Three term relations formultivariate Uvarov orthogonal polynomials

Three term relations for orthogonal polynomials in several variables associated to a moment linear functional obtained by a Uvarov modification of a givenmoment functional are studied. Existence of Uvarov orthogonal polynomials is analyzed, stating conditions to ensure it. The matrices of the three term relations of the Uvarov orthogonal polynomials are explicitly given in terms of the matrices of the three term relations satisfied by the original family. Two examples are presented in order to show that the results are valid for positive definite linear functionals and also for some quasi definite linear functionals which are not positive definite.Turkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) 120F140Spanish Government PID2020-113275GB-I00European CommissionFEDER/J. Andalucia A-FQM-246-UGR20MCIN/AEI PGC2018-094932-B-I00European Commission PGC2018-094932-B-I00IMAG-Maria de Maeztu grant CEX2020-001105-

Two variable Freud orthogonal polynomials and matrix Painlevé-type difference equations

We study bivariate orthogonal polynomials associated with Freud weight functions depending on real parameters. We analyse relations between the matrix coefficients of the three term relations for the orthonormal polynomials as well as the coefficients of the structure relations satisfied by these bivariate semiclassical orthogonal polynomials, also a matrix differentialdifference equation for the bivariate orthogonal polynomials is deduced. The extension of the Painlev´e equation for the coefficients of the three term relations to the bivariate case and a two dimensional version of the Langmuir lattice are obtained.Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES) 88887.310463/2018-00 88887.575407/2020-00FEDER/Junta de Andalucia A-FQM-246-UGR20MCIN PGC2018-094932B-I00European CommissionIMAG-Maria de Maeztu grant CEX2020-00 1105-

Simultaneous Approximation via Laplacians on the Unit Ball

We study the orthogonal structure on the unit ball Bd of Rd with respect to the Sobolev inner products f, g Δ = λL(f, g) + Bd Δ[(1 − x 2)f(x)] Δ[(1 − x 2)g(x)] dx, where L(f, g) = Sd−1 f(ξ) g(ξ) dσ(ξ) or L(f, g) = f(0)g(0), λ > 0, σ denotes the surface measure on the unit sphere Sd−1, and Δ is the usual Laplacian operator. Our main contribution consists in the study of orthogonal polynomials associated with ·, · Δ, giving their explicit expression in terms of the classical orthogonal polynomials on the unit ball, and proving that they satisfy a fourth-order partial differential equation, extending the well-known property for ball polynomials, since they satisfy a second-order PDE.We also study the approximation properties of the Fourier sums with respect to these orthogonal polynomials and, in particular, we estimate the error of simultaneous approximation of a function, its partial derivatives, and its Laplacian in the L2(Bd) space.Funding for open access publishing: Universidad de Granada/CBUAFunding for open access charge: Universidad de Granad

Sobolev orthogonal polynomials and spectral methods in boundary value problems

The work by FM has been supported by FEDER/Ministerio de Ciencia e Innovación-Agencia Estatal de Investigación of Spain, grant PID2021-122154NB-I00, and the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors, grant EPUC3M23 in the context of the V PRICIT (Regional Program of Research and Technological Innovation). LF, TEP and MAP thanks Grant FQM-246-UGR20 funded by Consejería de Universidad, Investigación e Innovación and by European Union NextGenerationEU/PRTR; and Grant CEX2020-001105-M funded by MCIN/AEI/10.13039/501100011033. Funding for APC: Universidad Carlos III de Madrid (Agreement CRUE-Madroño 2023).In the variational formulation of a boundary value problem for the harmonic oscillator, Sobolev inner products appear in a natural way. First, we study the sequences of Sobolev orthogonal polynomials with respect to such an inner product. Second, their representations in terms of a sequence of Gegenbauer polynomials are deduced as well as an algorithm to generate them in a recursive way is stated. The outer relative asymptotics between the Sobolev orthogonal polynomials and classical Legendre polynomials is obtained. Next we analyze the solution of the boundary value problem in terms of a Fourier-Sobolev projector. Finally, we provide numerical tests concerning the reliability and accuracy of the Sobolev spectral method.FEDER/Ministerio de Ciencia e Innovación-Agencia Estatal de Investigación of Spain PID2021-122154NB-I00Madrid Government EPUC3M23Consejería de Universidad, Investigación e Innovación FQM-246-UGR20European Union NextGenerationEU/PRTRMCIN/AEI/10.13039/501100011033: CEX2020-001105-MUniversidad Carlos III de Madrid CRUE-Madroño 202

Approximation via gradients on the ball. The Zernike case

In this work, we deal in a d dimensional unit ball equipped with an inner product constructed by adding a mass point at zero to the classical ball inner product applied to the gradients of the functions. Apart from determining an explicit orthogonal polynomial basis, we study approximation properties of Fourier expansions in terms of this basis. In particular, we deduce relations between the partial Fourier sums in terms of the new orthogonal polynomials and the partial Fourier sums in terms of the classical ball polynomials. We also give an estimate of the approximation error by polynomials of degree at most n in the corresponding Sobolev space, proving that we can approximate a function by using its gradient. Numerical examples are given to illustrate the approximation behavior of the Sobolev basis.Ministerio de Ciencia, Innovacion y Universidades (MICINN), Spain PGC2018-096504-B-C33Comunidad de MadridUniversidad Rey Juan Carlos, Spain M2731FEDER/Junta de Andalucia, Spain A-FQM-246-UGR20MCIN/AEIFEDER, Spain funds PGC2018-094932-B-I00IMAG-Maria de Maeztu, Spain CEX2020-001105-

A Novel Halophilic Lipase, LipBL, Showing High Efficiency in the Production of Eicosapentaenoic Acid (EPA)

Background: Among extremophiles, halophiles are defined as microorganisms adapted to live and thrive in diverse extreme saline environments. These extremophilic microorganisms constitute the source of a number of hydrolases with great biotechnological applications. The interest to use extremozymes from halophiles in industrial applications is their resistance to organic solvents and extreme temperatures. Marinobacter lipolyticus SM19 is a moderately halophilic bacterium, isolated previously from a saline habitat in South Spain, showing lipolytic activity. Methods and Findings: A lipolytic enzyme from the halophilic bacterium Marinobacter lipolyticus SM19 was isolated. This enzyme, designated LipBL, was expressed in Escherichia coli. LipBL is a protein of 404 amino acids with a molecular mass of 45.3 kDa and high identity to class C b-lactamases. LipBL was purified and biochemically characterized. The temperature for its maximal activity was 80uC and the pH optimum determined at 25uC was 7.0, showing optimal activity without sodium chloride, while maintaining 20% activity in a wide range of NaCl concentrations. This enzyme exhibited high activity against short-medium length acyl chain substrates, although it also hydrolyzes olive oil and fish oil. The fish oil hydrolysis using LipBL results in an enrichment of free eicosapentaenoic acid (EPA), but not docosahexaenoic acid (DHA), relative to its levels present in fish oil. For improving the stability and to be used in industrial processes LipBL was immobilized in different supports. The immobilized derivatives CNBr-activated Sepharose were highly selective towards the release of EPA versus DHA. The enzyme is also active towards different chiral and prochiral esters. Exposure of LipBL to buffer-solvent mixtures showed that the enzyme had remarkable activity and stability in all organic solvents tested. Conclusions: In this study we isolated, purified, biochemically characterized and immobilized a lipolytic enzyme from a halophilic bacterium M. lipolyticus, which constitutes an enzyme with excellent properties to be used in the food industry, in the enrichment in omega-3 PUFAs

Development and validation of a nomogram to predict kidney survival at baseline in patients with C3 glomerulopathy

Background C3 glomerulopathy is a rare and heterogeneous complement-driven disease. It is often challenging to accurately predict in clinical practice the individual kidney prognosis at baseline. We herein sought to develop and validate a prognostic nomogram to predict long-term kidney survival. Methods We conducted a retrospective, multicenter observational cohort study in 35 nephrology departments belonging to the Spanish Group for the Study of Glomerular Diseases. The dataset was randomly divided into a training group (n = 87) and a validation group (n = 28). The least absolute shrinkage and selection operator (LASSO) regression was used to screen the main predictors of kidney outcome and to build the nomogram. The accuracy of the nomogram was assessed by discrimination and risk calibration in the training and validation sets. Results The study group comprised 115 patients, of whom 46 (40%) reached kidney failure in a median follow-up of 49 months (range 24?112). No significant differences were observed in baseline estimated glomerular filtration rate (eGFR), proteinuria or total chronicity score of kidney biopsies, between patients in the training versus those in the validation set. The selected variables by LASSO were eGFR, proteinuria and total chronicity score. Based on a Cox model, a nomogram was developed for the prediction of kidney survival at 1, 2, 5 and 10 years from diagnosis. The C-index of the nomogram was 0.860 (95% confidence interval 0.834?0.887) and calibration plots showed optimal agreement between predicted and observed outcomes. Conclusions We constructed and validated a practical nomogram with good discrimination and calibration to predict the risk of kidney failure in C3 glomerulopathy patients at 1, 2, 5 and 10 years.ACKNOWLEDGEMENTS: Work on this study was supported by the Instituto de Salud Carlos III / Fondo Europeo de Desarrollo Regional (ISCIII/FEDER; grants PI16/01685 and PI19/1624) and Red de Investigación Renal (RD12/0021/0029; to M.P.) and the Autonomous Region of Madrid (S2017/BMD-3673; to M.P.). S.R.d.C. is supported by the Ministerio de Economia y Competitividad (grant PID2019-104912RB-I00) and the Autonomous Region of Madrid (grant S2017/BMD-3673). None of the funders had any role in the study design, data collection, analyses, reporting or decision to submit for publication

Recicland, demostration on the management of organic and inorganic waste from agriculture

La agricultura protegida que se desarrolla principalmente en el litoral oriental andaluz es una actividad de gran importancia económica y social para Andalucía. Sin embargo, el crecimiento exponencial de la superficie de invernadero ha dado lugar a un incremento del volumen de residuos agrarios. Además, este sistema agrícola está evolucionando hacia nuevas técnicas de cultivo que implican, no sólo la generación de residuos, sino también una mayor diversificación que hace más complicada su gestión. El principal problema para la gestión de estos residuos agrarios no está sólo en su dispersión geográfica, sino también en su estacionalidad, ya que se genera gran cantidad en determinados periodos anuales, coincidiendo con la finalización de las campañas agrícolas. Por este motivo, la capacidad máxima de recogida y almacenamiento y el proceso de gestión están condicionados por el volumen generado al finalizar los ciclos de cultivo. En este contexto, surge el proyecto RECICLAND que pretende palear dichos problemas y contribuir a la gestión sostenible de los residuos generados en los procesos productivos. Concretamente, el objetivo general de este proyecto es desarrollar actividades demostrativas piloto, informando de modo práctico sobre diferentes técnicas para la gestión específica de residuos inorgánicos y restos vegetales. Para ello, se ha establecido un área de reciclaje, junto con actividades de transferencia (jornadas prácticas, visitas, vídeos demostrativos y publicaciones) en el Centro IFAPA La Mojonera (Almería).Protected agriculture, which takes place mainly on the eastern coast of Andalusia, constitutes the major economic and social activity for this region. However, greenhouse area exponential growth has led to an increase in the volume of agricultural waste. In addition, this agricultural system is evolving towards new cultivation techniques that not only involve the generation of waste, but also a greater diversification that makes its management hard to tackle. The main issue regarding management of this agricultural waste is not only its geographical dispersion, but also its seasonality, as a large quantity is generated during certain periods of the year, coinciding with the end of agricultural campaigns. Indeed, the maximum collection and storage capacity and the management process itself are conditioned by the volume generated at the end of cropping cycles. In this context, the RECICLAND project arises, which aims to alleviate these problems and contribute to the sustainable management of the waste generated in the production processes. Specifically, the general objective of project is to develop pilot demonstration activities, providing practical information on different techniques for the specific management of inorganic waste and plant debris. For this purpose, a recycling area has been set up, where transference activities such as practical workshops, guide visits, demonstration, videos, and publications are being carried out in IFAPA La Mojonera (Almería)

Development and validation of a nomogram to predict kidney survival at baseline in patients with C3 glomerulopathy

10 p.-4 fig.-2 tab. 1 graph. abst.Background: C3 glomerulopathy is a rare and heterogeneous complement-driven disease. It is often challenging to accurately predict in clinical practice the individual kidney prognosis at baseline. We herein sought to develop and validate a prognostic nomogram to predict long-term kidney survival.Methods: We conducted a retrospective, multicenter observational cohort study in 35 nephrology departments belonging to the Spanish Group for the Study of Glomerular Diseases. The dataset was randomly divided into a training group (n = 87) and a validation group (n = 28). The least absolute shrinkage and selection operator (LASSO) regression was used to screen the main predictors of kidney outcome and to build the nomogram. The accuracy of the nomogram was assessed by discrimination and risk calibration in the training and validation sets.Results: The study group comprised 115 patients, of whom 46 (40%) reached kidney failure in a median follow-up of 49 months (range 24–112). No significant differences were observed in baseline estimated glomerular filtration rate (eGFR), proteinuria or total chronicity score of kidney biopsies, between patients in the training versus those in the validation set. The selected variables by LASSO were eGFR, proteinuria and total chronicity score. Based on a Cox model, a nomogram was developed for the prediction of kidney survival at 1, 2, 5 and 10 years from diagnosis. The C-index of the nomogram was 0.860 (95% confidence interval 0.834–0.887) and calibration plots showed optimal agreement between predicted and observed outcomes.Conclusions: We constructed and validated a practical nomogram with good discrimination and calibration to predict the risk of kidney failure in C3 glomerulopathy patients at 1, 2, 5 and 10 years.Work on this study was supported by the Instituto de Salud Carlos III / Fondo Europeo de Desarrollo Regional (ISCIII/FEDER; grants PI16/01685 and PI19/1624) and Red de Investigación Renal (RD12/0021/0029; to M.P.) and the Autonomous Region of Madrid (S2017/BMD-3673; to M.P.). S.R.d.C. is supported by the Ministerio de Economia y Competitividad (grant PID2019-104912RB-I00) and the Autonomous Region of Madrid (grant S2017/BMD-3673).Peer reviewe

Validation of a histologic scoring index for C3 glomerulopathy

12 p.-4 fig.-4 tab.Rationale & objective: A previous study that evaluated associations of kidney biopsy findings with disease progression in patients with C3 glomerulopathy (C3G) proposed a prognostic histologic index (C3G-HI) that has not yet been validated. Our objective was to validate the performance of the C3G-HI in a new patient population.Study design: Multicenter, retrospective cohort study.Setting & participants: 111 patients fulfilling diagnostic criteria of C3G between January 1995 and December 2019, from 33 nephrology departments belonging to the Spanish Group for the Study of Glomerular Diseases (GLOSEN).Predictors: Demographic, clinical parameters, C3G-HI total activity score, and the C3G-HI total chronicity score.Outcome: Time to kidney failure.Analytical approach: Intraclass correlation coefficients and κ statistic were used to summarize inter-rater reproducibility for assessment of histopathology in kidney biopsies. The nonlinear relationships of risk of kidney failure with the total activity score and total chronicity score were modeled using Cox proportional hazards analysis that incorporated cubic splines.Results: The study group included 93 patients with C3 glomerulonephritis and 18 with dense-deposit disease. Participants had an overall meanage of 35±22 (SD) years. Forty-eight patients (43%) developed kidney failure after a mean follow-up of 65±27 months. The overall inter-rater reproducibility was very good for the total activity score (intraclass correlation coefficient [ICC]=0.63) and excellent for total chronicity score (ICC=0.89). Baseline estimated glomerular filtration rate (eGFR), 24-hour proteinuria, and treatment with immunosuppression were the main determinants of kidney failure in a model with only clinical variables. Only tubular atrophy and interstitial fibrosis were identified as predictors in a model with histological variables. When the total activity score and total chronicity score were added to the model, only the latter was identified as an independent predictor of kidney failure.Limitations: Only a subset of the kidney biopsies was centrally reviewed. Residual confounding.Conclusions: We validated the performance of C3G-HI as a predictor of kidney failure in patients with C3G. The total chronicity score was the principal histologic correlate of kidney failure.Work in this study was supported by the Instituto de Salud Carlos III /Fondo Europeo de Desarrollo Regional (ISCIII/FEDER) grant PI16/01685 and Red de Investigación Renal (RedInRen) (RD12/0021/0029) (to MP), the Autonomous Region of Madrid (S2017/BMD-3673) (to MP); EGdeJ is supported by the Spanish “Ministerio de Ciencia, Innovación y Universidades" (RYC-2013-13395 and RTI2018-095955-B-100).Peer reviewe