Numerical approximation of solution derivatives of singularly peprturbed parabolic problems of convection-difffusion type

Numerical approximations to the solution of a linear singularly perturbed parabolic convection-diffusion problem are generated using a backward Euler method in time and an upwinded finite difference operator in space on a piecewise-uniform Shishkin mesh. A proof is given to show first order convergence of these numerical approximations in an appropriately weighted C^1$-norm. Numerical results are given to illustrate the theoretical error bounds

Singularly perturbed initial-boundary value problem with a pulse in the initial condition

A singularly perturbed parabolic equation of reaction-diffusion type is examined. Initially the solution approximates a concentrated source, which causes an interior layer to form within the solution for all future times. Combining a classical finite difference operator with a layer-adapted mesh, parameter-uniform convergence is established. Numerical results are presented to illustrate the theoretical error bounds

Formal consistency versus actual convergence rates of difference schemes for fractional-derivative boundary value problems

Finite difference methods for approximating fractional derivatives are often analyzed by determining their order of consistency when applied to smooth functions, but the relationship between this measure and their actual numerical performance is unclear. Thus in this paper several wellknown difference schemes are tested numerically on simple Riemann-Liouville and Caputo boundary value problems posed on the interval [0, 1] to determine their orders of convergence (in the discrete maximum norm) in two unexceptional cases: (i) when the solution of the boundary-value problem is a polynomial (ii) when the data of the boundary value problem is smooth. In many cases these tests reveal gaps between a method’s theoretical order of consistency and its actual order of convergence. In particular, numerical results show that the popular shifted Gr¨unwald-Letnikov scheme fails to converge for a Riemann-Liouville example with a polynomial solution p(x), and a rigorous proof is given that this scheme (and some other schemes) cannot yield a convergent solution when p(0)¿ 0

Convergence in positive time for a finite difference method applied to a fractional convection-diffusion equation

A standard finite difference method on a uniform mesh is used to solve a time-fractional convection-diffusion initial-boundary value problem. Such problems typically exhibit a mild singularity at the initial time t=0. It is proved that the rate of convergence of the maximum nodal error on any subdomain that is bounded away from t=0 is higher than the rate obtained when the maximum nodal error is measured over the entire space-time domain. Numerical results are provided to illustrate the theoretical error bounds

Efficient resolution of singularly perturbed coupled systems: Equations of reaction-diffusion

In this communication we consider a class of singularly perturbed linear system of reaction-diffusion type coupled in the reaction terms. To approximate its solution, in [3] J.L. Gracia, F. Lisbona, A uniformly convergent scheme for a system of reaction–diffusion equations, To appear in J. Comp. Appl. Math. the backward Euler method and the central difference scheme on a layer–adapted mesh of Shishkin type was used. We propose a new semi-implicit method which decouples the linear system to be solved at each time level and we prove that it is a uniformly convergent scheme (with respect to the diffusion parameters) in the discrete maximum norm. We display some numerical experiments illustrating in practice the theoretical results. From these examples we can see both the uniform convergence of the numerical method and also its efficiency to approximate the solution of the reaction–diffusion system

Zoning of potential areas for the production of oleaginous species in Colombia under agroforestry systems

Producción CientíficaDue to the need to develop more agroforestry systems, the Moringa oleifera, Olea Europea, Glycine max, Brassica napus, Helianthus annuus, and Jatropha curcas are identified as unconventional species for their expansion under these systems in Colombia. With the Colombian Environmental Information System (SIAC) database, zoning was carried out according to the agroclimatic species requirements and optimal coverage for their production. As a result, a total area of 212,977.2 km2 was identified, mainly including the departments of Casanare, Arauca, Vichada, Guajira, Córdoba, Meta, Magdalena, Cesar, Tolima, and Cundinamarca. The species and associations species with the most options for productive expansion are Moringa (75,758 km2), Moringa, Jatropha, and Sunflower (42,515.1 km2), Moringa and Jatropha (37,180.4 km2), Jatropha (20,840 km2), Jatropha and Sunflower (17,692.1 km2), Olive (7332.1 km2), and Soybean (3586.3 km2). Of the potential agroforestry areas to their establishment, 36% correspond to herbaceous and/or shrubby vegetation, 34% to grasses, and 22% to heterogeneous agricultural areas. This research is the first step to representing the agronomic versatility of these promising species and their potential contribution to the diversification of the agri-food and agroforestry sectors

A New POD Method for Transport Equations

A novel implementation of the reduced-order model (ROM) of 1D advection-diffusion equation by means of a modified Proper Orthogonal Decomposition (POD) method is presented. This modified method is based on a coordinate transformation (CT-POD) that allows prediction beyond a training time horizon for advection dominated equations

Association between serum copper levels and risk of cardiovascular disease: a nested case-control study in the PREDIMED trial

Background and aim: Certain trace elements have been associated with increased cardiovascular risk. The aim of this study was to evaluate the association between serum copper (SeCu) levels and the risk of a first event of cardiovascular disease (CVD) in a population of older adults with high cardiovascular risk. Methods and results: We conducted a case-control study nested within the PREDIMED trial. During a median follow-up of 4.8 years, a total of 207 incident cases diagnosed with CVD were matched for sex, age, and intervention group with 436 controls. Personal interviews, reviews of medical records, and validated questionnaires were used to assess known CVD risk factors. Biological serum samples were collected annually. Inductively coupled plasma mass spectrometry analysis was used to determine SeCu levels. Adjusted odds ratios were calculated using multivariate conditional logistic regression models. All participants had SeCu levels within the reference values, 750 mg/L to 1450 mg/L. Among men, but not among women, the mean SeCu concentration was higher in cases 1014.1 mg/L than in controls 959.3 mg/L; (p Z 0.004). In men, the multivariable-adjusted odds ratio for CVD was 2.36 (95% CI 1.07e5.20 for the comparison of the highest vs. the lowest quartile; p for trend Z 0.02), in women, it was 0.43 (95% CI 0.11 e1.70; p for trend Z 0.165). Conclusion: In older Spanish men with high cardiovascular risk, a significant association was observed between high SeCu levels, but still within the reference values, and an increased risk of a first event of CVD. Our findings suggest a sex difference in CVD risk and SeCu levels. To confirm this relationship and to analyze the differences observed between men and women, further studies are needed.Funding for open access charge: Universidad de Málaga / CBUA. This research was funded by the official funding agency for biomedical research of the Spanish government, Instituto de Salud Carlos III (ISCIII), through grants provided to research networks specifically developed for the trial (RTIC G03/140; RTIC RD 06/0045 “PREDIMED”), and JR14/00008, and through Centro de Investigación Biomédica en Red de Fisiopatología de la Obesidad y Nutrición (CIBERobn), and by grants from Centro Nacional de Investigaciones Cardiovasculares (CNIC06/2007), the Fondo de Investigación Sanitaria–Fondo Europeo de Desarrollo Regional (Proyecto de Investigación (PI04-2239, PI05/2584, CP06/00100, PI07/0240, PI07/1138, PI07/0954, PI 07/0473, PI10/01407, PI10/02658, PI11/01647, P11/02505 and PI13/00462), the Ministerio de Ciencia e Innovación (Recursos y teconologia agroalimentarias (AGL)-2009-13906-C02 and AGL2010-22319-C03 and AGL2013-49083C3-1-R), the Ministerio de Economía y Competitividad-Fondos FEDER-Instituto de Salud Carlos III (UNGR15-CE-3380), the Fundación Mapfre 2010, the Consejería de Salud de la Junta de Andalucía (PI0105/2007), the Public Health Division of the Department of Health of the Autonomous Government of Catalonia, the Generalitat Valenciana (Generalitat Valenciana Ayuda Complementatia GVACOMP) 06109, GVACOMP2010-181, GVACOMP2011-151), Conselleria de Sanitat y AP; Atención Primaria (CS) 2010-AP-111, and CS2011-AP-042), Regional Government of Navarra (P27/2011), and Centre Català de la Nutrició de l'Institut d'Estudis Catalans. Hojiblanca and Patrimonio Communal Olivarero donated extra-virgin olive oil; the California Walnut Commission donated walnuts; Borges donated almonds; La Morella Nuts donated hazelnuts

Resumen ejecutivo del documento de consenso sobre el manejo de la patología renal en pacientes con infección por VIH

El objetivo de este documento es actualizar las recomendaciones sobre la evaluación y el manejo de la afectación renal en pacientes con infección por el VIH del año 2010. La función renal debe monitorizarse en todos los pacientes e incluir la medida de la concentración sérica de creatinina, la estimación del filtrado glomerular (ecuación CKD-EPI), la medida del cociente proteína/creatinina en orina y un sedimento urinario. El estudio básico de la función tubular ha de incluir la concentración sérica de fosfato y la tira reactiva de orina (glucosuria). En ausencia de alteraciones, el cribado será anual. En pacientes tratados con tenofovir o con factores de riesgo para el desarrollo de enfermedad renal crónica (ERC), se recomienda una evaluación más frecuente. Se debe evitar el uso de antirretrovirales potencialmente nefrotóxicos en pacientes con ERC o factores de riesgo para evitar su progresión. También se revisan las indicaciones de la biopsia renal, cuándo enviar el paciente al nefrólogo y las indicaciones, evaluación y manejo del paciente en diálisis o del trasplante renal