WIRIS OM tools: a semantic formula editor

With the increasing reliance on computers for the automatic processing of information a new method is needed for editing mathematical formulae. We are used to WYSIWYG editors that produce beautiful presentations of formulae and store the typesetting primitives rather than the meaning of the formulas. However, new services such as database searching or calculation web-services work best if they have access to the semantic information behind a formula. This can only be done with a new generation of formula editors. In this paper we present WIRIS OM Tools [17], a semantic oriented formula editor which addresses these concerns. It is based on the OpenMath language and a suitable transformation process between OpenMath and MathML ex- pressions. Additionally, this approach adds new features for the users such as error, type and syntax checking. The editor is currently being used in the LeActiveMath and WebALT projects

Оценка числа решетчатых разбиений плоскости на полимино заданной площади

We study a problem of a number of lattice plane tilings by given area polyominoes. A polyomino is a connected plane geometric figure formed by joining edge to edge a finite number of unit squares. A tiling is a lattice tiling if each tile can be mapped to any other tile by translation which maps the whole tiling to itself. Let T(n) be a number of lattice plane tilings by given area polyominoes such that its translation lattice is a sublattice of Z². It is proved that 2n−3 + 2[ n−3 2 ] ≤ T(n) ≤ C(n + 1)3 (2.7)n+1. In the proof of a lower bound we give an explicit construction of required lattice plane tilings. The proof of an upper bound is based on a criterion of the existence of lattice plane tiling by polyomino and on the theory of self-avoiding walk. Also, it is proved that almost all polyominoes that give lattice plane tilings have sufficiently large perimeters.Рассматривается задача о числе решетчатых разбиений плоскости на полимино заданной площади. Полимино представляет собой связную фигуру на плоскости, составленную из конечного числа единичных квадратов, примыкающих друг к другу по сторонам. Разбиение называется решетчатым, если любую фигуру разбиения можно перевести в любую другую фигуру параллельным переносом, переводящим все разбиение в себя. Пусть T(n) – число решетчатых разбиений плоскости на полимино площади n, решетка периодов которых является подрешеткой решетки Z² . Доказано, что 2 n−3 + 2[ n−3 2 ] ≤ T(n) ≤ C(n + 1)3 (2.7)n+1. При доказательстве нижней оценки использована явная конструкция, позволяющая построить требуемое число решетчатых разбиений плоскости. Доказательство верхней оценки основано на одном критерии существования решетчатого разбиения плоскости на полимино, а также на теории самонепересекающихся блужданий на квадратной решетке. Также доказано, что почти все полимино, дающие решетчатые разбиения плоскости, имеют большой периметр

WIRIS OM Tools: a Semantic Formula Editor

With the increasing reliance on computers for the automatic processing of information a new method is needed for editing mathematical formulae. We are used to WYSIWYG editors that produce beautiful presentations of formulae and store the typesetting primitives rather than the meaning of the formulas. However, new services such as database searching or calculation web-services work best if they have access to the semantic information behind a formula. This can only be done with a new generation of formula editors. In this paper we present WIRIS OM Tools [17], a semantic oriented formula editor which addresses these concerns. It is based on the OpenMath language and a suitable transformation process between OpenMath and MathML ex- pressions. Additionally, this approach adds new features for the users such as error, type and syntax checking. The editor is currently being used in the LeActiveMath and WebALT projects

Genèse de l’ordonnance du 23 décembre 1958 sur l’enfance en danger

Notre propos se limitera à la période la plus récente qui précède la construction de l’ordonnance, celle qui à partir de 1942 se déroule sur un fond d’enjeux de territoire entre le ministère de la Justice, le ministère de la Santé et à un degré moindre le ministère de l’Éducation nationale. On sait combien pendant la guerre et l’après-guerre, le gouvernement de Vichy et les gouvernements qui suivent la Libération attachent une grande importance à l’enfance, à la jeunesse. Une enfance qu’il fa..

Crossing-free paths in the square grid

We consider paths in the 2D square grid, composed of grid edges, given as a sequence of moves in the four cardinal compass directions, without U-turns, but possibly passing several times through the same vertex or the same edge (if the path is open, it cannot pass twice through its starting vertex). We propose an algorithm which reports a self-crossing if there is one, or otherwise draws the path without self-crossings. The algorithm follows the intuitive idea naturally applied by humans to draw a curve: at each vertex that has already been visited, it tries to insert two new segments in such a way that they do not cross the existing ones. If this is not possible, a self-crossing is reported. This procedure is supported by a data structure combining a doubly-linked circular list and a skip list. The time and space complexity is linear in the length of the path

O cristianismo como estilo e igreja em saída: convergências entre a teologia de Christoph Theobald e a perspectiva eclesial do Papa Francisco

Os autores levantam a hipótese de uma convergência entre a teologia de Christoph Theobald e a igreja em saída do Papa Francisco. O artigo parte do itinerário do teólogo europeu para identificar os traços biográficos de uma nova maneira de fazer teologia caracterizada como uma teologia “em saída”. Na sequência, a reflexão abre três dossiês com base, fundamentalmente, em três obras para destacar as evoluções do pensamento theobaldeano. Primeiro mostra-se como o autor encara os desafios do crer e da transmissão da fé na pós-modernidade. Segundo: trata-se a questão doutrinal do autor, objeto da principal crítica feita à sua teologia. Enfim, apresenta-se uma reflexão na qual Theobald, apoiando-se em algumas expressões-chaves do Papa Francisco, postula a necessária e urgente transformação missionária da Igreja

The q-exponential Generating Function for Permutations by Consecutive Patterns and Inversions

The inverse of Fedou\u27s insertion-shift bijection is used to deduce a general form for the q-exponential generating function for permutations by consecutive patterns (overlaps allowed) and inversion number from a result due to Jackson and Goulden for enumerating words by distinguished factors. Explicit q-exponential generating functions are then derived for permutations by the consecutive patterns 12…m, 12…(m−2)m(m−1), 1m(m−1)…2, and by the pair of consecutive patterns (123,132)

Adjacencies in Words

Based on two inversion formulas for enumerating words in the free monoid by adjacencies, we present a new approach to a class of permutation problems having Eulerian-type generating functions. We also show that a specialization of one of the inversion formulas gives Diekert\u27s lifting to the free monoid of an inversion theorem due to Cartier and Foata