Isoperimetric inequalities in Riemann surfaces of infinite type

75 pages, 1 figure.-- MSC2000 code: 30F45.MR#: MR1715412 (2000j:30075)Zbl#: Zbl 0935.30028Research partially supported by a grant from Dirección General de Enseñanza Superior (Ministerio de Educación y Ciencia), Spain.Publicad

Approximation theory for weighted Sobolev spaces on curves

17 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.MR#: MR1882649 (2003c:42002)In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete. We also prove the density of the polynomials in these spaces for non-closed compact curves and, finally, we find conditions under which the multiplication operator is bounded on the completion of polynomials. These results have applications to the study of zeroes and asymptotics of Sobolev orthogonal polynomials.Research of V. Álvarez, D. Pestana and J.M. Rodríguez partially supported by a grant from DGI, BFM2000-0206-C04-01, Spain.Publicad

Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials, I

36 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.-- Part II of this paper published in: Approx. Theory Appl. 18(2): 1-32 (2002), available at: http://e-archivo.uc3m.es/handle/10016/6483MR#: MR2047389 (2005k:42062)Zbl#: Zbl 1081.42024In this paper we present a definition of Sobolev spaces with respect to general measures, prove some useful technical results, some of them generalizations of classical results with Lebesgue measure and find general conditions under which these spaces are complete. These results have important consequences in approximation theory. We also find conditions under which the evaluation operator is bounded.Research by first (J.M.R.), third (E.R.) and fourth (D.P.) authors was partially supported by a grant from DGI (BFM 2000-0206-C04-01), Spain.Publicad

Weighted Sobolev spaces on curves

45 pages, no figures.-- MSC1987 codes: 41A10, 46E35, 46G10.MR#: MR1934626 (2003j:46038)Zbl#: Zbl 1019.46026In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete for non-closed compact curves. We also prove the density of the polynomials in these spaces and, finally, we find conditions under which the multiplication operator is bounded in the space of polynomials.Research of second (D.P.), third (J.M.R.) and fourth (E.R.) authors was partially supported by a grant from DGI (BFM 2000-0206-C04-01), Spain.Publicad

Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials, II

32 pages, no figures.-- MSC1987 codes: 41A10, 46E35, 46G10.-- Part I of this paper published in: Acta Appl. Math. 80(3): 273-308 (2004), available at: http://e-archivo.uc3m.es/handle/10016/6482MR#: MR1928169 (2003h:42034)Zbl#: Zbl 1095.42014^aWe present a definition of general Sobolev spaces with respect to arbitrary measures, $W^{k,p}(\Omega,\mu)$ for $1\leq p\leq\infty$. In Part I [Acta Appl. Math. 80(3): 273-308 (2004), http://e-archivo.uc3m.es/handle/10016/6482] we proved that these spaces are complete under very mild conditions. Now we prove that if we consider certain general types of measures, then $C^\infty_c({\bf R})$ is dense in these spaces. As an application to Sobolev orthogonal polynomials, we study the boundedness of the multiplication operator. This gives an estimation of the zeroes of Sobolev orthogonal polynomials.Research partially supported by a grant from DGES (MEC), Spain.Publicad

Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials: a survey

6 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.MR#: MR2219917 (2006k:42051)Zbl#: Zbl 1146.42005In this paper we present a definition of Sobolev spaces with respect to general measures, prove some useful technical results, some of them generalizations of classical results with Lebesgue measure and find general conditions under which these spaces are complete. These results have important consequences in approximation theory. We also find conditions under which the evaluation operator is bounded.Research by first author (J.M.R.) was partially supported by grants from DGI (BFM 2003-06335-C03-02 and BFM 2003-04870), Spain. Research by second author (V.A.) was partially supported by grants from MCYT (MTM 2004-00078) and Junta de Andalucía (FQM-210), Spain. Research by third author (E.R.) was partially supported by a grant from DGI (BFM 2003-06335-C03-02), Spain. Research by fourth author (D.P.) was partially supported by grants from DGI (BFM 2003-06335-C03-02 and BFM 2003-04870), Spain.Publicad

Exploring genetic factors involved in huntington disease age of onset. E2F2 as a new potential modifier gene

Age of onset (AO) of Huntington disease (HD) is mainly determined by the length of the CAG repeat expansion (CAGexp) in exon 1 of the HTT gene. Additional genetic variation has been suggested to contribute to AO, although the mechanism by which it could affect AO is presently unknown. The aim of this study is to explore the contribution of candidate genetic factors to HD AO in order to gain insight into the pathogenic mechanisms underlying this disorder. For that purpose, two AO definitions were used: the earliest age with unequivocal signs of HD (earliest AO or eAO), and the first motor symptoms age (motor AO or mAO). Multiple linear regression analyses were performed between genetic variation within 20 candidate genes and eAO or mAO, using DNA and clinical information of 253 HD patients from REGISTRY project. Gene expression analyses were carried out by RT-qPCR with an independent sample of 35 HD patients from Basque Country Hospitals. We found suggestive association signals between HD eAO and/or mAO and genetic variation within the E2F2, ATF7IP, GRIN2A, GRIN2B, LINC01559, HIP1 and GRIK2 genes. Among them, the most significant was the association between eAO and rs2742976, mapping to the promoter region of E2F2 transcription factor. Furthermore, rs2742976 T allele patient carriers exhibited significantly lower lymphocyte E2F2 gene expression, suggesting a possible implication of E2F2-dependent transcriptional activity in HD pathogenesis. Thus, E2F2 emerges as a new potential HD AO modifier factor

Differences in the clinical management of women and men after detection of a solitary pulmonary nodule in clinical practice

Objectives To explore differences in the clinical management of men and women in the 5 years after detecting a solitary pulmonary nodule (SPN) by chest radiograph or CT in routine clinical practice. Methods We followed up 545 men and 347 women with an SPN detected by chest radiograph or CT in a retrospective cohort of 25,422 individuals undergoing routine thoracic imaging in 2010–2011.We compared the frequency of each management strategy (no further test, immediate intervention or follow up) according to sex by means of chi-squared.We estimated the relative risk of women versus men of having been followed up instead of an immediate intervention using multivariate logistic regression. We compared by sex the time between detection of the nodule and lung cancer diagnosis, the time between diagnosis and death by means of Mann-Whitney U test and the cumulative effective dose of radiation in each management strategy by means of t test. Results Women were more likely than men to have follow-up rather than immediate intervention (aRR = 1.8, CI 1.3–2.7, p = 0.002), particularly in those who underwent CT (aRR = 4.2, CI 1.9–9.3, p < 0.001). The median time between SPN detection and lung cancer diagnosis was higher in women (4.2 months, interquartile range (IQR) 5.1) than in men (1.5 months, IQR 16.2). The mean cumulative effective dose was 21.3 mSv, 19.4 mSv in men and 23.9mv in women (p = 0.023). Conclusions Our results could reflect decisions based on a greater suspicion of lung cancer in men. The incidental detection of SPNs is increasing, and it is necessary to establish clear strategies aimed to reduce variability in their management according to patient’s sex

Lamellarin D bioconjugates II: synthesis and cellular internalization of dendrimer and nuclear location signal derivatives

The design and synthesis of Lamellarin D conjugates with a nuclear localization signal peptide and a poly(ethylene glycol)-based dendrimer are described. Conjugates 1-4 were obtained in 8-84% overall yields from the corresponding protected Lamellarin D. Conjugates 1 and 4 are 1.4 to 3.3-fold more cytotoxic than the parent compound against three human tumor cell lines(MDA-MB-231 breast, A-549 lung, and HT-29 colon). Besides, conjugates 3, 4 showed a decrease in activity potency in BJ skin fibroblasts, a normal cell culture. Cellular internalization was analyzed and nuclear distribution pattern was observed for 4, which contains a nuclear localization signalling sequence

The Imaging Magnetograph eXperiment (IMaX) for the Sunrise balloon-borne solar observatory

The Imaging Magnetograph eXperiment (IMaX) is a spectropolarimeter built by four institutions in Spain that flew on board the Sunrise balloon-borne telesocope in June 2009 for almost six days over the Arctic Circle. As a polarimeter IMaX uses fast polarization modulation (based on the use of two liquid crystal retarders), real-time image accumulation, and dual beam polarimetry to reach polarization sensitivities of 0.1%. As a spectrograph, the instrument uses a LiNbO3 etalon in double pass and a narrow band pre-filter to achieve a spectral resolution of 85 mAA. IMaX uses the high Zeeman sensitive line of Fe I at 5250.2 AA and observes all four Stokes parameters at various points inside the spectral line. This allows vector magnetograms, Dopplergrams, and intensity frames to be produced that, after reconstruction, reach spatial resolutions in the 0.15-0.18 arcsec range over a 50x50 arcsec FOV. Time cadences vary between ten and 33 seconds, although the shortest one only includes longitudinal polarimetry. The spectral line is sampled in various ways depending on the applied observing mode, from just two points inside the line to 11 of them. All observing modes include one extra wavelength point in the nearby continuum. Gauss equivalent sensitivities are four Gauss for longitudinal fields and 80 Gauss for transverse fields per wavelength sample. The LOS velocities are estimated with statistical errors of the order of 5-40 m/s. The design, calibration and integration phases of the instrument, together with the implemented data reduction scheme are described in some detail.Comment: 17 figure