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

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

Black-hole binaries: life begins at 40 keV

In the study of black-hole transients, an important problem that still needs to be answered is how the high-energy part of the spectrum evolves from the low-hard to the high-soft state, given that they have very different properties. Recent results obtained with RXTE and INTEGRAL have given inconsistent results. With RXTE, we have found that the high-energy cutoff in GX 339-4 during the transition first decreases (during the low-hard state), then increases again across the Hard-Intermediate state, to become unmeasurable in the soft states (possibly because of statistical limitations). We show Simbol-X will be able to determine the spectral shape with superb accuracy. As the high-energy part of the spectrum is relatively less known than the one below 20 keV, Simbol-X will provide important results that will help out understanding of the extreme physical conditions in the vicinity of a stellar-mass black hole.Comment: Proc. "Simbol-X: Focusing on the Hard X-Ray Universe", Paris, 2-5 Dec. 2008, ed. J. Rodriguez and P. Ferrando; 4 pages, 3 figure

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

Automatic classification system of Raman spectra applied to pigments analysis

Raman spectroscopy is one of the few non-destructive techniques capable of identifying pigments in art works. Raman spectra contain powerful information that can be used to identify unknown compounds and their chemical structures. However, the analysis of spectral data comes with some difficulties, and therefore the spectral interpretation is not straightforward. Sometimes, there are very little differences in the spectral data concerning to specific identification objectives, for instance, in polymorphic discrimination or in the discrimination of natural and synthetic forms of certain pigments. Moreover, this discrimination is often performed manually so that the process can be repetitive, subjective and particularly time-consuming. The result is an increasing motivation to automate the identification process involved in the classification of pigments in paint. In this paper, we propose a system to automatically classify the spectral data into specific and well-known classes, i.e. reference classes. The proposal is based on a combination of chemometric techniques, which provides a powerful way to achieve spectral separability so that it is possible to discriminate between very similar spectra in an automatic way. In this regard, a decision-making algorithm was specifically developed to select the corresponding reference class with no user input, which was successfully validated using simulated spectra. The implemented methodology was used to classify Raman spectra of pigments commonly present in artist's paints in experimental cases, providing reliable and consistent results. Therefore, the presented system can play a good auxiliary role in the analysts' endpoint classification.Peer ReviewedPostprint (author's final draft