The quantum chiral Minkowski and conformal superspaces

We give a quantum deformation of the chiral super Minkowski space in four dimensions as the big cell inside a quantum super Grassmannian. The quantization is performed in such way that the actions of the Poincar\'e and conformal quantum supergroups on the quantum Minkowski and quantum conformal superspaces are presented.Comment: 54 page

Quadratic deformation of Minkowski space

We present a deformation of the Minkowski space as embedded into the conformal space (in the formalism of twistors) based in the quantum versions of the corresponding kinematic groups. We compute explicitly the star product, whose Poisson bracket is quadratic. We show that the star product although defined on the polynomials can be extended differentiably. Finally we compute the Eucliden and Minkowskian real forms of the deformation.Comment: Presented at XVII European Workshop on String Theory 2011. Padova (Italy) September 05-09; Fortschr. Phys. 1-7 (2012

Remark on charge conjugation in the non relativistic limit

We study the non relativistic limit of the charge conjugation operation $\cal C$ in the context of the Dirac equation coupled to an electromagnetic field. The limit is well defined and, as in the relativistic case, $\cal C$, $\cal P$ (parity) and $\cal T$ (time reversal) are the generators of a matrix group isomorphic to a semidirect sum of the dihedral group of eight elements and $\Z_2$. The existence of the limit is supported by an argument based in quantum field theory. Also, and most important, the limit exists in the context of galilean relativity. Finally, if one complexifies the Lorentz group and therefore the galilean spacetime $x_\mu$, then the explicit form of the matrix for $\cal C$ allows to interpret it, in this context, as the complex conjugation of the spatial coordinates: $\vec{x} \to \vec{x}^*$. This result is natural in a fiber bundle description.Comment: 8 page

Variational collocation on finite intervals

In this paper we study a new family of sinc--like functions, defined on an interval of finite width. These functions, which we call ``little sinc'', are orthogonal and share many of the properties of the sinc functions. We show that the little sinc functions supplemented with a variational approach enable one to obtain accurate results for a variety of problems. We apply them to the interpolation of functions on finite domain and to the solution of the Schr\"odinger equation, and compare the performance of present approach with others.Comment: 12 pages, 8 figures, 1 tabl

On the Quantum-like Contextuality of Ambiguous Phrases

Language is contextual as meanings of words are dependent on their contexts. Contextuality is, concomitantly, a well-defined concept in quantum mechanics where it is considered a major resource for quantum computations. We investigate whether natural language exhibits any of the quantum mechanics' contextual features. We show that meaning combinations in ambiguous phrases can be modelled in the sheaf-theoretic framework for quantum contextuality, where they can become possibilistically contextual. Using the framework of Contextuality-by-Default (CbD), we explore the probabilistic variants of these and show that CbD-contextuality is also possible

Isotropization of Bianchi type models and a new FRW solution in Brans-Dicke theory

Using scaled variables we are able to integrate an equation valid for isotropic and anisotropic Bianchi type I, V, IX models in Brans-Dicke (BD) theory. We analyze known and new solutions for these models in relation with the possibility that anisotropic models asymptotically isotropize, and/or possess inflationary properties. In particular, a new solution of curve ($k\neq0$) Friedmann-Robertson-Walker (FRW) cosmologies in Brans-Dicke theory is analyzed.Comment: 15 pages, 4 postscript figures, to appear in Gen. Rel. Grav., special issue dedicated in honour of Prof. H. Dehne

Quantum twistors

We compute explicitly a star product on the Minkowski space whose Poisson bracket is quadratic. This star product corresponds to a deformation of the conformal spacetime, whose big cell is the Minkowski spacetime. The description of Minkowski space is made in the twistor formalism and the quantization follows by substituting the classical conformal group by a quantum group.Comment: 47 pages. references added, some parts rewritten. To appear in 'p-adic Numbers, Ultrametric Analysis and Applicarions

Analysing Ambiguous Nouns and Verbs with Quantum Contextuality Tools

Psycholinguistic research uses eye-tracking to show that polysemous words are disambiguated differently from homonymous words, and that ambiguous verbs are disambiguated differently than ambiguous nouns. Research in Compositional Distributional Semantics uses cosine distances to show that verbs are disambiguated more efficiently in the context of their subjects and objects than when on their own. These two frameworks both focus on one ambiguous word at a time and neither considers ambiguous phrases with two (or more) ambiguous words. We borrow methods and measures from Quantum Information Theory, the framework of Contextuality-by-Default and degrees of contextual influences, and work with ambiguous subject-verb and verb-object phrases of English, where both the subject/object and the verb are ambiguous. We show that differences in the processing of ambiguous verbs versus ambiguous nouns, as well as between different levels of ambiguity in homonymous versus polysemous nouns and verbs can be modelled using the averages of the degrees of their contextual influences

A SAURON study of dwarf elliptical galaxies in the Virgo Cluster: kinematics and stellar populations

Dwarf elliptical galaxies (dEs) are the most common galaxy type in nearby galaxy clusters; even so, many of their basic properties have yet to be quantified. Here we present the results of our study of 4 Virgo dwarf ellipticals obtained with the SAURON integral field unit on the William Herschel Telescope (La Palma, Spain). While traditional long-slit observations are likely to miss more complicated kinematic features, with SAURON we are able to study both kinematics and stellar populations in two dimensions, obtaining a much more detailed view of the mass distribution and star formation histories. What is visible even in such a small sample is that dEs are not a uniform group, not only morphologically, but also as far as their kinematic and stellar population properties are concerned. We find the presence of substructures, varying degrees of flattening and of rotation, as well as differences in age and metallicity gradients. We confirm that two of our galaxies are significantly flattened, yet non-rotating objects, which makes them likely triaxial systems. The comparison between the dwarf and the giant groups shows that dEs could be a low-mass extension of Es in the sense that they do seem to follow the same trends with mass. However, dEs as progenitors of Es seem less likely as we have seen that dEs have much lower abundance ratios.Comment: 8 pages, 6 figures; to appear in the proceedings of the JENAM 2010 Symposium on Dwarf Galaxies (Lisbon, September 9-10, 2010); minor edits and references adde

Effect of maternal age on ATP content and distribution of mitochondria in bovine oocytes.

Our objective was to understand how maternal age influences the mitochondrial population and ATP content of in vivo matured bovine oocytes