1,720,966 research outputs found
L'opera di É. Galois: punto di arrivo e punto di partenza nella ricerca matematica
No full textIn questo si ripercorre brevemente la biografia di Galois e si cerca di
inquadrare la sua opera in un contesto storico in cui prima si chiarisce
la natura e l'importanza del problema affrontato da Galois e poi si
mostrano i vari passi storici che hanno segnato l'evoluzione e le
soluzioni parziali del problema, fino ad arrivare all'opera risolutrice
di Galois
Computer Algebra
No full textQueste note nascono come le dispense del corso di Computer Algebra
del Corso di Laurea Specialistica in Informatica
dell'Università di Ferrara.
Esse coprono tutti gli argomenti affrontati nel corso, aggiungendo quanto
necessario per rendere la trattazione organica ed autosufficiente.
In particolare vengono fornite tutte le nozioni algebriche necessarie
partendo dal presupposto che gli studenti di informatica non ne abbiano
alcuna, come spesso è il caso.
Il corso ha un carattere introduttivo: fornisce le basi dell'algebra
computazionale e mostra alcune importanti applicazioni (crittografia,
codici autocorrettivi) mettendo lo
studente in condizione di approfondire autonomamente gli argomenti che
troverà di maggiore interesse
Crittografia
No full textIn questo progetto viene sviluppato un percorso per introdurre nelle scuole superiori la crittografia con una discussione che include sia aspetti storici che algoritmi moderni di uso corrente.
In particolare, vengono fornite le basi matematiche per poter arrivare alla comprensione di un fondamentale algoritmo della crittografia a chiave pubblica, il codice RS
Artin groups associated to infinite Coxeter groups
No full textAbstractFirst we remark that the cellular complex constructed by Salvetti (1994) can be considered as a ‘topological’ invariant of a graph, so its cohomology is also an invariant. We use the construction of Salvetti (1994) to calculate the cohomology of the Artin group associated to the complete graph Kn, using coefficients in a local system over Z[q,q−1]. The standard cohomology over Z is obtained by specializing q to 1. While doing such computations, we obtain also an explicit rational function for the Poincaré series of the Coxeter group associated to Kπ, and note that it has exponential growth for n⩾4
Ferrara Algebra Workshop
No full textPlenary Speakers:
- Nicolas Andruskiewitsch, Universidad de Córdoba (Argentina)
- Peter Schauenburg, University of Munich (Germany)
- Corrado De Concini, Università di Roma "La Sapienza" (Italy)
- Shahn Majid, Queen Mary, University (U.K.
Quadratic Lie Algebras
No full textIn this paper, the notion of universal enveloping algebra introduced
in [A. Ardizzoni, \emph{A First Sight Towards Primitively Generated Connected Braided Bialgebras}, submitted. (arXiv:0805.3391v3)] is specialized to the case of braided vector spaces whose Nichols algebra is quadratic as an algebra. In this setting a classification of universal enveloping algebras for braided vector spaces of dimension not greater than is handled. As an application, we investigate the structure of primitively generated connected braided bialgebras whose braided vector space of primitive elements forms a Nichols algebra which is quadratic algebra
A new discrete dynamical system of signed integer partitions
No full textIn Brylawski (1973) Brylawski described the covering property for the domination order on non-negative integer partitions by means of two rules. Recently, in Bisi et al. (in press), Cattaneo et al. (2014), Cattaneo et al. (2015) the two classical Brylawski covering rules have been generalized in order to obtain a new lattice structure in the more general signed integer partition context. Moreover, in Cattaneo et al. (2014), Cattaneo et al. (2015), the covering rules of the above signed partition lattice have been interpreted as evolution rules of a discrete dynamical model of a two-dimensional p-n semiconductor junction in which each positive number represents a distribution of holes (positive charges) located in a suitable strip at the left semiconductor of the junction and each negative number a distribution of electrons (negative charges) in a corresponding strip at the right semiconductor of the junction. In this paper we introduce and study a new sub-model of the above dynamical model, which is constructed by using a single vertical evolution rule. This evolution rule describes the natural annihilation of a hole-electron pair at the boundary region of the two semiconductors. We prove several mathematical properties of such new discrete dynamical model and we provide a discussion of its physical properties
Small bialgebras with a projection
Full text linkAbstractLet A be a bialgebra with an H-bilinear coalgebra projection over an arbitrary subbialgebra H with antipode. In characteristic zero, we completely describe the bialgebra structure of A whenever H is either f.d. or cosemisimple and the H-coinvariant part R of A is connected with one-dimensional space of primitive elements
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