Relative asymptotics and Fourier series of orthogonal polynomials with a discrete Sobolev inner product

21 pages, no figures.-- MSC2000 codes: 42C05, 33C47.MR#: MR1971776 (2004a:42035)Zbl#: Zbl 1014.42019^aLet μ be a finite positive Borel measure supported in [−1,1] and introduce the discrete Sobolev-type inner product $$\langle f,g\rangle = \int^1_{-1} f(x)g(x)d\mu(x)+\sum^K_{k=1} \sum^{N_k}_{i=0} M_{k,i} f^{(i)}(a_k)g^{(i)}(a_k),$$ where the mass points $a_k$ belong to [−1,1], $M_{k,i}\geq 0$, $i = 0,\dots,N_k-1$, and $M_{k,N_k} >0$. In this paper, we study the asymptotics of the Sobolev orthogonal polynomials by comparison with the orthogonal polynomials with respect to the measure μ and we prove that they have the same asymptotic behaviour. We also study the pointwise convergence of the Fourier series associated to this inner product provided that μ is the Jacobi measure. We generalize the work done by F. Marcellán and W. Van Assche where they studied the asymptotics for only one mass point in [−1,1]. The same problem with a finite number of mass points off [−1,1] was solved by G. López, F. Marcellán and W. Van Assche in a more general setting: they consider the constants Mk,i to be complex numbers. As regards the Fourier series, we continue the results achieved by F. Marcellán, B. Osilenker and I.A. Rocha for the Jacobi measure and mass points in R\[-1,1].The work of F. Marcellán was supported by a grant of Dirección General de Investigación (Ministerio de Ciencia y Tecnología) of Spain BFM-2000-0206-C04-01 and INTAS Project, INTAS 00-272.Publicad

Report of experience in the use of palate prosthesis

La disfunción velofaríngea (DVF) es el resultado de un inadecuado funcionamiento de estructuras dinámicas que trabajan para controlar el mecanismo velofaringeo, (paladar blando, las paredes laterales y pared posterior de faringe) que separa las cavidades nasal y oral durante el habla. La DVF, causada por falta de tejidos se denomina insuficiencia velofaríngea (IVF), y es un factor generador de problemas en el habla por defecto estruc-tural, que requiere tratamiento de manejo físico pudiendo ser este abordado desde la reparación quirúrgica o con prótesis de paladar1, 2.La corrección de la IVF debe ser realizada por un equipo interdisciplinario3. Método: se confeccionaron las correspondientes prótesis de paladar en cuatro pacientes adolescente/adultos seleccionados, sin posibilidades de reparación quirúrgica del esfínter velofaríngeo. Se realizó seguimiento, control y terapia. Se analizaron los resultados obtenidos. Conclusiones: Los resultados positivos solo fueron observados claramente en los pacientes que realizaron su tratamiento fonoaudiológico específico luego de la colocación de su prótesis de paladar obturadora con bulbo.Velopharyngeal dysfunction (DVF) is the result of an inadequate functioning of dynamic structures who work to control the velopharyngeal mechanism (soft palate, lateral walls and posterior pharyngeal wall) that separates the nasal and oral cavities during speech. FVD, caused by lack of tissues, is called velopharyngeal insufficiency (IVF), and it is a factor that generates problems in speech due to a structural defect, which requires physical manage ment treatment, which can be approached from surgical repair or with palatal prosthesis1,2. The correction of the IVF must be carried out by an interdisciplinary team3. Method: the corresponding palate prostheses were made in four selected adolescent / adult patients, without the possibility of surgical repair of the velopharyngeal sphincter. Follow-up, control and therapy were carried out. The results obtained were analyzed. Conclusions: The positive results were only clearly observed in the patients who underwent their specific speech therapy treatment after the placement of their bulbous obturator palate prosthesis.Fil: Fernández Salto, María Laura . Universidad Nacional de Cuyo. Facultad de OdontologíaFil: Denegri, María Alicia. Universidad Nacional de Cuyo. Facultad de OdontologíaFil: Monllor, María Laura. Mendoza. Ministerio de SaludFil: González Marotta, Alejandra. Mendoza. Ministerio de SaludFil: Díaz, Daniel. Universidad Nacional de Cuyo. Facultad de OdontologíaFil: Aferri, Homero Carneiro. Universidade de São Paulo (Brasil)Fil: Dutka, Jeniffer de Cássia Rillo. Universidade de São Paulo (Brasil

Treatment with tocilizumab or corticosteroids for COVID-19 patients with hyperinflammatory state: a multicentre cohort study (SAM-COVID-19)

Objectives: The objective of this study was to estimate the association between tocilizumab or corticosteroids and the risk of intubation or death in patients with coronavirus disease 19 (COVID-19) with a hyperinflammatory state according to clinical and laboratory parameters. Methods: A cohort study was performed in 60 Spanish hospitals including 778 patients with COVID-19 and clinical and laboratory data indicative of a hyperinflammatory state. Treatment was mainly with tocilizumab, an intermediate-high dose of corticosteroids (IHDC), a pulse dose of corticosteroids (PDC), combination therapy, or no treatment. Primary outcome was intubation or death; follow-up was 21 days. Propensity score-adjusted estimations using Cox regression (logistic regression if needed) were calculated. Propensity scores were used as confounders, matching variables and for the inverse probability of treatment weights (IPTWs). Results: In all, 88, 117, 78 and 151 patients treated with tocilizumab, IHDC, PDC, and combination therapy, respectively, were compared with 344 untreated patients. The primary endpoint occurred in 10 (11.4%), 27 (23.1%), 12 (15.4%), 40 (25.6%) and 69 (21.1%), respectively. The IPTW-based hazard ratios (odds ratio for combination therapy) for the primary endpoint were 0.32 (95%CI 0.22-0.47; p < 0.001) for tocilizumab, 0.82 (0.71-1.30; p 0.82) for IHDC, 0.61 (0.43-0.86; p 0.006) for PDC, and 1.17 (0.86-1.58; p 0.30) for combination therapy. Other applications of the propensity score provided similar results, but were not significant for PDC. Tocilizumab was also associated with lower hazard of death alone in IPTW analysis (0.07; 0.02-0.17; p < 0.001). Conclusions: Tocilizumab might be useful in COVID-19 patients with a hyperinflammatory state and should be prioritized for randomized trials in this situatio

Risk factors for unfavorable outcome and impact of early post-transplant infection in solid organ recipients with COVID-19: a prospective multicenter cohort study

The aim was to analyze the characteristics and predictors of unfavorable outcomes in solid organ transplant recipients (SOTRs) with COVID-19. We conducted a prospective observa tional cohort study of 210 consecutive SOTRs hospitalized with COVID-19 in 12 Spanish centers from 21 February to 6 May 2020. Data pertaining to demographics, chronic underly ing diseases, transplantation features, clinical, therapeutics, and complications were col lected. The primary endpoint was a composite of intensive care unit (ICU) admission and/or death. Logistic regression analyses were performed to identify the factors associated with these unfavorable outcomes. Males accounted for 148 (70.5%) patients, the median age was 63 years, and 189 (90.0%) patients had pneumonia. Common symptoms were fever, cough, gastrointestinal disturbances, and dyspnea. The most used antiviral or host-targeted therapies included hydroxychloroquine 193/200 (96.5%), lopinavir/ritonavir 91/200 (45.5%), and tocilizumab 49/200 (24.5%). Thirty-seven (17.6%) patients required ICU admission, 12 (5.7%) suffered graft dysfunction, and 45 (21.4%) died. A shorter interval between trans plantation and COVID-19 diagnosis had a negative impact on clinical prognosis. Four base line features were identified as independent predictors of intensive care need or death: advanced age, high respiratory rate, lymphopenia, and elevated level of lactate dehydroge nase. In summary, this study presents comprehensive information on characteristics and complications of COVID-19 in hospitalized SOTRs and provides indicators available upon hospital admission for the identification of SOTRs at risk of critical disease or death, under lining the need for stringent preventative measures in the early post-transplant period