Laws of large numbers for non-additive probabilities

We apply the concept of exchangeable random variables to the case of non-additive robability distributions exhibiting ncertainty aversion, and in the lass generated bya convex core convex non-additive probabilities, ith a convex core). We are able to rove two versions of the law of arge numbers (de Finetti's heorems). By making use of two efinitions. of independence we rove two versions of the strong law f large numbers. It turns out that e cannot assure the convergence of he sample averages to a constant. e then modal the case there is a true" probability distribution ehind the successive realizations of the uncertain random variable. In this case convergence occurs. This result is important because it renders true the intuition that it is possible "to learn" the "true" additive distribution behind an uncertain event if one repeatedly observes it (a sufficiently large number of times). We also provide a conjecture regarding the "Iearning" (or updating) process above, and prove a partia I result for the case of Dempster-Shafer updating rule and binomial trials.

Um estudo de práticas matemáticas históricas e sugestões de uso na matemática escolar

This dissertation aims to contribute on teaching of mathematics for enabling learning connected to the relationship among science, society, culture and cognition. To this end, we propose the involvement of our students with social practices found in history, since. Our intention is to create opportunities for school practices that these mathematical arising from professional practice historical, provide strategies for mathematical thinking and reasoning in the search for solutions to problematizations found today. We believe that the propose of producing Basic Problematization Units, or simply UBPs, in math teacher formation, points to an alternative that allows better utilization of the teaching and learning process of mathematics. The proposal has the aim of primary education to be, really forming the citizen, making it critical and society transformative agent. In this sense, we present some recommendations for exploration and use of these units for teachers to use the material investigated by us, in order to complement their teaching work in mathematics lessons. Our teaching recommendations materialized as a product of exploration on the book, Instrumentos nuevos de geometria muy necessários para medir distancia y alturas sem que interuengan numeros como se demuestra em la practica , written by Andrés de Cespedes, published in Madrid, Spain, in 1606. From these problematizations and the mathematics involved in their solutions, some guidelines for didactic use of the book are presented, so that the teacher can rework such problematizations supported on current issues, and thus use them in the classroom

Plankton-feeding aggregation and occasional cleaning by adult butterflyfish, Chaetodon striatus (Chaetodontidae), in Southwestern Atlantic

Butterflyfishes of the genus Chaetodon (Chaetodontidae) are mostly bottom-feeders, and juveniles of some Pacific species are known to clean other fish, Herein we report on occasional cleaning by adult individuals of the Western Atlantic butterflyfish Chaetodon striatus, during their plankton-feeding aggregation, Four species of reef fish solicited cleaning to the butterflyfish amidst the aggregation.

Further notes on the capture of a Carcharhinus leucas in a northeastern Atlantic oceanic insular shelf, the Azores Archipelago, Portugal

In March 1993, a specimen of Carcharhinus leucas was captured by fishermen on the south coast of Terceira Island, the Azores Archipelago. Its head was recovered and its jaws were preserved. This is the first capture of this species on an oceanic insular shelf in the Atlantic. The distribution of C. leucas in this ocean is commented.

Anuario estadístico de América Latina y el Caribe, 1985 = Statistical yearbook for Latin America and the Caribbean, 1985

Publicado en agosto de 1986

Anuario estadístico de América Latina y el Caribe, 1986 = Statistical yearbook for Latin America and the Caribbean, 1986

Publicado en junio de 1987

Anuario estadístico de América Latina y el Caribe, 1987 = Statistical yearbook for Latin America and the Caribbean, 1987

Incluye Bibliografía

Anuario estadístico de América Latina, 1983 = Statistical yearbook for Latin America, 1983

Publicado en junio de 1984

Reticulados modulares em espaços euclidianos

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Unidades em corpos abelianos

Pós-graduação em Matemática - IBILCE

Caracteres estruturais e dimensão fractal da folha de espécies de Arachis e sua relação com a cercosporiose

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Uso social e escolar dos números racionais: representação fracionária e decimal

Pós-graduação em Educação - FFC

Números complexos e geogebra

Pós-graduação em Matemática em Rede Nacional - IBILCE