Quasi-exact solvability beyond the SL(2) algebraization

We present evidence to suggest that the study of one dimensional quasi-exactly solvable (QES) models in quantum mechanics should be extended beyond the usual \sla(2) approach. The motivation is twofold: We first show that certain quasi-exactly solvable potentials constructed with the \sla(2) Lie algebraic method allow for a new larger portion of the spectrum to be obtained algebraically. This is done via another algebraization in which the algebraic hamiltonian cannot be expressed as a polynomial in the generators of \sla(2). We then show an example of a new quasi-exactly solvable potential which cannot be obtained within the Lie-algebraic approach.Comment: Submitted to the proceedings of the 2005 Dubna workshop on superintegrabilit

New Algebraic Quantum Many-body Problems

We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to root systems, in some cases with an additional external field. The quasi-exactly solvable models can be considered as deformations of the previous ones which share their algebraic character.Comment: LaTeX 2e with amstex package, 36 page

Star formation history of the post-collisional Cartwheel galaxy using Astrosat/UVIT FUV images

We present the results obtained by analysing new Astrosat/UVIT far ultraviolet (FUV) image of the collisional-ring galaxy Cartwheel. The FUV emission is principally associated with the star-forming outer ring, with no UV detection from the nucleus and inner ring. A few sources are detected in the region between the inner and the outer rings, all of which lie along the spokes. The FUV fluxes from the detected sources are combined with aperture-matched multi-band photometric data from archival images to explore the post-collision star formation history of the Cartwheel. The data were corrected for extinction using Av derived from the Balmer decrement ratios and commonly used extinction curves. We find that the ring regions contain stellar populations of wide range of ages, with the bulk of the FUV emission coming from non-ionizing stars, formed over the last 20 to 150 Myr, that are ~25 times more massive than the ionizing populations. On the other hand, regions belonging to the spokes have negligible current star formation, with the age of the dominant older population systematically increasing as its distance from the outer ring increases. The presence of populations of a wide range of ages in the ring suggests that the stars formed in the wave in the past were dragged along it to the current position of the ring. We derive an average steady star formation rate, SFR=5 Msun/yr, over the past 150 Myr, with an increase to ~18 Msun/yr in the recent 10 Myr.Comment: 16 pages, to appear in MNRA

Additional restrictions on quasi-exactly solvable systems

In this paper we discuss constraints on two-dimensional quantum-mechanical systems living in domains with boundaries. The constrains result from the requirement of hermicity of corresponding Hamiltonians. We construct new two-dimensional families of formally exactly solvable systems and applying such constraints show that in real the systems are quasi-exactly solvable at best. Nevertheless in the context of pseudo-Hermitian Hamiltonians some of the constructed families are exactly solvable.Comment: 11 pages, 3 figures, extended version of talk given at the International Workshop on Classical and Quantum Integrable Systems "CQIS-06", Protvino, Russia, January 23-26, 200

Wolf-Rayet stars in the Antennae unveiled by MUSE

We present the analysis of archival Very Large Telescope (VLT) Multi Unit Spectroscopic Explorer (MUSE) observations of the interacting galaxies NGC 4038/39 (a.k.a. the Antennae) at a distance of 18.1 Mpc. Up to 38 young star-forming complexes with evident contribution from Wolf-Rayet (WR) stars are unveiled. We use publicly available templates of Galactic WR stars in conjunction with available photometric extinction measurements to quantify and classify the WR population in each star-forming region, on the basis of its nearly Solar oxygen abundance. The total estimated number of WR stars in the Antennae is 4053 $\pm$ 84, of which there are 2021 $\pm$ 60 WNL and 2032 $\pm$ 59 WC-types. Our analysis suggests a global WC to WN-type ratio of 1.01 $\pm$ 0.04, which is consistent with the predictions of the single star evolutionary scenario in the most recent BPASS stellar population synthesis models.Comment: 20 pages, 16 figures, 5 tables; accepted to MNRA

Planetary nebulae with Wolf-Rayet-type central stars -- I. The case of the high-excitation NGC 2371

We present the analysis of the planetary nebula (PN) NGC 2371 around the [Wolf-Rayet] ([WR]) star WD 0722$+$295. Our Isaac Newton Telescope (INT) Intermediate Dispersion Spectrograph (IDS) spectra, in conjunction with archival optical and UV images, unveil in unprecedented detail the high-ionisation of NGC 2371. The nebula has an apparent multipolar morphology, with two pairs of lobes protruding from a barrel-like central cavity, a pair of dense low-ionisation knots misaligned with the symmetry axis embedded within the central cavity, and a high excitation halo mainly detected in He II. The abundances from the barrel-like central cavity and dense knots agree with abundance determinations for other PNe with [WR]-type CSPNe. We suggest that the densest knots inside NGC 2371 are the oldest structures, remnant of a dense equatorial structure, whilst the main nebular shell and outer lobes resulted from a latter ejection that ended the stellar evolution. The analysis of position-velocity diagrams produced from our high-quality spectra suggests that NGC 2371 has a bipolar shape with each lobe presenting a double-structure protruding from a barrel-like central region. The analysis of the spectra of WD 0722$+$295 results in similar stellar parameters as previously reported. We corroborate that the spectral sub-type corresponds with a [WO1] type.Comment: 15 pages, 12 figures, 5 tables; accepted to MNRA

Validación del monitor de medición de la grasa corporal por impedancia bioeléctrica OMRON BF 300

ObjetivosValorar la precisión del monitor de grasa corporal por impedancia bioeléctrica OMRON BF 300 y validar su medición del porcentaje de grasa corporal (%GC) frente a la ecuación de Siri. Diseño. Estudio descriptivo, transversal.EmplazamientoAtención primaria. Centros de Salud Coronel de Palma y San Fernando, Móstoles.ParticipantesEn la valoración de la precisión del monitor participaron 88 personas y 91 en la validación.Mediciones y resultados principalesLas determinaciones de %GC se realizaron por triplicado, anotándose la media. La precisión se evaluó mediante el coeficiente de correlación intraclase (CCI) y el coeficiente de variación (CV). La validez, mediante el error técnico, el CCI y el método de Bland-Altman. En la ecuación de Siri la densidad corporal se calculó con la ecuación de Durnin-Womersley. Precisión: el CCI fue de 0,999 y el CV de 0,4 ± 0,03. Validación: la diferencia de %GC monitor (26,6 ± 9,1%) – ecuación de Siri (27,8 ± 8,2%) fue de –1,27% (p < 0,01; IC del 95%, –1,97 a –0,57), el error técnico del monitor del 2,2% y el CCI de 0,956 (IC del 95%, 0,9335–0,9710), situándose un 80,2% de las diferencias monitor – ecuación por debajo del 5%, con un intervalo de concordancia por el método de Bland-Altman de +5,45 a –7,99%.ConclusionesEl monitor OMRON BF 300 satisface los criterios de precisión (CCI > 0,95 y CV bajo) y validación (error técnico excelente, CCI > 0,75 y diferencias clínicamente aceptables) y supone una alternativa válida a los pliegues cutáneos en la valoración nutricional del paciente.ObjectivesTo assess the accuracy of the OMRON BF 300 body fat monitor using bioelectric impedance and to validate its measurement of body fat percentage (BF%) against the Siri equation.DesignCross-sectional descriptive study.SettingPrimary care. Coronel de Palma and San Fernando Health Centres, Móstoles.Participants88 people took part in the assessment of the accuracy of the monitor, and 91 in the validation.Measurements and main resultsThe BF% were recorded in triplicate, with the mean being the figure noted. Precision was evaluated through the intra-class correlation coefficient (ICC) and the coefficient of variation (CV); validity, through technical error, the ICC and the Bland-Altman method. In the Siri equation, body density was calculated through the Durnin-Womersley equation. Precision: ICC was 0.999 and CV 0.4 ± 0.03. Validation: the difference between the BF% monitor (26.6 ± 9.1%) and the Siri equation (27.8 ± 8.2%) was –1.27% (p < 0.01; 95% CI –1.97 to –0.57); the technical error of the monitor was 2.2% and of the ICC 0.956 (95% CI, 0.9335–0.9710). Thus, 80.2% of the monitor-equation differences were below 5%, with a concordance interval under the Bland-Altman method of +5.45 to –7.99%.ConclusionsThe OMRON BF 300 monitor satisfies the precision criteria (ICC > 0.95 and low CV) and validation (excellent technical error, ICC > 0.75 and clinically acceptable differences) and is a valid alternative to cutaneous folds as a method of assessing nutrition of the patient

Unveiling the stellar origin of the Wolf-Rayet nebula NGC6888 through infrared observations

We present a comprehensive infrared (IR) study of the iconic Wolf-Rayet (WR) wind-blown bubble NGC6888 around WR136. We use Wide-field Infrared Survey Explorer (WISE), Spitzer IRAC and MIPS and Herschel PACS IR images to produce a sharp view of the distribution of dust around WR136. We complement these IR photometric observations with Spitzer IRS spectra in the 5-38 $\mu$m wavelength range. The unprecedented high-resolution IR images allowed us to produce a clean spectral energy distribution, free of contamination from material along the line of sight, to model the properties of the dust in NGC6888. We use the spectral synthesis code Cloudy to produce a model for NGC6888 that consistently reproduces its optical and IR properties. Our best model requires a double distribution with the inner shell composed only of gas, whilst the outer shell requires a mix of gas and dust. The dust consists of two populations of grain sizes, one with small sized grains $a_\mathrm{small}$=[0.002-0.008] $\mu$m and another one with large sized grains $a_\mathrm{big}$=[0.05-0.5] $\mu$m. The population of big grains is similar to that reported for other red supergiants stars and dominates the total dust mass, which leads us to suggest that the current mass of NGC6888 is purely due to material ejected from WR136, with a negligible contribution of swept up interstellar medium. The total mass of this model is 25.5$^{+4.7}_{-2.8}$ M$_{\odot}$, a dust mass of $M_\mathrm{dust}=$0.14$^{+0.03}_{-0.01}$ M$_{\odot}$, for a dust-to-gas ratio of $5.6\times10^{-3}$. Accordingly, we suggest that the initial stellar mass of WR136 was $\lesssim$50 M$_{\odot}$, consistent with current single stellar evolution models.Comment: 13 pages, 11 figures, 6 tables; Accepted to MNRA