be further tested by local probe spectroscopies