Spectral characterization of families of split graphs

An upper bound for the sum of the squares of the entries of the principal eigenvector corresponding to a vertex subset inducing a k-regular subgraph is introduced and applied to the determination of an upper bound on the order of such induced subgraphs. Furthermore, for some connected graphs we establish a lower bound for the sum of squares of the entries of the principal eigenvector corresponding to the vertices of an independent set. Moreover, a spectral characterization of families of split graphs, involving its index and the entries of the principal eigenvector corresponding to the vertices of the maximum independent set is given. In particular, the complete split graph case is highlighted

Approximate solution of the Duffin-Kemmer-Petiau equation for a vector Yukawa potential with arbitrary total angular momenta

The usual approximation scheme is used to study the solution of the Duffin-Kemmer-Petiau (DKP) equation for a vector Yukawa potential in the framework of the parametric Nikiforov-Uvarov (NU) method. The approximate energy eigenvalue equation and the corresponding wave function spinor components are calculated for arbitrary total angular momentum in closed form. Further, the approximate energy equation and wave function spinor components are also given for case. A set of parameter values is used to obtain the numerical values for the energy states with various values of quantum levelsComment: 17 pages; Communications in Theoretical Physics (2012). arXiv admin note: substantial text overlap with arXiv:1205.0938, and with arXiv:quant-ph/0410159 by other author

Logarithmic Corrections to N=2 Black Hole Entropy: An Infrared Window into the Microstates

Logarithmic corrections to the extremal black hole entropy can be computed purely in terms of the low energy data -- the spectrum of massless fields and their interaction. The demand of reproducing these corrections provides a strong constraint on any microscopic theory of quantum gravity that attempts to explain the black hole entropy. Using quantum entropy function formalism we compute logarithmic corrections to the entropy of half BPS black holes in N=2 supersymmetric string theories. Our results allow us to test various proposals for the measure in the OSV formula, and we find agreement with the measure proposed by Denef and Moore if we assume their result to be valid at weak topological string coupling. Our analysis also gives the logarithmic corrections to the entropy of extremal Reissner-Nordstrom black holes in ordinary Einstein-Maxwell theory.Comment: LaTeX file, 66 page

Logarithmic Corrections to Rotating Extremal Black Hole Entropy in Four and Five Dimensions

We compute logarithmic corrections to the entropy of rotating extremal black holes using quantum entropy function i.e. Euclidean quantum gravity approach. Our analysis includes five dimensional supersymmetric BMPV black holes in type IIB string theory on T^5 and K3 x S^1 as well as in the five dimensional CHL models, and also non-supersymmetric extremal Kerr black hole and slowly rotating extremal Kerr-Newmann black holes in four dimensions. For BMPV black holes our results are in perfect agreement with the microscopic results derived from string theory. In particular we reproduce correctly the dependence of the logarithmic corrections on the number of U(1) gauge fields in the theory, and on the angular momentum carried by the black hole in different scaling limits. We also explain the shortcomings of the Cardy limit in explaining the logarithmic corrections in the limit in which the (super)gravity description of these black holes becomes a valid approximation. For non-supersymmetric extremal black holes, e.g. for the extremal Kerr black hole in four dimensions, our result provides a stringent testing ground for any microscopic explanation of the black hole entropy, e.g. Kerr/CFT correspondence.Comment: LaTeX file, 50 pages; v2: added extensive discussion on the relation between boundary condition and choice of ensemble, modified analysis for slowly rotating black holes, all results remain unchanged, typos corrected; v3: minor additions and correction

Twistors and Black Holes

Motivated by black hole physics in N=2, D=4 supergravity, we study the geometry of quaternionic-Kahler manifolds M obtained by the c-map construction from projective special Kahler manifolds M_s. Improving on earlier treatments, we compute the Kahler potentials on the twistor space Z and Swann space S in the complex coordinates adapted to the Heisenberg symmetries. The results bear a simple relation to the Hesse potential \Sigma of the special Kahler manifold M_s, and hence to the Bekenstein-Hawking entropy for BPS black holes. We explicitly construct the ``covariant c-map'' and the ``twistor map'', which relate real coordinates on M x CP^1 (resp. M x R^4/Z_2) to complex coordinates on Z (resp. S). As applications, we solve for the general BPS geodesic motion on M, and provide explicit integral formulae for the quaternionic Penrose transform relating elements of H^1(Z,O(-k)) to massless fields on M annihilated by first or second order differential operators. Finally, we compute the exact radial wave function (in the supergravity approximation) for BPS black holes with fixed electric and magnetic charges.Comment: 47 pages, v2: typos corrected, reference added, v3: minor change

Estabilidad oxidativa de aceites de soja y maíz enriquecidos con extracto hidroalcohólico de Pluchea quitoc

Soybean and corn oils are among the most popular vegetable oils, and are ingredients which are widely used in cooking and in the food industry. These oils contain many unsaturated fatty acids such as oleic, linoleic and linolenic acids, which makes them easily oxidized by oxygen. Extensive efforts are being made to prevent or minimize vegetable oil oxidation through the development of antioxidants. Phenolic antioxidants which are present in some extracts can be used as food additives to prevent lipid oxidation. In this study chromatographic analyses (HPLC and GC) of the Pluchea quitoc hydroalcoholic extract were performed. The content of phenolic compounds by the Folin-Ciocalteau method and the antioxidant properties against radicals 1,1-diphenyl-2-picrylhydrazyl (DPPH) and 2,2′-azino-bis-3-ethylbenzthiazoline-6-sulphonic acid (ABTS) were also evaluated. The effect of samples prepared with soybean and corn oils enriched with Pluchea quitoc hydroalcoholic extract was determined and compared with samples of these oils which were free of antioxidants and with samples containing the synthetic antioxidant BHT. The results showed potential for application of the extract. A high content of phenolic compounds (314 milligrams of gallic acid equivalents (GAE)/g of extract) and good IC50 values were detected for the inhibition of the radicals DPPH and ABTS (13.2 µg·mL-1 and 5.6 µg·mL-1). In the evaluation of the oxidative stability of the oils enriched with this extract, it was found that at 1% concentration it was possible to obtain values of induction period (IP) close to the samples with added BHT.Los aceites de soja y maíz se encuentran entre los aceites vegetales más populares, ingredientes ampliamente utilizados en la cocina y también en la industria alimentaria. Estos aceites contienen muchos ácidos grasos insaturados como los ácidos oleico, linoleico y linolénico que se oxidan fácilmente con el oxígeno. Se están realizando grandes esfuerzos para prevenir o minimizar la oxidación de los aceites vegetales mediante el desarrollo de antioxidantes. Los antioxidantes fenólicos presentes en algunos extractos se pueden utilizar como aditivos alimentarios para prevenir la oxidación de lípidos. En este estudio se realizó la obtención y análisis cromatográficos (HPLC y GC) del extracto hidroalcohólico de Pluchea quitoc. El contenido de compuestos fenólicos se evaluó por el método de Folin-Ciocalteau y las propiedades antioxidantes frente a radicales DPPH y ABTS. Se determinó el efecto de muestras preparadas con aceites de soja y maíz enriquecidas con extracto hidroalcohólico de Pluchea quitoc y se comparó con muestras de estos aceites libres de antioxidantes y con el antioxidante sintético BHT. Los resultados mostraron potencial para la aplicación del extracto. Se detectó un alto contenido de compuestos fenólicos (314 mg GAE) y buenos valores de IC50 para la inhibición de los radicales DPPH y ABTS (13.2 µg·mL-1 y 5.6 µg·mL-1). En la evaluación de la estabilidad oxidativa de los aceites enriquecidos con este extracto, se encontró que para la concentración del 1% es posible obtener valores de período de inducción (IP) cercanos a las muestras adicionadas con BHT

Composition-, temperature- and pressure-induced transitions between high-pressure stabilized perovskite phases of the (1-x)BiFe0.5Sc0.5O3 - xLaFe0.5Sc0.5O3 series

Crystal structures of the high-pressure synthesized perovskite phases of the (1-x)BiFe0.5Sc0.5O3-xLaFe0.5Sc0.5O3 (0 ​= ​x ​≤ ​1) system and their temperature and pressure behaviours were studied using laboratory and synchrotron X-ray diffractions as well as neutron diffraction. At room temperature, the as-prepared phases with x ​≤ ​0.05 have an antipolar structure with the Pnma symmetry and with the √2ap ​× ​4ap ​× ​2√2ap superstructure (where ap is the pseudocubic perovskite unit-cell parameter). An incommensurately modulated phase with the Imma(00γ)s00 superspace group is observed for 0.10 ​= ​x ​≤ ​0.33, while a non-polar Pnma phase (√2ap ​× ​2ap ​× ​√2ap) is stable when x ​≥ ​0.34. The antipolar Pnma phase in the as-prepared samples with composition corresponding to x ​= ​0 transforms into the polar Ima2 one via irreversible annealing-caused transformation accompanied by a formation of a high-temperature intermediate polar R3c polymorph, while the antipolar Pnma phase in samples with x ​= ​0.05 is stable until the decomposition temperature. In the solid solutions with 0.10 ​= ​x ​≤ ​0.33, increasing temperature was found to result in a reversible transformation of the Imma(00γ)s00 phase into a non-polar Pnma one. The transition temperature decreases with increasing x. A hydrostatic pressure of few GPa was also shown to induce a reversible Imma(00γ)s00 → Pnma transformation.publishe

Some general properties of the renormalized stress-energy tensor for static quantum states on (n+1)-dimensional spherically symmetric black holes

We study the renormalized stress-energy tensor (RSET) for static quantum states on (n+1)-dimensional, static, spherically symmetric black holes. By solving the conservation equations, we are able to write the stress-energy tensor in terms of a single unknown function of the radial co-ordinate, plus two arbitrary constants. Conditions for the stress-energy tensor to be regular at event horizons (including the extremal and ``ultra-extremal'' cases) are then derived using generalized Kruskal-like co-ordinates. These results should be useful for future calculations of the RSET for static quantum states on spherically symmetric black hole geometries in any number of space-time dimensions.Comment: 9 pages, no figures, RevTeX4, references added, accepted for publication in General Relativity and Gravitatio

Schwarzschild black hole surrounded by quintessence: Null geodesics

We have studied the null geodesics of the Schwarzschild black hole surrounded by quintessence matter. Quintessence matter is a candidate for dark energy. Here, we have done a detailed analysis of the geodesics and exact solutions are presented in terms of Jacobi-elliptic integrals for all possible energy and angular momentum of the photons. The circular orbits of the photons are studied in detail. As an application of the null geodesics, the angle of deflection of the photons are computed.Comment: 25 pages, 20 figures. typos corrected and some of the notation change

Quantum Attractor Flows

Motivated by the interpretation of the Ooguri-Strominger-Vafa conjecture as a holographic correspondence in the mini-superspace approximation, we study the radial quantization of stationary, spherically symmetric black holes in four dimensions. A key ingredient is the classical equivalence between the radial evolution equation and geodesic motion of a fiducial particle on the moduli space M^*_3 of the three-dimensional theory after reduction along the time direction. In the case of N=2 supergravity, M^*_3 is a para-quaternionic-Kahler manifold; in this case, we show that BPS black holes correspond to a particular class of geodesics which lift holomorphically to the twistor space Z of M^*_3, and identify Z as the BPS phase space. We give a natural quantization of the BPS phase space in terms of the sheaf cohomology of Z, and compute the exact wave function of a BPS black hole with fixed electric and magnetic charges in this framework. We comment on the relation to the topological string amplitude, extensions to N>2 supergravity theories, and applications to automorphic black hole partition functions.Comment: 43 pages, 6 figures; v2: typos and references added; v3: published version, minor change