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The aim of this paper is to find a closed form of the integrals ∫ 0 π cos( x sin( t ) − nt ) d t for n = 0, 1, 2, … using the Maple computer algebra system. Although Maple 10 is not capable to calculate these integrals in one step, it turns out to be a very useful tool to solve this and similar kind of complex mathematical problems. During the problem solving process Maple proves that it is useful and, what is more, it is an indispensable partner. Maple helps us to formulate our conjecture, acts as an advisor and, last but not least, performs complex symbolic calculation instead of us.

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The graph of a set grammar is introduced in such a way that each set rule of the grammar is represented by a cartesian subgraph of it. The correspondence between cartesian subgraphs and transitions of Petri nets (which satisfy the axiom of extensionality) is established. The set grammars with input (initial) and output (terminal) elements are studied in an analogy to Chomsky's string grammars and their strong equivalence. Permit rules and parallel permit rules are introduced in such a way that parallel permit grammars are more general tools than Petri nets themselves, because the equivalence between homogeneous parallel permit grammars and set grammars (and Petri nets) is proved.

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The first known drawings of machines can be found in warfare-themed manuscripts. The oldest of them dates back to the 14th century, but their proliferation took place in the 15th century. During the century an almost standardized drawing style, vocabulary was developed, which also survived throughout the Renaissance.

Compared to the relatively high number of the survived warfare-related manuscripts that included drawings (their number is above 50), the representation of machines for civil usage is very rare throughout the century, even though the architectural drawings also proliferated during this century, and they also introduced a distinct representation style.

The survived portfolio of the Strasbourg master builder Hans Hammer lies at the intersection of this two disciplines: it includes both machine and architectural drawings in a large number. Given the occupation of the master, it can safely assumed that in contrast to those found in the majority of the contemporary machine drawings, his machines served civil purposes.

In this article the following questions are discussed: how do Hans Hammer’s machine drawings fit in the corpus of the contemporary machine drawings both by drawing style and function; and with which manuscripts can a direct connection be made?

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The essay contextualizes the theory of culture of the philosopher, sociologist, novelist and intellectual Abdelkebir Khatibi in theories of ‘Francophony’ and ‘Post-Coloniality’ which de Toro develops further, proposing a model about hybridity on the basis of some central epistemologies as the “End of the Logos”, the “End of Meta-Discourses”, the “Decentration of the Subject”. Hybridity is defined as “the emphasizing of the difference by simultaneous recognition of the difference of the other in a common territory that all the time has to be inhabited all over again”. In order to avoid the terminological labyrinth related to the concept of hybridity, de Toro offers a first model for a classification of the different levels on which hybridity can be thought and applied, and he distinguishes between eight different fields or levels for locating hybridity: (1) Hybridity as a epistemological category or as a category of philosophy of sciences; (2) as a theoretical/methodological category; (3) as a category of cultural theory, as the strategy to manage with different cultural, ethnical and religious groups; (4) as transmedial category, the use of various media, systems of signs; (5) as an urban category, as form and different types of organisation, plurality of products and heterogeneous objects, such as art, city culture, architecture, companies, ecology, nature, societies, politics, life styles; (6) as territory of the body; (7) as technology (natural sciences: i.e. molecular biology; medicine: micro artificial limbs, virtual surgery; industries: engines with hybrid drive), and (8) as transtextuality. The second part of the essay offers a new concept of Francophony as an “espace éclaté”, as a hybrid and fundamentally plural and anti-hierarchically cartography. The third part of the essay is dedicated to Khatibi’s concepts of the pensée autre and the double critique as well of the corps, désir, androgynéité, migration et le bi-langue.

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