Different moments in the participatory stage of the secondary students’ abstraction of mathematical conceptions

This study provides support to the characteristics of participatory and anticipatory stages in secondary school pupils’ abstraction of mathematical conceptions. We carried out clinical task-based interviews with 71 secondary-school pupils to obtain evidence of the different constructed mathematical conceptions (Participatory Stage) and how they were used (Anticipatory Stage). We distinguish two moments in the Participatory Stage based on the coordination of information from particular cases by activity-effect reflection which, in some cases, lead to a change of focus enabling secondary-school pupils to achieve a reorganization of their knowledge. We argue that (a) the capacity of perceiving regularities in sets of particular cases is a characteristic of activity-effect reflection in the abstraction of mathematical conceptions in secondary school, and (b) the coordination of information by pupils provides opportunities for changing the attention-focus from the particular results to the structure of properties.

Models of social networks based on social distance attachment

We propose a class of models of social network formation based on a mathematical abstraction of the concept of social distance. Social distance attachment is represented by the tendency of peers to establish acquaintances via a decreasing function of the relative distance in a representative social space. We derive analytical results (corroborated by extensive numerical simulations), showing that the model reproduces the main statistical characteristics of real social networks: large clustering coefficient, positive degree correlations, and the emergence of a hierarchy of communities. The model is confronted with the social network formed by people that shares confidential information using the Pretty Good Privacy (PGP) encryption algorithm, the so-called web of trust of PGP.

Topological Invariants in Hydrodynamics and Hydromagnetics

In this thesis we are studying possible invariants in hydrodynamics and hydromagnetics. The concept of flux preservation and line preservation of vector fields, especially vorticity vector fields, have been studied from the very beginning of the study of fluid mechanics by Helmholtz and others. In ideal magnetohydrodynamic flows the magnetic fields satisfy the same conservation laws as that of vorticity field in ideal hydrodynamic flows. Apart from these there are many other fields also in ideal hydrodynamic and magnetohydrodynamic flows which preserves flux across a surface or whose vector lines are preserved. A general study using this analogy had not been made for a long time. Moreover there are other physical quantities which are also invariant under the flow, such as Ertel invariant. Using the calculus of differential forms Tur and Yanovsky classified the possible invariants in hydrodynamics. This mathematical abstraction of physical quantities to topological objects is needed for an elegant and complete analysis of invariants.Many authors used a four dimensional space-time manifold for analysing fluid flows. We have also used such a space-time manifold in obtaining invariants in the usual three dimensional flows.In chapter one we have discussed the invariants related to vorticity field using vorticity field two form w2 in E4. Corresponding to the invariance of four form w2 ^ w2 we have got the invariance of the quantity E. w. We have shown that in an isentropic flow this quantity is an invariant over an arbitrary volume.In chapter three we have extended this method to any divergence-free frozen-in field. In a four dimensional space-time manifold we have defined a closed differential two form and its potential one from corresponding to such a frozen-in field. Using this potential one form w1 , it is possible to define the forms dw1 , w1 ^ dw1 and dw1 ^ dw1 . Corresponding to the invariance of the four form we have got an additional invariant in the usual hydrodynamic flows, which can not be obtained by considering three dimensional space.In chapter four we have classified the possible integral invariants associated with the physical quantities which can be expressed using one form or two form in a three dimensional flow. After deriving some general results which hold for an arbitrary dimensional manifold we have illustrated them in the context of flows in three dimensional Euclidean space JR3. If the Lie derivative of a differential p-form w is not vanishing,then the surface integral of w over all p-surfaces need not be constant of flow. Even then there exist some special p-surfaces over which the integral is a constant of motion, if the Lie derivative of w satisfies certain conditions. Such surfaces can be utilised for investigating the qualitative properties of a flow in the absence of invariance over all p-surfaces. We have also discussed the conditions for line preservation and surface preservation of vector fields. We see that the surface preservation need not imply the line preservation. We have given some examples which illustrate the above results. The study given in this thesis is a continuation of that started by Vedan et.el. As mentioned earlier, they have used a four dimensional space-time manifold to obtain invariants of flow from variational formulation and application of Noether's theorem. This was from the point of view of hydrodynamic stability studies using Arnold's method. The use of a four dimensional manifold has great significance in the study of knots and links. In the context of hydrodynamics, helicity is a measure of knottedness of vortex lines. We are interested in the use of differential forms in E4 in the study of vortex knots and links. The knowledge of surface invariants given in chapter 4 may also be utilised for the analysis of vortex and magnetic reconnections.

Construção, caracterização global e local de redes biológicas

A Biologia Sistêmica visa a compreensão da vida através de modelos integrativos que enfatizem as interações entre os diferentes agentes biológicos. O objetivo é buscar por leis universais, não nas partes componentes dos sistemas mas sim nos padrões de interação dos elementos constituintes. As redes complexas biológicas são uma poderosa abstração matemática que permite a representação de grandes volumes de dados e a posterior formulação de hipóteses biológicas. Nesta tese apresentamos as redes biológicas integradas que incluem interações oriundas do metabolismo, interação física de proteínas e regulação. Discutimos sua construção e ferramentas para sua análise global e local. Apresentamos também resultados do uso de ferramentas de aprendizado de máquina que nos permitem compreender a relação entre propriedades topológicas e a essencialidade gênica e a previsão de genes mórbidos e alvos para drogas em humanos

Estruturas metodológicas direcionadas ao ensino de cinemática para educandos diagnosticados com TDAH : utilizando o modellus como interface interativa entre a teoria e a experimentação

Dissertação (mestrado)—Universidade de Brasília, Instituto de Física, Programa de Pós-Graduação em Física, 2015.

Generalization by symbolic abstraction in cascaded recurrent networks

Generalization performance in recurrent neural networks is enhanced by cascading several networks. By discretizing abstractions induced in one network, other networks can operate on a coarse symbolic level with increased performance on sparse and structural prediction tasks. The level of systematicity exhibited by the cascade of recurrent networks is assessed on the basis of three language domains. (C) 2004 Elsevier B.V. All rights reserved.

Reading comprehension and mathematical concept acquisition through the use of math stories with bilingual children

Math storybooks are picture books in which the understanding of mathematical concepts is central to the comprehension of the story. Math stories have provided useful opportunities for children to expand their skills in the language arts area and to talk about mathematical factors that are related to their real lives. The purpose of this study was to examine bilingual children's reading and math comprehension of the math storybooks. ^ The participants were randomly selected from two Korean schools and two public elementary schools in Miami, Florida. The sample consisted of 63 Hispanic American and 43 Korean American children from ages five to seven. A 2 x 3 x (2) mixed-model design with two between- and one within-subjects variable was used to conduct this study. The two between-subjects variables were ethnicity and age, and the within-subjects variable was the subject area of comprehension. Subjects were read the three math stories individually, and then they were asked questions related to reading and math comprehension. ^ The overall ANOVA using multivariate tests was conducted to evaluate the factor of subject area for age and ethnicity. As follow-up tests for a significant main effect and a significant interaction effect, pairwise comparisons and simple main effect tests were conducted, respectively. ^ The results showed that there were significant ethnicity and age differences in total comprehension scores. There were also age differences in reading and math comprehension, but no significant differences were found in reading and math by ethnicity. Korean American children had higher scores in total comprehension than those of Hispanic American children, and they showed greater changes in their comprehension skills at the younger ages, from five to six, whereas Hispanic American children showed greater changes at the older ages, from six to seven. Children at ages five and six showed higher scores in reading than in math, but no significant differences between math and reading comprehension scores were found at age seven. ^ Through schooling with integrated instruction, young bilingual children can move into higher levels of abstraction and concepts. This study highlighted bilingual children's general nature of thinking and showed how they developed reading and mathematics comprehension in an integrated process. ^

Simplified Mathematical Model for an Anaerobic Sequencing Batch Biofilm Reactor Treating Lipid-Rich Wastewater Subject to Rising Organic Loading Rates

This study proposes a simplified mathematical model to describe the processes occurring in an anaerobic sequencing batch biofilm reactor (ASBBR) treating lipid-rich wastewater. The reactor, subjected to rising organic loading rates, contained biomass immobilized cubic polyurethane foam matrices, and was operated at 32 degrees C +/- 2 degrees C, using 24-h batch cycles. In the adaptation period, the reactor was fed with synthetic substrate for 46 days and was operated without agitation. Whereas agitation was raised to 500 rpm, the organic loading rate (OLR) rose from 0.3 g chemical oxygen demand (COD) . L(-1) . day(-1) to 1.2 g COD . L(-1) . day(-1). The ASBBR was fed fat-rich wastewater (dairy wastewater), in an operation period lasting for 116 days, during which four operational conditions (OCs) were tested: 1.1 +/- 0.2 g COD . L(-1) . day(-1) (OC1), 4.5 +/- 0.4 g COD . L(-1) . day(-1) (OC2), 8.0 +/- 0.8 g COD . L(-1) . day(-1) (OC3), and 12.1 +/- 2.4 g COD . L(-1) . day(-1) (OC4). The bicarbonate alkalinity (BA)/COD supplementation ratio was 1:1 at OC1, 1:2 at OC2, and 1:3 at OC3 and OC4. Total COD removal efficiencies were higher than 90%, with a constant production of bicarbonate alkalinity, in all OCs tested. After the process reached stability, temporal profiles of substrate consumption were obtained. Based on these experimental data a simplified first-order model was fit, making possible the inference of kinetic parameters. A simplified mathematical model correlating soluble COD with volatile fatty acids (VFA) was also proposed, and through it the consumption rates of intermediate products as propionic and acetic acid were inferred. Results showed that the microbial consortium worked properly and high efficiencies were obtained, even with high initial substrate concentrations, which led to the accumulation of intermediate metabolites and caused low specific consumption rates.

Deterministic mathematical model for the prediction of the as-cast macrostructure

A multiphase deterministic mathematical model was implemented to predict the formation of the grain macrostructure during unidirectional solidification. The model consists of macroscopic equations of energy, mass, and species conservation coupled with dendritic growth models. A grain nucleation model based on a Gaussian distribution of nucleation undercoolings was also adopted. At some solidification conditions, the cooling curves calculated with the model showed oscillations (""wiggles""), which prevented the correct prediction of the average grain size along the structure. Numerous simulations were carried out at nucleation conditions where the oscillations are absent, enabling an assessment of the effect of the heat transfer coefficient on the average grain size and columnar-to-equiaxed transition.

On the solubility of proteins as a function of pH: Mathematical development and application

Thermodynamic relations between the solubility of a protein and the solution pH are presented in this work. The hypotheses behind the development are that the protein chemical potential in liquid phase can be described by Henry`s law and that the solid-liquid equilibrium is established only between neutral molecules. The mathematical development results in an analytical expression of the solubility curve, as a function of the ionization equilibrium constants, the pH and the solubility at the isoelectric point. It is shown that the same equation can be obtained either by directly calculating the fraction of neutral protein molecules or by integrating the curve of the protein average charge. The methodology was successfully applied to the description of the solubility of porcine insulin as a function of pH at three different temperatures and of bovine beta-lactoglobulin at four different ionic strengths. (C) 2011 Elsevier B.V. All rights reserved.

A mathematical view of biological complexity

This essay is a trial on giving some mathematical ideas about the concept of biological complexity, trying to explore four different attributes considered to be essential to characterize a complex system in a biological context: decomposition, heterogeneous assembly, self-organization, and adequacy. It is a theoretical and speculative approach, opening some possibilities to further numerical and experimental work, illustrated by references to several researches that applied the concepts presented here. (C) 2008 Elsevier B.V. All rights reserved.

A mathematical model of HIV transmission in NSW prisons

A mathematical model was developed to estimate HIV incidence in NSW prisons. Data included: duration of imprisonment; number of inmates using each needle; lower and higher number of shared injections per IDU per week; proportion of IDUs using bleach; efficacy of bleach; HIV prevalence and probability of infection. HIV prevalence in IDUs in prison was estimated to have risen from 0.8 to 5.7% (12.2%) over 180 weeks when using lower (and higher) values for frequency of shared injections. The estimated minimum (and maximum) number of IDU inmates infected with HIV in NSW prisons was 38 (and 152) in 1993 according to the model. These figures require confirmation by seroincidence studies. (C) 1998 Published by Elsevier Science Ireland Ltd. All rights reserved.

A mathematical model for estimating the extent of solute- and water-flux heterogeneity in multiple sample percolation experiments

Multiple sampling is widely used in vadose zone percolation experiments to investigate the extent in which soil structure heterogeneities influence the spatial and temporal distributions of water and solutes. In this note, a simple, robust, mathematical model, based on the beta-statistical distribution, is proposed as a method of quantifying the magnitude of heterogeneity in such experiments. The model relies on fitting two parameters, alpha and zeta to the cumulative elution curves generated in multiple-sample percolation experiments. The model does not require knowledge of the soil structure. A homogeneous or uniform distribution of a solute and/or soil-water is indicated by alpha = zeta = 1, Using these parameters, a heterogeneity index (HI) is defined as root 3 times the ratio of the standard deviation and mean. Uniform or homogeneous flow of water or solutes is indicated by HI = 1 and heterogeneity is indicated by HI > 1. A large value for this index may indicate preferential flow. The heterogeneity index relies only on knowledge of the elution curves generated from multiple sample percolation experiments and is, therefore, easily calculated. The index may also be used to describe and compare the differences in solute and soil-water percolation from different experiments. The use of this index is discussed for several different leaching experiments. (C) 1999 Elsevier Science B.V. All rights reserved.

Modelling socially optimal land allocations for sugar cane growing in North Queensland: a linked mathematical programming and choice modelling study

A modelling framework is developed to determine the joint economic and environmental net benefits of alternative land allocation strategies. Estimates of community preferences for preservation of natural land, derived from a choice modelling study, are used as input to a model of agricultural production in an optimisation framework. The trade-offs between agricultural production and environmental protection are analysed using the sugar industry of the Herbert River district of north Queensland as an example. Spatially-differentiated resource attributes and the opportunity costs of natural land determine the optimal tradeoffs between production and conservation for a range of sugar prices.