Heat and Poisson semigroups for Fourier-Neumann expansions

Given $\alpha > -1$, consider the second order differential operator in $(0,\infty)$, $$L_\alpha f \equiv (x^2 \frac{d^2}{dx^2} + (2\alpha+3)x \frac{d}{dx} + x^2 + (\alpha+1)^2)(f),$$ which appears in the theory of Bessel functions. The purpose of this paper is to develop the corresponding harmonic analysis taking $L_\alpha$ as the analogue to the classical Laplacian. Namely we study the boundedness properties of the heat and Poisson semigroups. These boundedness properties allow us to obtain some convergence results that can be used to solve the Cauchy problem for the corresponding heat and Poisson equations.Comment: 16 page

The role of the Public University of Navarre in achieving the 1st SDG for the end of poverty

The end of poverty is the first of the 17 sustainable development goals of the United Nations. Universities are strategic spaces for promoting the SDGs, from training, research, and outreach capacity to implementing sustainable actions, helping to reduce inequalities and, significantly, promoting sustainable cities and communities. This article aims to answer how the Public University of Navarre contributes to promoting the 1st SDG, what mechanisms for the end of poverty endorses in its territory, and what can we learn from these experiences. To this end, a case study has been carried out based on qualitative techniques. This work analyzes the strategies implemented, such as incorporating social clauses for responsible recruiting, the development of applied research and teaching or network participation. From this example, some engaging lessons will be extracted to address this issue in other contexts, promoting their consolidation and identifying the obstacles that may hinder their spread

Identidad contra identidades : el destino contra Babelia

El impulso de los nacionalismos y la constatación de la crisis ecológica global, son fenómenos paradójicos y contradictorios. En base a las contribuciones desde la sociología de Eisenstadt y Geisen, y desde el derecho y la teoría política de Wendt y Falk, nosotros argumentamos que el concepto de identidad planetaria, al tiempo que se opone conceptualmente al babelismo nacionalista dominante en ciertos sectores intelectuales, puede cimentar las bases para un entendimiento racional del devenir en este fin de siglo.Nationalism and environmental global conscience are contradictory ideas. We argue in this paper, using as a source from the sociological point of view the work of Eisenstadt and Giesen and from the point of view of legal theory the work of Wendt and Falk, that the concept of planetarian identity is rationally sound. We defend that planetarian collective identity may work against the shortcomings of this return to Babelia represented by nationalism, and it may also set a valid framework of reference to understand developments at the end of the twentieth century

Executive functions and their relationship with intellectual capacity and age in schoolchildren with intellectual disability

Background: There is certain empirical evidence of, on the one hand, a positive correlation between executive functions (EFs) and intelligence in people with intellectual disability (ID) and, on the other hand, a slower rate of development of EFs in these people relative to people without ID. This evidence is not, however, unequivocal, and further studies are required. Methods: We analysed the relationship between development of EFs and both age and intellectual capacity, in a sample of 106 students with either ID or borderline intellectual functioning (BIF) at a special education centre [63 boys and 43 girls, 11-18 years old, mean total intelligence quotient (TIQ) of 59.6]. We applied nine instruments to evaluate both neuropsychological development (working memory, inhibitory control, cognitive flexibility, planning, processing speed and verbal fluency) and behavioural development [teachers' perceptions of the EFs of their students by Behavior Rating Inventory of Executive Function - Second Edition (BRIEF-2) School]. ID and BIF groups were statistically compared in terms of mean performance measures in EF tests. We looked at the correlation between EFs and age, and correlations between EFs and intelligence: TIQ, fluid intelligence [measured by the perceptual reasoning (PR) sub-index of Wechsler Intelligence Scale for Children-IV (WISC-IV)] and crystallised intelligence (measured by the verbal comprehension (VC) sub-index of WISC-IV). Regression models were built for variables with strong correlation. Results: In most of the tests used to evaluate EFs, the ID subgroup performed significantly worse than the subgroup with BIF. In general, teachers' thought that participants had 'medium-low' levels of EFs. TIQ, by WISC-IV scale, correlated significantly with scores in all tests for all EFs. The PR sub-index correlated significantly with 14 of the tests for EFs; 35% of the variation in PR can be explained by variation in performance in Picture Span (working memory) and Mazes (planning). The VC sub-index correlated weakly with seven of the EF tests. We found significant correlations in the ID group between age and scores in all tests of working memory and inhibitory control. Age - considering all participants - did not correlate with any of the variables of teachers' perception except for working memory, and this correlation was not strong. Conclusions: The results of our study are consistent with descriptions of the typical population: (1) fluid intelligence is more related to EFs than crystallised intelligence is; and (2) working memory capacity is the EF most strongly related with general, fluid and crystallised forms of intelligence. The results suggest that as children and adolescents with ID/BIF get older, their capacities for working memory and inhibitory control increase; development of the other EFs studied was less evident. Teachers' perceptions of the EFs of children with ID or BIF were independent of intellectual capacity and age. More research is needed to delve further into the development of EFs in people with ID/BIF

Effect of feed evaluation system on the cost of rations for dairy cows

El objetivo del presente trabajo fue comparar la valoración de las necesidades y los aportes de energía calculados según sistemas históricos y modernos de alimentación para vacas lecheras -unidades alimenticias escandinavas (UA), energía neta grasa (ROSTOCK), energía metabolizable (MAFF), energía neta de lactación (NRC) y unidades forrajeras leche (INRA)- con el fin de investigar la repercusión de aquella en el coste de la ración diaria. Las necesidades energéticas se expresaron como energía neta de lactación (ENL) y se calcularon a intervalos de 30 días en leche (DEL) para una vaca Holstein adulta de 680 kg de peso vivo con una producción de 10000 kg de leche en 305 días y un intervalo entre partos de un año. El aporte de ENL según cada sistema se calculó a partir de diez raciones optimizadas con el programa CPMDairy 1.0 para satisfacer las necesidades nutritivas de la vaca modelo cada 30 DEL. Exceptuando los valores obtenidos con el sistema de unidades alimenticias y el comienzo inmediato de la lactación, las diferencias entre las necesidades de ENL calculadas según los distintos sistemas fueron relativamente bajas (entre 1,1 y 7,5%) y achacables fundamentalmente a la valoración energética del cambio de peso. El aporte calculado de energía mostró diferencias importantes entre los sistemas, oscilando de 19,1 a 25,2%. A lo largo de la lactación, los aportes calculados fueron inferiores a las necesidades en todos los sistemas, con la excepción de NRC y MAFF a 30 y 270 DEL, respectivamente, y UA desde 90 DEL. La diferencia promedio estuvo comprendida entre -1,4 ± 1,1 Mcal d-1 (4,5 ± 2,9%; MAFF) y -5,5 ± 1,7 Mcal d-1 (15,6 ± 4,5%; INRA). El coste unitario de la Mcal varió notablemente entre sistemas (de 18,7 a 25,5%) al igual que el coste de satisfacer los requerimientos diarios de energía (de 13,5 a 50,2%). Se concluyó que, independientemente de cual sea la precisión real, el sistema de valoración de energía empleado en la formulación tiene una importante repercusión sobre el coste de las raciones para vacas lecherasThe objective of the present work was to compare energy requirements and supply calculated according to old and modern feed evaluation systems for dairy cattle - Scandinavian feed units (UA), net energy fat (ROSTOCK), metabolizable energy (MAFF), net energy of lactation (NRC) and milk fodder units (INRA) - to assess the differences in the cost of the ration. The energy requirements were expressed as net energy of lactation (NEL) and were calculated every 30 days in milk (DIM) for a mature Holstein cow weighing 680 kg, producing 10000 kg of milk in 305 days, and calving every year. Ten rations optimized with CPM-Dairy 1.0 to satisfy the nutritional requirements of the model cow every 30 DIM were used to compare the calculated NEL supply according to the systems being evaluated. Except for the values obtained according to the feed units system and the onset of lactation, the differences between the systems in the calculated energy requirements were relatively low (from 1.1% to 7.5%) and mainly attributable to the energy value assigned to the live weight change. The differences between the systems in the NEL supply of the rations were high and oscillated between 19.1% and 25.2%. The calculated supplies were smaller than the requirements in all the systems throughout lactation, except for UA from 90 DIM and NRC and MAFF at 30 and 270 DIM, respectively. The average differences were in the range from -1.4 ± 1.1 Mcal d-1 (4.5 ± 2.9%; MAFF) to -5.5 ± 1.7 Mcal d-1 (15.6 ± 4.5%; INRA). The cost of the Mcal differed between the systems (from 18.7% to 25.5%) and the same was true for the cost of satisfying the daily energy requirements (from 13.5% to 50.2%). It was concluded that, without taking into account the real accuracy, the energy evaluation system used in the formulation affects considerably the cost of rations for lactating dairy cattle