Density-metric unimodular gravity: vacuum maximal symmetry

We have investigated the vacuum maximally symmetric solutions of recently proposed density-metric unimodular gravity theory,the results are widely different from inflationary senario.The exponential dependence on time in deSitter space is substiuted by a power law. Open space-times with non-zero cosmological constant are excluded in this theoryComment: 15 pages, no figures,stability section omitte

On certain classes of solutions of the Weierstrass-Enneper system inducing constant mean curvature surfaces

Analysis of the generalized Weierstrass-Enneper system includes the estimation of the degree of indeterminancy of the general analytic solution and the discussion of the boundary value problem. Several different procedures for constructing certain classes of solutions to this system, including potential, harmonic and separable types of solutions, are proposed. A technique for reduction of the Weierstrass-Enneper system to decoupled linear equations, by subjecting it to certain differential constraints, is presented as well. New elementary and doubly periodic solutions are found, among them kinks, bumps and multi-soliton solutions

Kerr/CFT Correspondence in the Low Energy Limit of Heterotic String Theory

We investigate the recently proposed Kerr/CFT correspondence in the context of heterotic string theory. The Kerr/CFT correspondence states that the near-horizon states of an extremal four (or higher) dimensional black hole could be identified with a certain chiral conformal field theory under the conjecture that the central charges from the non-gravitational fields vanish. The corresponding Virasoro algebra is generated by a class of diffeomorphisms which preserves the appropriate boundary conditions on the near-horizon geometry. To understand the chiral conformal field theory, we consider the class of extremal Kerr-Sen black hole (that contains three non-gravitational fields) as a class of solutions in the low energy limit (effective field theory) of heterotic string theory. We derive the expression of the conserved charges for the extremal Kerr-Sen solutions that contain dilaton, abelian gauge filed and antisymmetric tensor filed. We confirm and extend the validity of the conjecture (that the central charges from the non-gravitational fields vanish) for theories including antisymmetric tensor fields. We combine the calculated central charges with the expected form of the temperature using the Cardy formula to obtain the entropy of the extremal black hole microscopically; in agreement with the macroscopic Bekenstein-Hawking entropy of the extremal black hole.Comment: 14 pages, a few sentences added to the introduction, version to appear in JHE

The use of an e-learning constructivist solution in workplace learning

We wished to investigate whether an e-learning approach which uses constructivist principles can be successfully applied to train employees in a highly specialised skill thought to require expert individuals and extensive prolonged training. The approach involved the development of an e-learning package which included simulations and interactivity, then experimental testing in a case study workplace environment with the collection of both quantitative and qualitative data to assess the effectiveness of the package. Our study shows that this e-learning strategy improved the skills of the inexperienced operator significantly. We therefore propose that such programmes could be used as a work based training aid and used as a model system for the training of employees in complex skilled tasks in the workplace. This research demonstrates that the e-learning can be applied outside the traditional learning environment to train unskilled employees to undertake complex practical tasks which traditionally would involve prohibitively expensive instruction. This work also illustrates that simulations and interactivity are powerful tools in the design of successful e-learning packages in preparing learners for real world practical situations. Finally this study shows that workplace learners can be better served by elearning environments rather than conventional training as they allow asynchronous learning and private study which are valued by employees who have other demands on their time and are more comfortable receiving tuition privately Relevance to industry: E-learning using constructivist principles, and incorporating simulations and interactivity can be used successfully in the training of highly specialised and skilled tasks required in the modern workplace

4d-Flat Compactifications With Brane Vorticities

We present solutions in six-dimensional gravity coupled to a sigma model, in the presence of three-brane sources. The space transverse to the branes is a compact non-singular manifold. The example of O(3) sigma model in the presence of two three-branes is worked out in detail. We show that the four-dimensional flatness is obtained with a single condition involving the brane tensions, which are in general different and may be both positive, and another characteristic of the branes, vorticity. We speculate that the adjustment of the effective four-dimensional cosmological constant may occur through the exchange of vorticity between the branes. We then give exact instanton type solutions for sigma models targeted on a general K\"ahler manifold, and elaborate in this framework on multi-instantons of the O(3) sigma model. The latter have branes, possibly with vorticities, at the instanton positions, thus generalizing our two-brane solution.Comment: 8 pages. New references added and minor typos are correcte

Decay of flux vacua to nothing

We construct instanton solutions describing the decay of flux compactifications of a $6d$ gauge theory by generalizing the Kaluza-Klein bubble of nothing. The surface of the bubble is described by a smooth magnetically charged solitonic brane whose asymptotic flux is precisely that responsible for stabilizing the 4d compactification. We describe several instances of bubble geometries for the various vacua occurring in a $6d$ Einstein-Maxwell theory namely, AdS_4 x S^2, R^{1,3} x S^2, and dS_4 x S^2. Unlike conventional solutions, the bubbles of nothing introduced here occur where a {\em two}-sphere compactification manifold homogeneously degenerates.Comment: 31 pages, 15 figure

Adiabatic following criterion, estimation of the nonadiabatic excitation fraction and quantum jumps

An accurate theory describing adiabatic following of the dark, nonabsorbing state in the three-level system is developed. An analytical solution for the wave function of the particle experiencing Raman excitation is found as an expansion in terms of the time varying nonadiabatic perturbation parameter. The solution can be presented as a sum of adiabatic and nonadiabatic parts. Both are estimated quantitatively. It is shown that the limiting value to which the amplitude of the nonadiabatic part tends is equal to the Fourier component of the nonadiabatic perturbation parameter taken at the Rabi frequency of the Raman excitation. The time scale of the variation of both parts is found. While the adiabatic part of the solution varies slowly and follows the change of the nonadiabatic perturbation parameter, the nonadiabatic part appears almost instantly, revealing a jumpwise transition between the dark and bright states. This jump happens when the nonadiabatic perturbation parameter takes its maximum value.Comment: 33 pages, 8 figures, submitted to PRA on 28 Oct. 200

Central Charges in Extreme Black Hole/CFT Correspondence

The Kerr/CFT correspondence has been recently broadened to the general extremal black holes under the assumption that the central charges from the non-gravitational fields vanish. To confirm this proposal, we derive the expression of the conserved charges in the Einstein-Maxwell-scalar theory with topological terms in four and five dimensions and check that the above assumption was correct. Combining the computed central charge with the expected form of the temperature, the Bekenstein-Hawking entropy of the general extremal black holes in four and five dimensions can be reproduced by using the Cardy formula.Comment: 20 pages, v2:references added, published in JHE

The languages of peace during the French religious wars

The desirability of peace was a common topos in sixteenth-century political rhetoric, and the duty of the king to uphold the peace for the benefit of his subjects was also a long-established tradition. However, the peculiar circumstances of the French religious wars, and the preferred royal policy of pacification, galvanized impassioned debate among both those who supported and those who opposed confessional coexistence. This article looks at the diverse ways in which peace was viewed during the religious wars through an exploration of language and context. It draws not only on the pronouncements of the crown and its officials, and of poets and jurists, but also on those of local communities and confessional groups. Opinion was not just divided along religious lines; political imperatives, philosophical positions and local conditions all came into play in the arguments deployed. The variegated languages of peace provide a social and cultural dimension for the contested nature of sixteenth-century French politics. However, they could not restore harmony to a war-torn and divided kingdom