Unesp Ciência, 2016, ano 7, número 74

Revista elaborada pela Assessoria de Comunicação e Imprensa da Reitoria da UNESP

A construção da ideia de número na educação infantil

This paper seeks to understand-the process by which the child in kindergarten builds the idea of number. Therefore we developed a qualitative study of phenomenological approach that involved field work in the classroom with children of four and five years. Starting from their real-world contexts, their experiences and using the natural language tasks are designed to help the student to go beyond the already known, analyzing how they thinks and what knowledge they bring their lived experience. By interference carried expanded mathematical ideas acquired. The analysis and interpretation of research data shows that the idea of number is built by children from all kinds of relationships created between objects and the world around them, and the more diverse are these experiences, the greater the understanding opportunities and development of mathematical skills and competencies. It showed also that, in kindergarten, children tread just a few ways to build the idea of number

Considerações históricas sobre o infinito e alguns de seus paradoxos

This research aims to elucidate some of the historical aspects of the idea of infinity during the creation of calculus and set theory. It also seeks to raise discussions about the nature of infinity: current infinite and potential infinite. For this, we conducted a survey with a qualitative approach in the form of exploratory study. This study was based on books of Mathematics' History and other scientific works such as articles, theses and dissertations on the subject. This work will bring the view of some philosophers and thinkers about the infinite, such as: Pythagoras, Plato, Aristotle, Galilei, Augustine, Cantor. The research will be presented according to chronological order. The objective of the research is to understand the infinite from ancient Greece with the paradoxes of Zeno, during the time which the conflict between the conceptions atomistic and continuity were dominant, and in this context that Zeno launches its paradoxes which contradict much a concept as another, until the theory Cantor set, bringing some paradoxes related to this theory, namely paradox of Russell and Hilbert's paradox. The study also presents these paradoxes mentioned under the mathematical point of view and the light of calculus and set theory

Estudo de sistemas não-lineares em mecânica quântica

The main goal of this work is to investigate the effects of a nonlinear cubic term inserted in the Schrödinger equation for one-dimensional potentials studied in Quantum Mechanics textbooks. Being the main tool the numerical analysis in a large number of works, the analysis of this effect by this term in the potential itself, in order to work with an analytical solution, can be considered something new. For the harmonic oscillator potential, the analysis was made from a numerical method, comparing the result with the known results in the literature. In the case of the infinite well potential and the step potential, hoping to work with an analytical solution, by construction we started with the known wavefunction for the linear case noting the effects in the other physical quantities. The coupling of the physical quantities involved in this work has yielded, besides many complications in the calculations, a series of conditions on the existence and validity of the solutions in regard to the system possible configurations

A construção da ideia de número na educação infantil

This paper seeks to understand-the process by which the child in kindergarten builds the idea of number. Therefore we developed a qualitative study of phenomenological approach that involved field work in the classroom with children of four and five years. Starting from their real-world contexts, their experiences and using the natural language tasks are designed to help the student to go beyond the already known, analyzing how they thinks and what knowledge they bring their lived experience. By interference carried expanded mathematical ideas acquired. The analysis and interpretation of research data shows that the idea of number is built by children from all kinds of relationships created between objects and the world around them, and the more diverse are these experiences, the greater the understanding opportunities and development of mathematical skills and competencies. It showed also that, in kindergarten, children tread just a few ways to build the idea of number

Considerações históricas sobre o infinito e alguns de seus paradoxos

This research aims to elucidate some of the historical aspects of the idea of infinity during the creation of calculus and set theory. It also seeks to raise discussions about the nature of infinity: current infinite and potential infinite. For this, we conducted a survey with a qualitative approach in the form of exploratory study. This study was based on books of Mathematics' History and other scientific works such as articles, theses and dissertations on the subject. This work will bring the view of some philosophers and thinkers about the infinite, such as: Pythagoras, Plato, Aristotle, Galilei, Augustine, Cantor. The research will be presented according to chronological order. The objective of the research is to understand the infinite from ancient Greece with the paradoxes of Zeno, during the time which the conflict between the conceptions atomistic and continuity were dominant, and in this context that Zeno launches its paradoxes which contradict much a concept as another, until the theory Cantor set, bringing some paradoxes related to this theory, namely paradox of Russell and Hilbert's paradox. The study also presents these paradoxes mentioned under the mathematical point of view and the light of calculus and set theory

Estudo de sistemas não-lineares em mecânica quântica

The main goal of this work is to investigate the effects of a nonlinear cubic term inserted in the Schrödinger equation for one-dimensional potentials studied in Quantum Mechanics textbooks. Being the main tool the numerical analysis in a large number of works, the analysis of this effect by this term in the potential itself, in order to work with an analytical solution, can be considered something new. For the harmonic oscillator potential, the analysis was made from a numerical method, comparing the result with the known results in the literature. In the case of the infinite well potential and the step potential, hoping to work with an analytical solution, by construction we started with the known wavefunction for the linear case noting the effects in the other physical quantities. The coupling of the physical quantities involved in this work has yielded, besides many complications in the calculations, a series of conditions on the existence and validity of the solutions in regard to the system possible configurations

Avaliação do número de células caliciformes nas criptas da mucosa colônica com e sem trânsito intestinal

OBJETIVO: Medir a espessura das criptas e quantificar o número de células caliciformes comparando a mucosa cólica com e sem trânsito intestinal, relacionando-as ao tempo de exclusão. MÉTODOS: Sessenta ratos Wistar, foram distribuídos em três grupos com 20 animais segundo a operação final para a retirada dos cólons, realizadas em seis, 12 ou 18 semanas. Em cada grupo, 15 animais foram submetidos à derivação do trânsito por colostomia proximal no cólon esquerdo e fístula mucosa distal e cinco apenas à laparotomia (controle). Os cólons com e sem trânsito fecal foram removidos, processados, submetidos a cortes histológicos corados pela hematoxilina-eosina. A altura das criptas colônicas e o número de células caliciformes foram mensurados por morfometria computadorizada. Foram utilizados os testes t de Student e Kruskal-Wallis para comparação e análise de variância, estabelecendo-se nível de significância de 5% (p<0,05). RESULTADOS: A altura das criptas diminui nos segmentos sem trânsito fecal (p=0,0001), reduzindo entre seis e 12 semanas de exclusão (p=0,0003), estabilizando-se após este período. O número de células caliciformes nas criptas é menor nos segmentos sem trânsito após 12 e 18 semanas (p=0,0001), porém aumenta com o decorrer do tempo de exclusão (p=0,04) CONCLUSÃO: A exclusão do trânsito intestinal diminui a espessura das criptas colônicas e o número de células caliciformes nos segmentos sem trânsito. Existe aumento do número de células caliciformes com o decorrer do tempo de exclusão.

Ensaio de migração de cloretos para concreto: influência do número de fatias extraídas

Ensaios de migração de cloretos são usados para mensurar a capacidade do concreto em inibir o ataque por cloretos. Muitos pesquisadores realizam esse ensaio em uma fatia de concreto extraída da parte central dos corpos de prova cilíndricos, descartando cerca de 75% do concreto usado para moldar os corpos de prova. Esse fato gerou a questão: Seria possível extrair mais fatias de um mesmo corpo de prova sem se perder a confiança nos resultados? O principal objetivo desse trabalho é responder a essa pergunta. Outro objetivo desse estudo foi mostrar a diferença da penetração de cloretos entre as faces finais e as superfícies internas das vigas e lajes de concreto. Os resultados indicaram que é possível usar mais fatias de um único corpo de prova para um teste de migração de cloretos. Além disso, foi demonstrado que houve significativa diferença da penetração de cloretos entre as superfícies acabadas (com desempenadeira - topo do corpo de prova) e as superfícies provenientes das paredes das fôrmas (base do corpo de prova).