A Geometrical Way to Sum Powers by Means of Tetrahedrons and Eulerian Numbers

We geometrically prove that in a d-dimensional cube with edges of length n, the number of particular d-dimensional tetrahedrons are given by Eulerian numbers. These tetrahedrons tassellate the cube, In this way the sum of the cubes are the sums of the tetrahedrons, whose calculation is trivial.Comment: 12 pages, based on lecture notes to undergraduaded student

Strategic environmental assessment implementation of transport and mobility plans. The case of italian regions and provinces

Transport and mobility plans imply strategies and actions that affect the environment. The European Union has introduced in 2001 the strategic environmental assessment (SEA) to take into account and mitigate adverse environmental effects in planning and decision-making. SEA limited implementation has attracted the interest of many scholars that have sought methods able to assess the quality of SEA processes by identifying vices and virtues in practice. In this paper, we measure the quality of eight SEAs for transport and mobility plans of regional and provincial administrations of Italy. Results show that the overall quality level of SEA reports is only barely sufficient, Abruzzo is among the virtuous and Piedmont among the critical administrations. We also stress that the determination of impact significance has received the worse quality score. We finally compare our results to other Italian and British homologous cases finding interesting and generally confirmative evidence

Des variantes invisibles à la fragmentation des langues romanes

Cet article propose un modèle descriptif de l’émergence des changements phonémiques, morphosyntaxiques et lexico-sémantiques. Il s’agit d’un modèle alternatif dans la mesure où le principe d’économie et l’axiome «  deux formes deux fonctions  » sont mis en cause. L’alternative proposée (qui plaide pour le polymorphisme ainsi que pour l’indéterminisme des descriptions grammaticales) s’appuie sur la notion de variante invisible  : un locuteur donné peut utiliser, pour une fonction donnée, des variantes non contrôlées et non perçues en tant que telles par l’allocutaire. Les variantes invisibles sont, dans cette démarche, considérées comme la source des changements qualitatifs dans l’histoire d’une langue ainsi que de la fragmentation ayant lieu dans un espace langagier donné. Les sauts qualitatifs (changement de grammaire) sont décrits comme l’intériorisation, par induction, de nouvelles règles par les locuteurs  ; règles dont dérivent des variantes non reliées entre elles à l’origine. Ce modèle, illustré par quelques exemples concernant certains phonèmes, les clitiques, la subordination, les négatives et les interrogatives, permet de formuler des hypothèses falsifiables à propos des règles innovatrices.This article aims at proposing a framework which should describe the way how phonemic, morphosyntactic and lexical-semantic changes emerge. This proposal runs counter to several claims such as the principle of economy, or the axiom “two forms – two functions”. It supports the view that grammatical descriptions contain a certain degree of polymorphism and indeterminism. It is based on the notion “invisible variant” : it is argued that speakers may use, for a given function, random variants which are not perceived as such, being fully well-formed according to the speakers’grammar. Invisible variants will be shown to be the source of qualitative changes in the history of languages, as well as of fragmentation of linguistic domains. Qualitative steps (i.e. grammatical changes) take place when speakers, by induction, acquire new rules, creating new variants which were not previously related. On the basis of a large array of data, concerning phonemes, clitics, subordinates, negative and interrogative clauses, it will be seen how our proposal allows to make falsifiable hypotheses on these new rules

Perylene-diimide molecules with cyano functionalization for electron-transporting transistors

Core-cyanated perylene diimide (PDI_CY) derivatives are molecular compounds exhibiting an uncommon combination of appealing properties, including remarkable oxidative stability, high electron affinities, and excellent self-assembling properties. Such features made these compounds the subject of study for several research groups aimed at developing electron-transporting (n-type) devices with superior charge transport performances. After about fifteen years since the first report, field-effect transistors based on PDI_CY thin films are still intensely investigated by the scientific community for the attainment of n-type devices that are able to balance the performances of the best p-type ones. In this review, we summarize the main results achieved by our group in the fabrication and characterization of transistors based on PDI8-CN2 and PDIF-CN2 molecules, undoubtedly the most renowned compounds of the PDI_CY family. Our attention was mainly focused on the electrical properties, both at the micro and nanoscale, of PDI8-CN2 and PDIF-CN2 films deposited using different evaporation techniques. Specific topics, such as the contact resistance phenomenon, the bias stress effect, and the operation in liquid environment, have been also analyzed

Faits et situations

Table des matières : Introduction ; 1. La proposition : des situations aux faits ; 2. La situation, 2.1. La situation partagée, 2.2. Les limites de la situation, 2.3. Les modes d’interprétation des stimuli, 2.4. Perception directe, mémoire et témoignage ; 3. La situation n’est pas un « grand fait » composé de faits plus petits ; 4. Les faits n’existent pas indépendamment de la proposition ; 5. Le fait comme « qualité » d’une situation, 5.1. Le problème des « faits négatifs », 5.2. Analogie, comparaison et métaphore; 6. Il n’y a d’autre situation que la situation actuelle, 6.1. Temps et situation actuelle, 6.2. La situation et les dépendances causales, 6.3. Les faits dans le passé et la situation actuelle, 6.4. Les faits dans le futur et la situation actuelle ; 7. Convergence et cohérence, 7.1. Convergence et pertinence, 7.2. Cohérence et vérit