29,960 research outputs found
Fractional Noether's Theorem with Classical and Riemann-Liouville Derivatives
We prove a Noether type symmetry theorem to fractional problems of the
calculus of variations with classical and Riemann-Liouville derivatives. As
result, we obtain constants of motion (in the classical sense) that are valid
along the mixed classical/fractional Euler-Lagrange extremals. Both Lagrangian
and Hamiltonian versions of the Noether theorem are obtained. Finally, we
extend our Noether's theorem to more general problems of optimal control with
classical and Riemann-Liouville derivatives.Comment: This is a preprint of a paper whose final and definite form will be
published in: 51st IEEE Conference on Decision and Control, December 10-13,
2012, Maui, Hawaii, USA. Article Source/Identifier: PLZ-CDC12.1832.45c07804.
Submitted 08-March-2012; accepted 17-July-2012. arXiv admin note: text
overlap with arXiv:1001.450
Noether's Symmetry Theorem for Variational and Optimal Control Problems with Time Delay
We extend the DuBois-Reymond necessary optimality condition and Noether's
symmetry theorem to the time delay variational setting. Both Lagrangian and
Hamiltonian versions of Noether's theorem are proved, covering problems of the
calculus of variations and optimal control with delays.Comment: This is a preprint of a paper whose final and definite form will
appear in the international journal Numerical Algebra, Control and
Optimization (NACO). Paper accepted for publication 15-March-201
Coupled quintessence and vacuum decay
We discuss observational consequences of a class of cosmological models
characterized by the dilution of pressureless matter attenuated with respect to
the usual scaling due to the decay of vacuum energy. We carry out a
joint statistical analysis of observational data from the new \emph{gold}
sample of 182 SNe Ia, recent estimates of the CMB shift parameter, and BAO
measurements from the SDSS to show that such models favor the decay of vacuum
only into the dark matter sector, and that the separately conserved baryons
cannot be neglected. In order to explore ways to more fundamentally motivated
models, we also derive a coupled scalar field version for this general class of
vacuum decay scenarios.Comment: 6 pages, 3 figures, LaTe
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