On algebraic classification of quasi-exactly solvable matrix models

We suggest a generalization of the Lie algebraic approach for constructing quasi-exactly solvable one-dimensional Schroedinger equations which is due to Shifman and Turbiner in order to include into consideration matrix models. This generalization is based on representations of Lie algebras by first-order matrix differential operators. We have classified inequivalent representations of the Lie algebras of the dimension up to three by first-order matrix differential operators in one variable. Next we describe invariant finite-dimensional subspaces of the representation spaces of the one-, two-dimensional Lie algebras and of the algebra sl(2,R). These results enable constructing multi-parameter families of first- and second-order quasi-exactly solvable models. In particular, we have obtained two classes of quasi-exactly solvable matrix Schroedinger equations.Comment: LaTeX-file, 16 pages, submitted to J.Phys.A: Math.Ge

Sparse Linear Models applied to Power Quality Disturbance Classification

Power quality (PQ) analysis describes the non-pure electric signals that are usually present in electric power systems. The automatic recognition of PQ disturbances can be seen as a pattern recognition problem, in which different types of waveform distortion are differentiated based on their features. Similar to other quasi-stationary signals, PQ disturbances can be decomposed into time-frequency dependent components by using time-frequency or time-scale transforms, also known as dictionaries. These dictionaries are used in the feature extraction step in pattern recognition systems. Short-time Fourier, Wavelets and Stockwell transforms are some of the most common dictionaries used in the PQ community, aiming to achieve a better signal representation. To the best of our knowledge, previous works about PQ disturbance classification have been restricted to the use of one among several available dictionaries. Taking advantage of the theory behind sparse linear models (SLM), we introduce a sparse method for PQ representation, starting from overcomplete dictionaries. In particular, we apply Group Lasso. We employ different types of time-frequency (or time-scale) dictionaries to characterize the PQ disturbances, and evaluate their performance under different pattern recognition algorithms. We show that the SLM reduce the PQ classification complexity promoting sparse basis selection, and improving the classification accuracy

Quasi-exactly Solvable Lie Superalgebras of Differential Operators

In this paper, we study Lie superalgebras of $2\times 2$ matrix-valued first-order differential operators on the complex line. We first completely classify all such superalgebras of finite dimension. Among the finite-dimensional superalgebras whose odd subspace is nontrivial, we find those admitting a finite-dimensional invariant module of smooth vector-valued functions, and classify all the resulting finite-dimensional modules. The latter Lie superalgebras and their modules are the building blocks in the construction of QES quantum mechanical models for spin 1/2 particles in one dimension.Comment: LaTeX2e using the amstex and amssymb packages, 24 page

Late Pleistocene and Holocene palaeoenvironments in and around the middle Caspian basin as reconstructed from a deep-sea core

This article has been made available through Open Access by the Brunel Open Access Publishing Fund.Late Pleistocene and/or Holocene high-resolution palynological studies are available for the south basin of the Caspian Sea (CS), the world's largest lake. However, the north and middle basins have not been the object of high-resolution palynological reconstructions. This new study presents the pollen, spores and dinoflagellate cysts records obtained from a 10m-long sediment core recovered in the middle basin, which currently has brackish waters and is surrounded by arid and semi-arid vegetation.An age-depth model built based on six radiocarbon dates on ostracod shells indicates that the sequence spans the period from 14.47 to 2.43cal.kaBP. The present palaeoenvironmental study focuses on the top 666cm, or from 12.44 to 2.43cal.kaBP.At the vegetation level, the Younger Dryas is characterised by an open landscape dominated by desert vegetation composed by Amaranthaceae with shrubs and salt-tolerant plants. However, although the Early Holocene is also characterised by desert vegetation, it is enriched in various shrubs such as Ephedra and Calligonum, but tree expansion is not important at the Holocene onset. After a major shift at 8.19cal.kaBP, the Middle Holocene displays now both the character of desert and of steppe, although some trees such as Quercus and Corylus slightly spread. The Late Holocene records steppe vegetation as dominant, with more tree diversity.Regarding the lacustrine signal, the dinocyst assemblage record fluctuates between slightly brackish conditions highlighted by Pyxidinopsis psilata and Spiniferites cruciformis, and more brackish ones - similar to the present day - with the dominance of Impagidinium caspienense. The Late Pleistocene is characterised by low salinities, related to the Khvalynian highstand. From 11.56cal.kaBP, slightly more saline waters are reconstructed with an increase of I.caspienense for a period of 1000 years, which could be attributed to the Mangyshlak lowstand. From 10.55cal.kaBP, low salinity conditions return with remains such as Anabaena and Botryococcus abundant until 8.83cal.kaBP, followed by a slow, progressive decrease of P. psilata and S. cruciformis until 4.11cal.kaBP, which is the main assemblage change at lacustrine scale. Since then, higher salinities, similar to the present one, are reconstructed. Finally, Lingulodinium machaerophorum starts its development only at 2.75cal.kaBP, in the Late Holocene.The present research revealed fundamental differences from previously published sea-level curves, in that a 6000yr-long highstand suggested by low salinities is shown between 10.55 and 4.11cal.kaBP. Amongst other arguments, using a comparison to a similar palynological regard but in the south basin, a N-S salinity gradient that is the reverse of the present one across the CS, suggests that the Amu Darya was flowing in the CS. Hence the CS levels during the Late Pleistocene and Holocene were influenced by a combination of precipitation over the high European latitudes and the indirect influence of the Indian summer monsoon over the Pamirs. © 2014.This study has been conducted within the European Contract INCO-Copernicus “Understanding the Caspian Sea erratic fluctuations” n IC15-CT96-0112. This was funded by the Centre National de la Recherche Scientifique within the framework of the INSUDYTEC (DYnamique de la Terre et du Climat) Program (France)

Comment on `Strong Vortex Liquid Correlation' from Multiterminal Measurements on Untwinned YBa2_2Cu3_3O7−δ_{7-\delta} Single Crystals'

A.Rydh and \"O.Rapp [Phys. Rev. Lett. {\bf 86}, 1873 (2001).] claim that the vortex liquid in untwinned YBa$_2$Cu$_3$O$_{7-\delta}$ crystals is correlated above the melting transition, in striking contrast to previous work [D.L\'opez {\it et al.}, Phys. Rev. Lett. {\bf 76}, 4034 (1996).]. In this Comment we present new measurements using the same experimental technique on twinned and untwinned YBa$_2$Cu$_3$O$_{7-\delta}$ crystals with similar overall characteristics as those reported by Rydh and Rapp . The comparison of the vortex correlation response in both cases indicates that the central conclusion of their work is not correct. Our results reconfirm the work by L\'opez {\it et al.} and points on the origin of the misinterpretation in the work of Rydh and Rapp.Comment: comment on A.Rydh and \"O.Rapp, Phys. Rev. Lett. {\bf 86}, 1873 (2001). accepted in Phys. Rev. Let