Factorization method for difference equations of hypergeometric type on nonuniform lattices

We study the factorization of the hypergeometric-type difference equation of Nikiforov and Uvarov on nonuniform lattices. An explicit form of the raising and lowering operators is derived and some relevant examples are given.Comment: 21 page

Relating harmonic and projective descriptions of N=2 nonlinear sigma models

Recent papers have established the relationship between projective superspace and a complexified version of harmonic superspace. We extend this construction to the case of general nonlinear sigma models in both frameworks. Using an analogy with Hamiltonian mechanics, we demonstrate how the Hamiltonian structure of the harmonic action and the symplectic structure of the projective action naturally arise from a single unifying action on a complexified version of harmonic superspace. This links the harmonic and projective descriptions of hyperkahler target spaces. For the two examples of Taub-NUT and Eguchi-Hanson, we show how to derive the projective superspace solutions from the harmonic superspace solutions.Comment: 25 pages; v3: typo fixed in eq (1.36

Solution--Generating Transformations and the String Effective Action

We study exhaustively the solution-generating transformations (dualities) that occur in the context of the low-energy effective action of superstring theory. We first consider target-space duality (``T duality'') transformations in absence of vector fields. We find that for one isometry the full duality group is (SO^{\uparrow}(1,1))^{3} x D_{4}, the discrete part (D_{4}) being non-Abelian. We, then, include non-Abelian Yang--Mills fields and find the corresponding generalization of the T duality transformations. We study the \alpha^{\prime} corrections to these transformations and show that the T duality rules considerably simplify if the gauge group is embedded in the holonomy group. Next, in the case in which there are Abelian vector fields, we consider the duality group that includes the transformation introduced by Sen that rotates among themselves components of the metric, axion and vector field. Finally we list the duality symmetries of the Type II theories with one isometry.Comment: latex file, 42 pages (less if you use optional commands) No changes at all. Resubmited due to mailer problem

Identification of critical variables in conventional transformers in distribution networks

Transformers are essential equipment to the operation of electrical power systems, a failure causes the lack of electricity supply to end-users, affecting the operating indicators of companies in the distribution sector. The investigation presents an identification of the faults in transformers through a fishbone diagram, an evaluation of the variables that cause the identified failure using the cross-impact matrix method and a proposal to improve the performance. The results will enable a plan to be developed for taking action with monitoring plans to avoid faults that could put the electrical asset at risk and achieve a better performance of the distribution network

Extended supersymmetric sigma models in AdS_4 from projective superspace

There exist two superspace approaches to describe N=2 supersymmetric nonlinear sigma models in four-dimensional anti-de Sitter (AdS_4) space: (i) in terms of N=1 AdS chiral superfields, as developed in arXiv:1105.3111 and arXiv:1108.5290; and (ii) in terms of N=2 polar supermultiplets using the AdS projective-superspace techniques developed in arXiv:0807.3368. The virtue of the approach (i) is that it makes manifest the geometric properties of the N=2 supersymmetric sigma-models in AdS_4. The target space must be a non-compact hyperkahler manifold endowed with a Killing vector field which generates an SO(2) group of rotations on the two-sphere of complex structures. The power of the approach (ii) is that it allows us, in principle, to generate hyperkahler metrics as well as to address the problem of deformations of such metrics. Here we show how to relate the formulation (ii) to (i) by integrating out an infinite number of N=1 AdS auxiliary superfields and performing a superfield duality transformation. We also develop a novel description of the most general N=2 supersymmetric nonlinear sigma-model in AdS_4 in terms of chiral superfields on three-dimensional N=2 flat superspace without central charge. This superspace naturally originates from a conformally flat realization for the four-dimensional N=2 AdS superspace that makes use of Poincare coordinates for AdS_4. This novel formulation allows us to uncover several interesting geometric results.Comment: 88 pages; v3: typos corrected, version published in JHE

Degenerate Stars and Gravitational Collapse in AdS/CFT

We construct composite CFT operators from a large number of fermionic primary fields corresponding to states that are holographically dual to a zero temperature Fermi gas in AdS space. We identify a large N regime in which the fermions behave as free particles. In the hydrodynamic limit the Fermi gas forms a degenerate star with a radius determined by the Fermi level, and a mass and angular momentum that exactly matches the boundary calculations. Next we consider an interacting regime, and calculate the effect of the gravitational back-reaction on the radius and the mass of the star using the Tolman-Oppenheimer-Volkoff equations. Ignoring other interactions, we determine the "Chandrasekhar limit" beyond which the degenerate star (presumably) undergoes gravitational collapse towards a black hole. This is interpreted on the boundary as a high density phase transition from a cold baryonic phase to a hot deconfined phase.Comment: 75 page

Opening the black box of mixed-metal TMP metallating reagents : direct cadmation or lithium-cadmium transmetallation?

Designed to remove some of the mystery surrounding mixed-metal TMP (2,2,6,6-tetramethylpiperidide) metallating reagents, this study examines in detail "LiCd(TMP)(3)'' in its own right. Previously established as an excellent "cadmating'' (Cd-H exchange) reagent towards a wide variety of aromatic substrates, "LiCd(TMP)(3)'' has been investigated by H-1, C-13 and Cd-113 NMR studies as well as by DOSY NMR spectroscopy. This evidence puts a question mark against its ate formulation implying it exists in THF solution as two independent homometallic amides. Exploring the reactivity of "LiCd(TMP)(3)'' with anisole as a test substrate, both experimentally by NMR studies and theoretically by DFT studies suggests a two-step lithiation/transmetallation process in which the initially formed ortho-lithiated species undergoes a reaction with Cd(TMP)(2) to form new Cd-C and Li-N bonds. For completeness, the homometallic cadmium component Cd(TMP)(2) has been comprehensively characterised for the first time including a crystal structure determination revealing a near-linear N-Cd-N arrangement

Estudios de campo con ácido fosfonico 2-cloroetilo (Ethephon) en cafetos.

In this paper the compound 2 chloroethlyphosphonic acid (Ethephon) is shown to have dramatic effects on the uniformity of coffee fruit ripening and the increase in size of the coffee fruit. The cultivar Coffea arabica,L. variety Bourbon was used; the ethephon caused excesive fruit and-leaf abscission in the cultivar Coffea robusta L.  in concentrations as low as 100 parts per million. Highest uniformity of fruit ripening (85 - 95%) was achieved with 500 parts per million ethephon in the sun, and 750 parts per million in partial shade. Defoliation and fruit drop were within acceptable limits. An increase in fruit size was noted only when ethephon was applied during phase II of fruit growth, while highest uniformity of ripening was achieved when ethephon was applied early in Phase III of the fruit growth curve. By giving coffee growers a "single harvest" capability and by increasing berry size, ethephon shows great potential in the culture of coffee.En este trabajo se demuestra que el compuesto ácido fosfórico 2-cloroetilo (Ethephon) tiene algunos efectos notables en uniformar la maduración del fruto en los cafetos y en aumentar su tamaño. Se utilizó el Coffea arabica L. cultivar Bourbon. En la especie Coffea robusta L. el ethephon ocasionó una defoliación y caída del fruto excesiva en concentración tan baja como 100 partes por millón. Se obtuvo la mayor uniformidad del fruto (85-95 por ciento) en café al sol con unas 500 partes por millón de ethephon y con 750 partes por millón con café a la sombra. La defoliación y la caída del fruto estuvo dentro de límites aceptables. Se observó un aumento en el tamaño del fruto solamente cuando se aplicó el ethephon en la segunda fase de crecimiento, mientras que la mayor uniformidad en la maduración se consiguió aplicando ethephon temprano en la tercera fase de la curva de crecimiento del fruto. El ethephon demuestra un gran potencial en el cultivo de café permitiendo que los caficultores realicen una sola cosecha y aumentando el tamaño de la uva

Massless D-strings and moduli stabilization in type I cosmology

We consider the cosmological evolution induced by the free energy F of a gas of maximally supersymmetric heterotic strings at finite temperature and weak coupling in dimension D>=4. We show that F, which plays the role of an effective potential, has minima associated to enhanced gauge symmetries, where all internal moduli can be attracted and dynamically stabilized. Using the fact that the heterotic/type I S-duality remains valid at finite temperature and can be applied at each instant of a quasi-static evolution, we find in the dual type I cosmology that all internal NS-NS and RR moduli in the closed string sector and the Wilson lines in the open string sector can be stabilized. For the special case of D=6, the internal volume modulus remains a flat direction, while the dilaton is stabilized. An essential role is played by light D-string modes wrapping the internal manifold and whose contribution to the free energy cannot be omitted, even when the type I string is at weak coupling. As a result, the order of magnitude of the internal radii expectation values on the type I side is (lambda_I alpha')^{1/2}, where lambda_I is the ten-dimensional string coupling. The non-perturbative corrections to the type I free energy can alternatively be described as effects of "thermal E1-instantons", whose worldsheets wrap the compact Euclidean time cycle.Comment: 39 pages, 1 figur