On the classification of type D spacetimes

We give a classification of the type D spacetimes based on the invariant differential properties of the Weyl principal structure. Our classification is established using tensorial invariants of the Weyl tensor and, consequently, besides its intrinsic nature, it is valid for the whole set of the type D metrics and it applies on both, vacuum and non-vacuum solutions. We consider the Cotton-zero type D metrics and we study the classes that are compatible with this condition. The subfamily of spacetimes with constant argument of the Weyl eigenvalue is analyzed in more detail by offering a canonical expression for the metric tensor and by giving a generalization of some results about the non-existence of purely magnetic solutions. The usefulness of these results is illustrated in characterizing and classifying a family of Einstein-Maxwell solutions. Our approach permits us to give intrinsic and explicit conditions that label every metric, obtaining in this way an operational algorithm to detect them. In particular a characterization of the Reissner-Nordstr\"{o}m metric is accomplished.Comment: 29 pages, 0 figure

On the separable quotient problem for Banach spaces

While the classic separable quotient problem remains open, we survey general results related to this problem and examine the existence of a particular infinitedimensional separable quotient in some Banach spaces of vector-valued functions, linear operators and vector measures. Most of the results presented are consequence of known facts, some of them relative to the presence of complemented copies of the classic sequence spaces c_0 and l_p, for 1 <= p <= \infty. Also recent results of Argyros - Dodos - Kanellopoulos, and Sliwa are provided. This makes our presentation supplementary to a previous survey (1997) due to Mujica

Vacuum type I spacetimes and aligned Papapetrou fields: symmetries

We analyze type I vacuum solutions admitting an isometry whose Killing 2--form is aligned with a principal bivector of the Weyl tensor, and we show that these solutions belong to a family of type I metrics which admit a group $G_3$ of isometries. We give a classification of this family and we study the Bianchi type for each class. The classes compatible with an aligned Killing 2--form are also determined. The Szekeres-Brans theorem is extended to non vacuum spacetimes with vanishing Cotton tensor.Comment: 19 pages; a reference adde

Angular Pseudomomentum Theory for the Generalized Nonlinear Schr\"{o}dinger Equation in Discrete Rotational Symmetry Media

We develop a complete mathematical theory for the symmetrical solutions of the generalized nonlinear Schr\"odinger equation based on the new concept of angular pseudomomentum. We consider the symmetric solitons of a generalized nonlinear Schr\"odinger equation with a nonlinearity depending on the modulus of the field. We provide a rigorous proof of a set of mathematical results justifying that these solitons can be classified according to the irreducible representations of a discrete group. Then we extend this theory to non-stationary solutions and study the relationship between angular momentum and pseudomomentum. We illustrate these theoretical results with numerical examples. Finally, we explore the possibilities of the generalization of the previous framework to the quantum limit.Comment: 18 pages; submitted to Physica

A topological charge selection rule for phase singularities

We present an study of the dynamics and decay pattern of phase singularities due to the action of a system with a discrete rotational symmetry of finite order. A topological charge conservation rule is identified. The role played by the underlying symmetry is emphasized. An effective model describing the short range dynamics of the vortex clusters has been designed. A method to engineer any desired configuration of clusters of phase singularities is proposed. Its flexibility to create and control clusters of vortices is discussed.Comment: 4 pages, 3 figure

The eclipsing bursting X-ray binary EXO 0748-676 revisited by XMM-Newton

The bright eclipsing and bursting low-mass X-ray binary EXO 0748-676 has been observed at several occasions by XMM-Newton during the initial calibration and performance verification (CAL/PV) phase. We present here the results obtained from observations with the EPIC cameras. Apart from several type-I X-ray bursts, the source shows a high degree of variability with the presence of soft flares. The wide energy coverage and high sensitivity of XMM-Newton allows for the first time a detailed description of the spectral variability. The source is found to be the superposition of a central (~2 10^8 cm) Comptonized emission, most probably a corona surrounding the inner edge of an accretion disk, associated with a more extended (~3 10^10 cm) thermal halo at a typical temperature of ~0.6 keV with an indication of non-solar abundances. Most of the variations of the source can be accounted for by a variable absorption affecting only the central comptonized component and reaching up to NH ~1.3 10^23 cm^{-2}. The characteristics of the surrounding halo are found compatible with an irradiated atmosphere of an accretion disc which intercepts the central emission due to the system high inclination.Comment: 6 pages, 4 figures, accepted for publication in A&A Letters, XMM special issu

Positioning systems in Minkowski space-time: from emission to inertial coordinates

The coordinate transformation between emission coordinates and inertial coordinates in Minkowski space-time is obtained for arbitrary configurations of the emitters. It appears that a positioning system always generates two different coordinate domains, namely, the front and the back emission coordinate domains. For both domains, the corresponding covariant expression of the transformation is explicitly given in terms of the emitter world-lines. This task requires the notion of orientation of an emitter configuration. The orientation is shown to be computable from the emission coordinates for the users of a `central' region of the front emission coordinate domain. Other space-time regions associated with the emission coordinates are also outlined.Comment: 20 pages; 1 figur

Solitons in combined linear and nonlinear lattice potentials

We study ordinary solitons and gap solitons (GSs) in the effectively one-dimensional Gross-Pitaevskii equation, with a combination of linear and nonlinear lattice potentials. The main points of the analysis are effects of the (in)commensurability between the lattices, the development of analytical methods, viz., the variational approximation (VA) for narrow ordinary solitons, and various forms of the averaging method for broad solitons of both types, and also the study of mobility of the solitons. Under the direct commensurability (equal periods of the lattices, the family of ordinary solitons is similar to its counterpart in the free space. The situation is different in the case of the subharmonic commensurability, with L_{lin}=(1/2)L_{nonlin}, or incommensurability. In those cases, there is an existence threshold for the solitons, and the scaling relation between their amplitude and width is different from that in the free space. GS families demonstrate a bistability, unless the direct commensurability takes place. Specific scaling relations are found for them too. Ordinary solitons can be readily set in motion by kicking. GSs are mobile too, featuring inelastic collisions. The analytical approximations are shown to be quite accurate, predicting correct scaling relations for the soliton families in different cases. The stability of the ordinary solitons is fully determined by the VK (Vakhitov-Kolokolov) criterion, while the stability of GS families follows an inverted ("anti-VK") criterion, which is explained by means of the averaging approximation.Comment: 9 pages, 6 figure

Nikodym boundedness property for webs in sigma-algebras

[EN] A subset B of an algebra A of subsets of Omega is said to have property N if a B-pointwise bounded subset M of ba(A ) is uniformly bounded on A , where ba(A ) is the Banach space of the real (or complex) finitely additive measures of bounded variation defined on A with the norm variation. Moreover B is said to have property sN if for each increasing countable covering (B_m)_m of B there exists B_n which has property N and B is said to have property wN if given the increasing countable coverings (B_m_1 )_m_1 of B and (B_m_1m_2...m_pm_(p+1) )_m_(p+1) of B_m_1m_2...m_p , for each p,m_i &#8712; N, 1<= i <= p + 1, there exists a sequence (n_i )_i such that each B_n_1n_2...n_r , r &#8712; N, has property N. For a &#963;-algebra S of subsets of Omega it has been proved that S has property N (Nikodym Grothendieck), property sN (Valdivia) and property w(sN) (Kakol López-Pellicer). We give a proof of property wN for a &#963;-algebra S which is independent of properties N and sN. This result and the equivalence of properties wN and w2N enable us to give some applications to localization of bounded additive vector measures.This work was supported for the second named author by the Spanish Ministerio de Economía y Competitividad under Grant MTM2014-58159-PLópez Alfonso, S.; Mas Marí, J.; Moll López, SE. (2016). Nikodym boundedness property for webs in sigma-algebras. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 110(2):711-722. https://doi.org/10.1007/s13398-015-0260-4S7117221102Diestel, J.: Sequences and Series in Banach Spaces. Springer, New York (1984)Diestel, J., Uhl, J.J.: Vector Measures. Mathematical Surveys and Monographs, vol. 15. American Mathematical Society, Providence (1977)Dieudonné, J.: Sur la convergence de suites de measures de Radon. An. Acad. Brasi. Ciên. 23, 277–282 (1951)Ferrando, J.C.: Strong barrelledness properties in certain l_{0}^{\infty }({{\fancyscript {A}}} ) l 0 ∞ ( A ) spaces. J. Math. Anal. Appl. 190, 194–202 (1995)Ferrando, J.C., López-Pellicer, M.: Strong barrelledness properties in $$l_{0}^{\infty }(X,{\cal A})$$ l 0 ∞ ( X , A ) and bounded finite additive measures. Math. Ann. 287, 727–736 (1990)Kakol, J., López-Pellicer, M.: On Valdivia strong version of Nikodym boundedness property, preprintKöthe, G.: Topological Vector Spaces I and II. Springer, Berlin (1979)López-Pellicer, M.: Webs and bounded finitely additive measures. J. Math. Anal. Appl. 210, 257–267 (1997)Nikodym, O.M.: Sur les familles bornées de fonctions parfaitement additives d’ensembles abstrait. Monatsh. Math. U. Phys. 40, 418–426 (1933)Schachermayer, W.: On some classical measure-theoretic theorems for non-sigma-complete Boolean algebras. Dissertationes Math. (Rozprawy Mat.) 214, 33 pp., 1982Valdivia, M.: On the closed graph theorem. Collect. Math. 22, 51–72 (1971)Valdivia, M.: On certain barrelled normed spaces. Ann. Inst. Fourier (Grenoble) 29, 39–56 (1979)Valdivia, M.: On Nikodym boundedness property, RACSAM Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 107, 355–372, 201