Alternative Tasks for the Teaching and the Learning of functions: analysis of an intervention in the High School

In this paper we focus on the application of two mathematical alternative tasks to the teaching and learning of functions with high school students. The tasks were elaborated according to the following methodological approach: (i) Problem Solving and/or mathematics investigation and (ii) a pedagogical proposal, which defends that mathematical knowledge is developed by means of a balance between logic and intuition. We employed a qualitative research approach (characterized as a case study) aimed at analyzing the didactic pedagogical potential of this type of methodology in high school. We found that tasks such as those presented and discussed in this paper provide a more significant learning for the students, allowing a better conceptual understanding, becoming still more powerful when one considers the social-cultural context of the students.

Differential calculus and integration of generalized functions over membranes

In this paper we continue the development of the differential calculus started in Aragona et al. (Monatsh. Math. 144: 13-29, 2005). Guided by the so-called sharp topology and the interpretation of Colombeau generalized functions as point functions on generalized point sets, we introduce the notion of membranes and extend the definition of integrals, given in Aragona et al. (Monatsh. Math. 144: 13-29, 2005), to integrals defined on membranes. We use this to prove a generalized version of the Cauchy formula and to obtain the Goursat Theorem for generalized holomorphic functions. A number of results from classical differential and integral calculus, like the inverse and implicit function theorems and Green's theorem, are transferred to the generalized setting. Further, we indicate that solution formulas for transport and wave equations with generalized initial data can be obtained as well.

Using exercise training to counterbalance chronotropic incompetence and delayed heart rate recovery in systemic lupus erythematosus: a randomized trial

Objective. To evaluate the efficacy of a 3-month exercise training program in counteracting the chronotropic incompetence and delayed heart rate recovery in patients with systemic lupus erythematosus (SLE). Methods. A 12-week randomized trial was conducted. Twenty-four inactive SLE patients were randomly assigned into 2 groups: trained (T; n = 15, 3-month exercise program) and nontrained (NT; n = 13). A sex-, body mass index-, and age-matched healthy control (C) group (n = 8) also underwent the exercise program. Subjects were assessed at baseline and at 12 weeks after training. Main measurements included the chronotropic reserve (CR) and the heart rate (HR) recovery (Delta HRR) as defined by the difference between HR at peak exercise and at both the first (Delta HRR1) and second (Delta HRR2) minutes after the exercise test. Results. Neither the NT SLE patients nor the C group presented any change in the CR or in Delta HRR1 and Delta HRR2 (P > 0.05). The exercise training program was effective in promoting significant increases in CR (P = 0.007, effect size [ES] 1.15) and in Delta HRR1 and Delta HRR2 (P = 0.009, ES 1.12 and P = 0.002, ES 1.11, respectively) in the SLE T group when compared with the NT group. Moreover, the HR response in SLE patients after training achieved parameters comparable to the C group, as evidenced by the analysis of variance and by the Z score analysis (P > 0.05, T versus C). Systemic Lupus Erythematosus Disease Activity Index scores remained stable throughout the study. Conclusion. A 3-month exercise training program was safe and capable of reducing the chronotropic incompetence and the delayed Delta HRR observed in physically inactive SLE patients.

The log-exponentiated generalized gamma regression model for censored data

For the first time, we introduce a generalized form of the exponentiated generalized gamma distribution [Cordeiro et al. The exponentiated generalized gamma distribution with application to lifetime data, J. Statist. Comput. Simul. 81 (2011), pp. 827-842.] that is the baseline for the log-exponentiated generalized gamma regression model. The new distribution can accommodate increasing, decreasing, bathtub- and unimodal-shaped hazard functions. A second advantage is that it includes classical distributions reported in the lifetime literature as special cases. We obtain explicit expressions for the moments of the baseline distribution of the new regression model. The proposed model can be applied to censored data since it includes as sub-models several widely known regression models. It therefore can be used more effectively in the analysis of survival data. We obtain maximum likelihood estimates for the model parameters by considering censored data. We show that our extended regression model is very useful by means of two applications to real data.

Growth parameters and mortality rate of the Scomber japonicus peruanus (Jordan & Hubb, 1925) along the Peruvian coast, South Pacific

The growth parameters and the mortality rates of the Scomber japonicus peruanus (Chub mackerel) were studied based on monthly data of frequency of fork length classes obtained from commercial landings off the Peruvian coast from 1996 to 1998. The asymptotic body length and growth rate values obtained by the ELEFAN I (Electronic Length Frequency Analysis) ranged from 40.20 cm to 42.20 cm and from 0.38 to 0.39, respectively. The oscillation amplitude was 0.60; the Winter point values varied from 0.50 to 0.60 and the performance index from 2.79 to 2.84. The total mortality rate of the Chub mackerel obtained by the linearized catch curve oscillated between 1.68 and 3.35. The rate of fishing mortality varied from 1.16 to 2.78 and the exploitation rate from 0.68 to 0.84. The annual rate of natural mortality estimated by the Pauly`s method ranged from 0.52 to 0.53. The results obtained allow us to conclude that the longevity of the Chub mackerel was slightly over seven years.

Generalized beta-generated distributions

This article introduces generalized beta-generated (GBG) distributions. Sub-models include all classical beta-generated, Kumaraswamy-generated and exponentiated distributions. They are maximum entropy distributions under three intuitive conditions, which show that the classical beta generator skewness parameters only control tail entropy and an additional shape parameter is needed to add entropy to the centre of the parent distribution. This parameter controls skewness without necessarily differentiating tail weights. The GBG class also has tractable properties: we present various expansions for moments, generating function and quantiles. The model parameters are estimated by maximum likelihood and the usefulness of the new class is illustrated by means of some real data sets. (c) 2011 Elsevier B.V. All rights reserved.

Improvement in ARDS experimental model installation: Low mortality rate and maintenance of hemodynamic stability

Introduction: Many experimental models using lung lavage have been developed for the study of acute respiratory distress syndrome (ARDS). The original technique has been modified by many authors, resulting in difficulties with reproducibility. There is insufficient detail on the lung injury models used, including hemodynamic stability during animal preparation and drawbacks encountered such as mortality. The authors studied the effects of the pulmonary recruitment and the use of fixed tidal volume (Vt) or fixed inspiratory pressure in the experimental ARDS model installation. Methods: Adult rabbits were submitted to repeated lung lavages with 30 ml/kg warm saline until the ARDS definition (PaO2/FiO(2) <= 100) was reached. The animals were divided into three groups, according to the technique used for mechanical ventilation: 1) fixed Vt of 10 ml/kg; 2) fixed inspiratory pressure (IP) with a tidal volume of 10 ml/kg prior to the first lung lavage; and 3) fixed Vt of 10 ml/kg with pulmonary recruitment before the first lavage. Results: The use of alveolar recruitment maneuvers, and the use of a fixed Vt or IP between the lung lavages did not change the number of lung lavages necessary to obtain the experimental model of ARDS or the hemodynamic stability of the animals during the procedure. A trend was observed toward an increased mortality rate with the recruitment maneuver and with the use of a fixed IP. Discussion: There were no differences between the three study groups, with no disadvantage in method of lung recruitment, either fixed tidal volume or fixed inspiratory pressure, regarding the number of lung lavages necessary to obtain the ARDS animal model. Furthermore, the three different procedures resulted in good hemodynamic stability of the animals, and low mortality rate. (C) 2012 Elsevier Inc. All rights reserved.

Analog circuit synthesis performing fast Pareto frontier exploration and analysis through 3D graphs

This paper presents a technique for performing analog design synthesis at circuit level providing feedback to the designer through the exploration of the Pareto frontier. A modified simulated annealing which is able to perform crossover with past anchor points when a local minimum is found which is used as the optimization algorithm on the initial synthesis procedure. After all specifications are met, the algorithm searches for the extreme points of the Pareto frontier in order to obtain a non-exhaustive exploration of the Pareto front. Finally, multi-objective particle swarm optimization is used to spread the results and to find a more accurate frontier. Piecewise linear functions are used as single-objective cost functions to produce a smooth and equal convergence of all measurements to the desired specifications during the composition of the aggregate objective function. To verify the presented technique two circuits were designed, which are: a Miller amplifier with 96 dB Voltage gain, 15.48 MHz unity gain frequency, slew rate of 19.2 V/mu s with a current supply of 385.15 mu A, and a complementary folded cascode with 104.25 dB Voltage gain, 18.15 MHz of unity gain frequency and a slew rate of 13.370 MV/mu s. These circuits were synthesized using a 0.35 mu m technology. The results show that the method provides a fast approach for good solutions using the modified SA and further good Pareto front exploration through its connection to the particle swarm optimization algorithm.

Effects of light intensity and temperature on Cylindrospermopsis raciborskii (Cyanobacteria) with straight and coiled trichomes: growth rate and morphology

Cylindrospermopsis raciborskii (Woloszynska) Seenayya et Subba Raju (Ordem Nostocales) is one of the most troublesome bloom-forming species in Brazil. Understanding the population dynamics of the different morphotypes of C. raciborskii (straight and coiled) could assist in the prediction of favourable conditions for the proliferation of this potentially toxin-producing species. The aim of the present study was to assess the effects of two different light intensities and temperatures on the growth rate and morphology of the trichomes of the straight and coiled morphotypes. For such, two non-toxin producing strains of C. raciborskii were used - one with a coiled trichome (ITEP31) and another with a straight trichome (ITEP28). The strains were cultured in BG-11 medium in a climatic chamber under controlled conditions. Two light intensities (30 and 90 mu mol.m(-2).s(-1)) were combined at temperatures of 21 and 31 degrees C and the growth rate and morphological changes were analysed. The morphotypes responded differently to the different temperatures and light intensities. Both strains exhibited faster growth velocities when submitted to higher light intensity and temperature. The lower temperature and higher luminosity hampered the development of both strains. Variations in cellular morphology and an absence of akinetes in both strains were related to the lower temperature (21 C). The coiled morphotype demonstrated considerable phenotype plasticity, changing the morphology of trichome throughout its growth curve. Although molecular analysis does not sustain the separation of the morphotypes as distinct species, their different eco-physiological responses should be considered further knowledge of extreme importance for the population control of these potentially toxic organisms.

Apoptosis rate and transcriptional response of pancreatic islets exposed to the PPAR gamma agonist Pioglitazone

To explore the molecular pathways underlying thiazolidinediones effects on pancreatic islets in conditions mimicking normo- and hyperglycemia, apoptosis rate and transcriptional response to Pioglitazone at both physiological and supraphysiological glucose concentrations were evaluated. Adult rat islets were cultured at physiological (5.6 mM) and supraphysiological (23 mM) glucose concentrations in presence of 10 μM Pioglitazone or vehicle. RNA expression profiling was evaluated with the PancChip 13k cDNA microarray after 24-h, and expression results for some selected genes were validated by qRT-PCR. The effects of Pioglitazone were investigated regarding apoptosis rate after 24-, 48- and 72-h. At 5.6 mM glucose, 101 genes were modulated by Pioglitazone, while 1,235 genes were affected at 23 mM glucose. Gene networks related to lipid metabolism were identified as altered by Pioglitazone at both glucose concentrations. At 23 mM glucose, cell cycle and cell death pathways were significantly regulated as well. At 5.6 mM glucose, Pioglitazone elicited a transient reduction in islets apoptosis rate while at 23 mM, Bcl2 expression was reduced and apoptosis rate was increased by Pioglitazone. Our data demonstrate that the effect of Pioglitazone on gene expression profile and apoptosis rate depends on the glucose concentration. The modulation of genes related to cell death and the increased apoptosis rate observed at supraphysiological glucose concentration raise concerns about Pioglitazone’s direct effects in conditions of hyperglycemia and reinforce the necessity of additional studies designed to evaluate TZDs effects on the preservation of β-cell function in situations where glucotoxicity might be more relevant than lipotoxicity.