2,984 research outputs found
The Bianchi-Darboux transform of L-isothermic surfaces
We study an analogue of the classical Bianchi-Darboux transformation for
L-isothermic surfaces in Laguerre geometry, the Bianchi-Darboux transformation.
We show how to construct the Bianchi-Darboux transforms of an L-isothermic
surface by solving an integrable linear differential system. We then establish
a permutability theorem for iterated Bianchi-Darboux transforms.Comment: 13 pages, amstex, to be published in IJ
Hamiltonian flows on null curves
The local motion of a null curve in Minkowski 3-space induces an evolution
equation for its Lorentz invariant curvature. Special motions are constructed
whose induced evolution equations are the members of the KdV hierarchy. The
null curves which move under the KdV flow without changing shape are proven to
be the trajectories of a certain particle model on null curves described by a
Lagrangian linear in the curvature. In addition, it is shown that the curvature
of a null curve which evolves by similarities can be computed in terms of the
solutions of the second Painlev\'e equation.Comment: 14 pages, v2: final version; minor changes in the expositio
Italy in the Middle East and the Mediterranean: The evolving relations with Egypt and Libya
The Mediterranean and the Middle East have long constituted an important “circle” in Italy’s foreign policy, with Egypt and Libya playing a particularly important role. During 2016, two sources of tension emerged in Italy’s relations with these countries. The first reflects a wider European situation. Like the rest of the EU, Italy has followed strategic interests—on migration, energy, and security—that sometimes conflict with the promotion of human rights, democracy, and the rule of law, which the EU claims to promote in its external relations. The Regeni affair, involving a murdered Italian graduate student, exemplified this tension. The second source results from the role of corporate interests in Italy, especially those of oil and energy companies, in relation to the country’s “national interests.” Italian foreign policy toward both Libya and Egypt seems to have been driven by a combination of somewhat overlapping but also divergent national and corporate interests
On the Reliability of the Langevin Pertubative Solution in Stochastic Inflation
A method to estimate the reliability of a perturbative expansion of the
stochastic inflationary Langevin equation is presented and discussed. The
method is applied to various inflationary scenarios, as large field, small
field and running mass models. It is demonstrated that the perturbative
approach is more reliable than could be naively suspected and, in general, only
breaks down at the very end of inflation.Comment: 7 pages, 3 figure
Reduction for constrained variational problems on 3D null curves
We consider the optimal control problem for null curves in de Sitter 3-space
defined by a functional which is linear in the curvature of the trajectory. We
show how techniques based on the method of moving frames and exterior
differential systems, coupled with the reduction procedure for systems with a
Lie group of symmetries lead to the integration by quadratures of the
extremals. Explicit solutions are found in terms of elliptic functions and
integrals.Comment: 16 page
Closed trajectories of a particle model on null curves in anti-de Sitter 3-space
We study the existence of closed trajectories of a particle model on null
curves in anti-de Sitter 3-space defined by a functional which is linear in the
curvature of the particle path. Explicit expressions for the trajectories are
found and the existence of infinitely many closed trajectories is proved.Comment: 12 pages, 1 figur
Classical Dynamical Systems from q-algebras:"cluster" variables and explicit solutions
A general procedure to get the explicit solution of the equations of motion
for N-body classical Hamiltonian systems equipped with coalgebra symmetry is
introduced by defining a set of appropriate collective variables which are
based on the iterations of the coproduct map on the generators of the algebra.
In this way several examples of N-body dynamical systems obtained from
q-Poisson algebras are explicitly solved: the q-deformed version of the sl(2)
Calogero-Gaudin system (q-CG), a q-Poincare' Gaudin system and a system of
Ruijsenaars type arising from the same (non co-boundary) q-deformation of the
(1+1) Poincare' algebra. Also, a unified interpretation of all these systems as
different Poisson-Lie dynamics on the same three dimensional solvable Lie group
is given.Comment: 19 Latex pages, No figure
Coriolano Alberini y Waldo Frank
Fil: Musso de Cavallaro, María E..Fil: Sánchez, Norma Isabel
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