199,050 research outputs found
Periodic Solutions of a System of Complex ODEs. II. Higher Periods
No full textIn a previous paper the real evolution of the system of ODEs ¨zn + zn = N m=1, m=n gnm(zn - zm) -3 , zn zn(t), zn dzn(t) dt , n = 1, . . . , N is discussed in CN , namely the N dependent variables zn, as well as the N(N - 1) (arbitrary!) "coupling constants" gnm, are considered to be complex numbers, while the independent variable t ("time") is real. In that context it was proven that there exists, in the phase space of the initial data zn(0), zn(0), an open domain having infinite measure, such that all trajectories emerging from it are completely periodic with period 2, zn(t + 2) = zn(t). In this paper we investigate, both by analytcal techniques and via the display of numerical simulations, the remaining solutions, and in particular we show that there exist many -- emerging out of sets of initial data having nonvanishing measures in the phase space of such data -- that are also completely periodic but with periods which are integer multiples of 2. We also elcidate the mechanism that yields nonperiodic solutions, including those characterized by a "chaotic" behavior, namely those associated, in the context of the initial-value problem, with a sensitive dependence on the initial data
On singular Calogero-Moser spaces
No full textUsing combinatorial properties of complex reflection groups, we show that the generalised Calogero-Moser space associated to the centre of the corresponding rational Cherednik algebra is singular for all values of its deformation parameter c if and only if the group is different from the wreath product and the binary tetrahedral group. This result and a theorem of Ginzburg and Kaledin imply that there does not exist a symplectic resolution of the singular symplectic variety h+h*/W outside of these cases; conversely we show that there exists a symplectic resolution for the binary tetrahedral group (Hilbert schemes provide resolutions for the wreath product case)
Generalized Calogero-Moser spaces and rational Cherednik algebras
No full textThe subject of this thesis is the interplay between the geometry and the representation theory of rational
Cherednik algebras at t = 0. Exploiting this relationship, we use representation theoretic techniques to
classify all complex re
ection groups for which the geometric space associated to a rational Cherednik
algebra, the generalized Calogero-Moser space, is singular. Applying results of Ginzburg-Kaledin and
Namikawa, this classification allows us to deduce a (nearly complete) classification of those symplectic
reflection groups for which there exist crepant resolutions of the corresponding symplectic quotient singularity.
Then we explore a particular way of relating the representation theory and geometry of a rational
Cherednik algebra associated to a group W to the representation theory and geometry of a rational
Cherednik algebra associated to a parabolic subgroup of W. The key result that makes this construction
possible is a recent result of Bezrukavnikov and Etingof on completions of rational Cherednik algebras.
This leads to the definition of cuspidal representations and we show that it is possible to reduce the
problem of studying all the simple modules of the rational Cherednik algebra to the study of these
nitely many cuspidal modules. We also look at how the Etingof-Ginzburg sheaf on the generalized
Calogero-Moser space can be "factored" in terms of parabolic subgroups when it is restricted to particular
subvarieties. In particular, we are able to confirm a conjecture of Etingof and Ginzburg on
"factorizations" of the Etingof-Ginzburg sheaf.
Finally, we use Clifford theoretic techniques to show that it is possible to deduce the Calogero-Moser partition of the irreducible representations of the complex reflection groups G(m; d; n) from the
corresponding partition for G(m; 1; n). This confirms, in the case W = G(m; d; n), a conjecture of
Gordon and Martino relating the Calogero-Moser partition to Rouquier families for the corresponding
cyclotomic Hecke algebra
Alfonso Lombardi, da Ferrara ai giorni dell’incoronazione. Un dialogo fra le arti
No full textNew documents and stylistic analysis shed light on the life and work of the Ferrarese sculptor Alfonso Lombardi (c. 1497-1537)
The Calogero-Moser partition for G(m,d,n)
No full textWe show that it is possible to deduce the Calogero-Moser partition of the irreducible representations of the complex reflection groups G(m,d,n) from the corresponding partition for G(m,1,n). This confirms, in the case W = G(m,d,n), a conjecture of Gordon and Martino relating the Calogero-Moser partition to Rouquier families for the corresponding cyclotomic Hecke algebra
Il rapporto tra Guido Calogero e Ugo Spirito attraverso il carteggio(1926-1945)
No full textIl saggio analizza attraverso il carteggio(1926-1978)il rapporto intellettuale e politico tra Calogero e Spirito. Le questioni centrali del confronto tra i due furono il rapporto con la filosofia e le concezioni politiche di Gentile; i diversi giudizi sulla politica e sull'economia; le diverse prospettive filosofich
Per i busti ritratto in marmo di Alfonso Lombardi (con una proposta per il perduto Carlo V e una lettera del cardinale Innocenzo Cibo
No full textAmong the many marble portrait busts executed by the Ferrarese sculptor Alfonso Lombardi (c. 1497 - 1537), Giorgio Vasari mentions only four in his biography of the artist: the portraits of Giuliano de’ Medici, Duke of Nemours and Pope Clement VII, now both in the Palazzo Vecchio in Florence, and two versions of the bust of Charles V, considered lost. The article seeks to retrace the physical history of these four objects, from their genesis to how they were collected. Thanks to a new photographic campaign, a thorough analysis of the Palazzo Vecchio busts can now be made. Viewed from the side, the bust of Giuliano is revealed as a faithful derivation from a medal produced in Rome in 1513. The bust of Clement VII shows that it was conceived in stylistic dialogue with portraits of the pontiff by other artists at the Papal Court: Sebastiano del Piombo, Benvenuto Cellini and Giovanni Bernardi. The second part of the article hypothesises that the lost bust of Charles V carved by Lombardi in 1533 was a portrait in armour. The sculptor’s correspondence reveals that a second version of this bust was made in the same year for Alessandro de’ Medici, Duke of Florence: once owned by Cardinal Innocenzo Cibo, this can be identified as the fragmentary sculpture now housed in the fortress in Massa
19MO CONGRESSO NAZIONALE DELLA SOCIETÀ ITALIANA DI CRIMINOLOGIA, (Gargnano 3-5 novembre 2005). e) “Fattori Di Predittività Nella Madre Figlicide” Mastronardi V.; Villanova M; Calogero A.
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Documenti per Girolamo da Treviso a Bologna (con una nuova data per Sabba da Castiglione)
No full textUnpublished documents provide new and valuable information on the career of the painter Girolamo da Treviso (d. ca. 1544). Notably, the overlooked date of a drawing in the Uffizi is a relevant new piece of information related to Girolamo's fresco in the church of the Commenda in Faenza. The celebrated man of letters Sabba da Castiglione commissioned this fresco from Girolamo in 1529, but the painter completed it only four years later. Two unpublished documents related to Girolamo's collaboration with stonecutters in 1531 and 1533 shed light on the architectural taste of Bolognese patrons around 1530
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