Graphical representation and generalization in sequences problems

In this paper we present different ways used by Secondary students to generalize when they try to solve problems involving sequences. 359 Spanish students solved generalization problems in a written test. These problems were posed through particular terms expressed in different representations. We present examples that illustrate different ways of achieving various types of generalization and how students express generalization. We identify graphical representation of generalization as a useful tool of getting other ways of expressing generalization, and we analyze its connection with other ways of expressing it

The role of pressure on the magnetism of bilayer graphene

We study the effect of pressure on the localized magnetic moments induced by vacancies in bilayer graphene in the presence of topological defects breaking the bipartite nature of the lattice. By using a mean-field Hubbard model we address the two inequivalent types of vacancies that appear in the Bernal stacking bilayer graphene. We find that by applying pressure in the direction perpendicular to the layers the critical value of the Hubbard interaction needed to polarize the system decreases. The effect is particularly enhanced for one type of vacancies, and admits straightforward generalization to multilayer graphene in Bernal stacking and graphite. The present results clearly demonstrate that the magnetic behavior of multilayer graphene can be affected by mechanical transverse deformation

Inductive reasoning in the justification of the result of adding two even numbers

In this paper we present an analysis of the inductive reasoning of twelve secondary students in a mathematical problem-solving context. Students were proposed to justify what is the result of adding two even numbers. Starting from the theoretical framework, which is based on Pólya’s stages of inductive reasoning, and our empirical work, we created a category system that allowed us to make a qualitative data analysis. We show in this paper some of the results obtained in a previous study

El pensamiento multiplicativo en los primeros niveles: una investigación en curso

Este artículo muestra los resultados parciales de un estudio empírico sobre el desarrollo de pensamiento multiplicativo en los primeros niveles escolares. Concretamente, se han realizado entrevistas a niños de tercer curso de segundo ciclo de Educación Infantil (cinco años) en las que se han planteado, mediante situaciones manipulables, varios problemas de división que no podían ser resueltos mediante reparto, así como algunas preguntas sobre pensamiento relacional (de tipo proporcional)

Reduced heart rate variability predicts fatigue severity in individuals with chronic fatigue syndrome/myalgic encephalomyelitis

Heart rate variability (HRV) is an objective, non-invasive tool to assessing autonomic dysfunction in chronic fatigue syndrome/myalgic encephalomyelitis (CFS/ME). People with CFS/ME tend to have lower HRV; however, in the literature there are only a few previous studies (most of them inconclusive) on their association with illness-related complaints. To address this issue, we assessed the value of different diurnal HRV parameters as potential biomarker in CFS/ME and also investigated the relationship between these HRV indices and self-reported symptoms in individuals with CFS/ME.Peer ReviewedPostprint (published version

On the computation of Bernstein–Sato ideals

In this paper we compare the approach of Brianc¸onand Maisonobe for computing Bernstein–Sato ideals—based on computations in a Poincar´e–Birkhoff–Witt algebra—with the readily available method of Oaku and Takayama. We show that it can deal with interesting examples that have proved intractable so far.Ministerio de Ciencia y Tecnología BFM-2001-3164Junta de Andalucía FQM-33

Explicit Comparison Theorems for D -modules

We prove in an explicit way a duality formula between two A2-modules Mlog and Mflog associated to a plane curve and we give an application of this duality to the comparison between Mflog and the A2-module of rational functions along the curve. We treat the analytic case as well

Studies on reproduction of the mullet Mugil platanus Günther, 1880 (Actinopterygii, Mugilidae) from the Mar Chiquita coastal lagoon, Argentina: Similarities and differences with related species

The aim of the present study is to provide the first results on the reproductive biology of Mugil platanus, from the Mar Chiquita coastal lagoon (Argentina). To address this topic, we employed mainly female gonads, at both microscopic and macroscopic levels. The following stages of oocyte development were observed: (A) oogonias, (B) primary growth oocyte, (C) cortical alveolus stage, (D) yolked oocytes, and (E) atretic follicle. Also five of the seven stages of gonad maturity were macro and microscopically stated. The potential fecundity ranged between 1,002,026 and 2,548,769 yolked oocytes, with a mean of around 1,800,000 oocytes. The length at first maturity (L 50) was 450.6 total length (TL) and 367.7 standard length (SL) for females, 436.3 TL and 354.9 SL for males, showing a late sexual maturity for both sexes. Seasonal changes in gonadosomatic index (GSI) of females were observed. The mean GSI was ≤1 during six months of the year (January, June-October). Two modes in the ovarian maturation were observed, the most important in April-May and a secondary one in November-December. Both modes, correlated with the CPUE values, are indicative of the mullet migration from the coastal lagoon towards the sea for spawning. Differences and similarities have been found between Mugil platanus and other mugilid species (Mugil cephalus, Mugil curema, Liza aurata, Liza abu, Liza argentea, Myxus elongatus, and Valamugil cunnesius), from the reproductive point of view. The length at first maturity obtained for M. platanus is higher than in other mugilid species and when a relationship between maximum length and L 50 is established the percentage corresponding to Mugil platanus is 75%, while the others range between 50 and 61%.Fil: González Castro, Mariano. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Ciencias Marinas; Argentina. Universidad Autónoma Metropolitana-Iztapalapa; MéxicoFil: Macchi, Gustavo Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Mar del Plata. Instituto de Investigaciones Marinas y Costeras. Subsede Instituto Nacional de Investigación y Desarrollo Pesquero; ArgentinaFil: Cousseau, María Berta. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Ciencias Marinas; Argentin