SOBRE OS ARRANJOS VISUAIS DOS LIVROS DIDÁTICOS DE GEOGRAFIA

O texto aborda a questão dos novos arranjos visuais dos livros didáticos de Geografia tendo como base a análise da coleção “Expedições Geográficas”, de autoria de Melhem Adas e Sérgio Adas. Essa coleção é editada pela Editora Moderna e marcou a preferência dos professores das escolas públicas brasileiras, ocupando o primeiro lugar no ranking das coleções adquiridas no Programa Nacional do Livro e do Material Didático (PNLD/2017). Foram distribuídas mais de três milhões de exemplares dessa obra em escolas de todo território nacional. Por meio da pesquisa documental o estudo mostra que os livros didáticos de Geografia estão se reestruturando em termos de seus aspectos formais do projeto editorial gráfico e de seus conteúdos enunciados (geográficos e pedagógicos), a partir de novas configurações icônicas, mais condizentes com o universo das mídias e dos layouts, do hipertexto e do ambiente digital. Palavras Chave Livro didático, Ensino de Geografia, Imagens. ABOUT THE VISUAL ARRANGEMENTS OF THE GEOGRAPHY TEXTBOOKS Abstract The text announces the issue of new visual arrangements for Geography textbooks based on the analysis of the collection “Expedições Geograficas”, by Melhem Adas and Sérgio Adas. This collection is edited by Editora Moderna and marked the preference of teachers from Brazilian public schools, occupying the first place in the ranking of collections acquired in the Programa Nacional do Livro e do Material Didático (PNLD / 2017). More than three million copies of this work were distributed to schools in the Brazil. Using document analysis, the study shows that Geography textbooks are restructuring in terms of their formal aspects of the graphic editorial project and their enunciated content (geographic and pedagogical), based on new iconic configurations, more consistent with the universe of media and layouts, hypertext and the digital nets. Keywords Textbook, Geography teaching, Images.

Richardson extrapolation allows truncation of higher-order digital nets and sequences

We study numerical integration of smooth functions defined over the $s$-dimensional unit cube. A recent work by Dick et al. (2019, Richardson extrapolation of polynomial lattice rules. SIAM J. Numer. Anal., 57, 44–69) has introduced so-called extrapolated polynomial lattice rules, which achieve the almost optimal rate of convergence for numerical integration, and can be constructed by the fast component-by-component search algorithm with smaller computational costs as compared to interlaced polynomial lattice rules. In this paper we prove that, instead of polynomial lattice point sets, truncated higher-order digital nets and sequences can be used within the same algorithmic framework to explicitly construct good quadrature rules achieving the almost optimal rate of convergence. The major advantage of our new approach compared to original higher-order digital nets is that we can significantly reduce the precision of points, i.e., the number of digits necessary to describe each quadrature node. This finding has a practically useful implication when either the number of points or the smoothness parameter is so large that original higher-order digital nets require more than the available finite-precision floating-point representations.

The Bb-adic Symmetrization of Digital Nets for Quasi-Monte Carlo Integration

The notion of symmetrization, also known as Davenport’s reflection principle, is well known in the area of the discrepancy theory and quasi- Monte Carlo (QMC) integration. In this paper we consider applying a symmetrization technique to a certain class of QMC point sets called digital nets over ℤb. Although symmetrization has been recognized as a geometric technique in the multi-dimensional unit cube, we give another look at symmetrization as a geometric technique in a compact totally disconnected abelian group with dyadic arithmetic operations. Based on this observation we generalize the notion of symmetrization from base 2 to an arbitrary base b ∈ ℕ, b ≥ 2. Subsequently, we study the QMC integration error of symmetrized digital nets over ℤb in a reproducing kernel Hilbert space. The result can be applied to component-by-component construction or Korobov construction for finding good symmetrized (higher order) polynomial lattice rules which achieve high order convergence of the integration error for smooth integrands at the expense of an exponential growth of the number of points with the dimension. Moreover, we consider two-dimensional symmetrized Hammersley point sets in prime base b, and prove that the minimum Dick weight is large enough to achieve the best possible order of Lp discrepancy for all 1 ≤ p < ∞.

A search for extensible low-WAFOM point sets

Matsumoto, Saito and Matoba recently proposed the Walsh figure of merit (WAFOM), which is a computable criterion for quasi-Monte Carlo point sets using digital nets. Several algorithms have been proposed for finding low-WAFOM point sets. In the existing algorithms, the number of points is fixed in advance, but extensible point sets are preferred in some applications. In this paper, we propose a random search algorithm for extensible low-WAFOM point sets. For this, we introduce a method that uses lookup tables to compute WAFOM faster. Numerical results show that our extensible low-WAFOM point sets are comparable with Niederreiter–Xing sequences for some low-dimensional and smooth test functions.