The introduction of real numbers in secondary education. An institutional analysis of textbooks

In this paper we analyse the introduction of irrational and real numbers in secondary textbooks, and specifically the propositions on how these should be taught, in a sample of Brazilian textbooks used in state schools and approved by the Ministry of Education. The analyses discussed in this paper follow an institutional perspective (using Chevallard's Anthropological Theory of Didactics). Our results indicate that the notion of irrational number is generally introduced on the basis of the decimal representation of numbers, and that the mathematical need for the construction of the field of real numbers remains unclear in the textbooks. It seems that textbooks used in secondary teaching institutions develop mathematical organisations which focus on the practical block

Derivatives of grindelic acid: from a non-active natural diterpene to synthetic antitumor derivatives

Using several reactions that include homologations and asymmetric epoxidations as well as Ugi and Huisgen couplings, we generated a small focused library of new derivatives from the labdane-type diterpene grindelic acid. These compounds were evaluated as cytotoxic agents against a panel of five human solid tumor cell lines (HBL-100, HeLa, SW1573, T-47D, and WiDr). The presence of the diamide functionalizations enhanced the cytotoxic effect. N-benzyl-N-(1-(benzylamino)-2-methyl-1-oxopropan-2-yl)grindelicamide, proved to be the most active product in all cell lines tested, with values of 0.95 (± 0.38) μM against HBL-100 cells.Fil: Reta, Guillermo Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Investigaciones En Tecnología Química; ArgentinaFil: Chiaramello, Alejandra Ilda. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Investigaciones en Tecnología Química; ArgentinaFil: García, Celina. Universidad de la Laguna. Departamento de Química Orgánica. Instituto Universitario de Bio-orgánica "Antonio Gonzalez"; EspañaFil: León, Leticia G.. Universidad de la Laguna. Departamento de Química Orgánica. Instituto Universitario de Bio-orgánica "Antonio Gonzalez"; EspañaFil: Martín, Victor S.. Universidad de la Laguna. Departamento de Química Orgánica. Instituto Universitario de Bio-orgánica "Antonio Gonzalez"; EspañaFil: Padrón, José M.. Universidad de la Laguna. Departamento de Química Orgánica. Instituto Universitario de Bio-orgánica "Antonio Gonzalez"; EspañaFil: Tonn, Carlos Eugenio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Investigaciones En Tecnología Química; ArgentinaFil: Donadel, Osvaldo Juan. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Investigaciones En Tecnología Química; Argentin

The three-dimensional randomly dilute Ising model: Monte Carlo results

We perform a high-statistics simulation of the three-dimensional randomly dilute Ising model on cubic lattices $L^3$ with $L\le 256$. We choose a particular value of the density, x=0.8, for which the leading scaling corrections are suppressed. We determine the critical exponents, obtaining $\nu = 0.683(3)$, $\eta = 0.035(2)$, $\beta = 0.3535(17)$, and $\alpha = -0.049(9)$, in agreement with previous numerical simulations. We also estimate numerically the fixed-point values of the four-point zero-momentum couplings that are used in field-theoretical fixed-dimension studies. Although these results somewhat differ from those obtained using perturbative field theory, the field-theoretical estimates of the critical exponents do not change significantly if the Monte Carlo result for the fixed point is used. Finally, we determine the six-point zero-momentum couplings, relevant for the small-magnetization expansion of the equation of state, and the invariant amplitude ratio $R^+_\xi$ that expresses the universality of the free-energy density per correlation volume. We find $R^+_\xi = 0.2885(15)$.Comment: 34 pages, 7 figs, few correction

Dynamic structure factor of the Ising model with purely relaxational dynamics

We compute the dynamic structure factor for the Ising model with a purely relaxational dynamics (model A). We perform a perturbative calculation in the $\epsilon$ expansion, at two loops in the high-temperature phase and at one loop in the temperature magnetic-field plane, and a Monte Carlo simulation in the high-temperature phase. We find that the dynamic structure factor is very well approximated by its mean-field Gaussian form up to moderately large values of the frequency $\omega$ and momentum $k$. In the region we can investigate, $k\xi \lesssim 5$, $\omega \tau \lesssim 10$, where $\xi$ is the correlation length and $\tau$ the zero-momentum autocorrelation time, deviations are at most of a few percent.Comment: 21 pages, 3 figure

Critical structure factor in Ising systems

We perform a large-scale Monte Carlo simulation of the three-dimensional Ising model on simple cubic lattices of size L^3 with L=128 and 256. We determine the corresponding structure factor (Fourier transform of the two-point function) and compare it with several approximations and with experimental results. We also compute the turbidity as a function of the momentum of the incoming radiation, focusing in particular on the deviations from the Ornstein-Zernicke expression of Puglielli and Ford.Comment: 16 page

Measurement of the cosmic ray spectrum above 4×10184{\times}10^{18} eV using inclined events detected with the Pierre Auger Observatory

A measurement of the cosmic-ray spectrum for energies exceeding $4{\times}10^{18}$ eV is presented, which is based on the analysis of showers with zenith angles greater than $60^{\circ}$ detected with the Pierre Auger Observatory between 1 January 2004 and 31 December 2013. The measured spectrum confirms a flux suppression at the highest energies. Above $5.3{\times}10^{18}$ eV, the "ankle", the flux can be described by a power law $E^{-\gamma}$ with index $\gamma=2.70 \pm 0.02 \,\text{(stat)} \pm 0.1\,\text{(sys)}$ followed by a smooth suppression region. For the energy ($E_\text{s}$) at which the spectral flux has fallen to one-half of its extrapolated value in the absence of suppression, we find $E_\text{s}=(5.12\pm0.25\,\text{(stat)}^{+1.0}_{-1.2}\,\text{(sys)}){\times}10^{19}$ eV.Comment: Replaced with published version. Added journal reference and DO

Risk factors for non-diabetic renal disease in diabetic patients

Background. Diabetic patients with kidney disease have a high prevalence of non-diabetic renal disease (NDRD). Renal and patient survival regarding the diagnosis of diabetic nephropathy (DN) or NDRD have not been widely studied. The aim of our study is to evaluate the prevalence of NDRD in patients with diabetes and to determine the capacity of clinical and analytical data in the prediction of NDRD. In addition, we will study renal and patient prognosis according to the renal biopsy findings in patients with diabetes. Methods. Retrospective multicentre observational study of renal biopsies performed in patients with diabetes from 2002 to 2014. Results. In total, 832 patients were included: 621 men (74.6%), mean age of 61.7 6 12.8 years, creatinine was 2.8 6 2.2 mg/dL and proteinuria 2.7 (interquartile range: 1.2–5.4) g/24 h. About 39.5% (n ¼ 329) of patients had DN, 49.6% (n ¼ 413) NDRD and 10.8% (n ¼ 90) mixed forms. The most frequent NDRD was nephroangiosclerosis (NAS) (n ¼ 87, 9.3%). In the multivariate logistic regression analysis, older age [odds ratio (OR) ¼ 1.03, 95% CI: 1.02–1.05, P < 0.001], microhaematuria (OR ¼ 1.51, 95% CI: 1.03–2.21, P ¼ 0.033) and absence of diabetic retinopathy (DR) (OR ¼ 0.28, 95% CI: 0.19–0.42, P < 0.001) were independently associated with NDRD. Kaplan–Meier analysis showed that patients with DN or mixed forms presented worse renal prognosis than NDRD (P < 0.001) and higher mortality (P ¼ 0.029). In multivariate Cox analyses, older age (P < 0.001), higher serum creatinine (P < 0.001), higher proteinuria (P < 0.001), DR (P ¼ 0.007) and DN (P < 0.001) were independent risk factors for renal replacement therapy. In addition, older age (P < 0.001), peripheral vascular disease (P ¼ 0.002), higher creatinine (P ¼ 0.01) and DN (P ¼ 0.015) were independent risk factors for mortality. Conclusions. The most frequent cause of NDRD is NAS. Elderly patients with microhaematuria and the absence of DR are the ones at risk for NDRD. Patients with DN presented worse renal prognosis and higher mortality than those with NDRD. These results suggest that in some patients with diabetes, kidney biopsy may be useful for an accurate renal diagnosis and subsequently treatment and prognosis

Mosquitoes infected with dengue viruses in Brazil

Dengue epidemics have been reported in Brazil since 1985. The scenery has worsened in the last decade because several serotypes are circulating and producing a hyper-endemic situation, with an increase of DHF/DSS cases as well as the number of fatalities. Herein, we report dengue virus surveillance in mosquitoes using a Flavivirus genus-specific RT-Hemi-Nested-PCR assay. The mosquitoes (Culicidae, n = 1700) collected in the Northeast, Southeast and South of Brazil, between 1999 and 2005, were grouped into 154 pools. Putative genomes of DENV-1, -2 and -3 were detected in 6 mosquito pools (3.8%). One amplicon of putative DENV-1 was detected in a pool of Haemagogus leucocelaenus suggesting that this virus could be involved in a sylvatic cycle. DENV-3 was found infecting 3 pools of larvae of Aedes albopictus and the nucleotide sequence of one of these viruses was identified as DENV-3 of genotype III, phylogenetically related to other DENV-3 isolated in Brazil. This is the first report of a nucleotide sequence of DENV-3 from larvae of Aedes albopictus