The generalized natural boundary conditions for fractional variational problems in terms of the Caputo derivative

This paper presents necessary and sufficient optimality conditions for problems of the fractional calculus of variations with a Lagrangian depending on the free end-points. The fractional derivatives are defined in the sense of Caputo.Comment: Accepted (19 February 2010) for publication in Computers and Mathematics with Application

Backward variational approach on time scales with an action depending on the free endpoints

We establish necessary optimality conditions for variational problems with an action depending on the free endpoints. New transversality conditions are also obtained. The results are formulated and proved using the recent and general theory of time scales via the backward nabla differential operator.Comment: Submitted 17-Oct-2010; revised 18-Dec-2010; accepted 4-Jan-2011; for publication in Zeitschrift fuer Naturforschung

Towards a combined fractional mechanics and quantization

A fractional Hamiltonian formalism is introduced for the recent combined fractional calculus of variations. The Hamilton-Jacobi partial differential equation is generalized to be applicable for systems containing combined Caputo fractional derivatives. The obtained results provide tools to carry out the quantization of nonconservative problems through combined fractional canonical equations of Hamilton type.Comment: This is a preprint of a paper whose final and definite form will be published in: Fract. Calc. Appl. Anal., Vol. 15, No 3 (2012). Submitted 21-Feb-2012; revised 29-May-2012; accepted 03-June-201

Nonessential Functionals in Multiobjective Optimal Control Problems

We address the problem of obtaining well-defined criteria for multiobjective optimal control systems. Necessary and sufficient conditions for an optimal control functional to be nonessential are proved. The results provide effective tools for determining nonessential objectives in vector-valued optimal control problems.Comment: Presented at the 5th Junior European Meeting on Control & Information Technology (JEM'06), September 20-22, 2006, Tallinn, Estoni

Finite size scaling of the bayesian perceptron

We study numerically the properties of the bayesian perceptron through a gradient descent on the optimal cost function. The theoretical distribution of stabilities is deduced. It predicts that the optimal generalizer lies close to the boundary of the space of (error-free) solutions. The numerical simulations are in good agreement with the theoretical distribution. The extrapolation of the generalization error to infinite input space size agrees with the theoretical results. Finite size corrections are negative and exhibit two different scaling regimes, depending on the training set size. The variance of the generalization error vanishes for $N \rightarrow \infty$ confirming the property of self-averaging.Comment: RevTeX, 7 pages, 7 figures, submitted to Phys. Rev.

Decoherence at constant excitation

We present a simple exactly solvable extension of of the Jaynes-Cummings model by adding dissipation. This is done such that the total number of excitations is conserved. The Liouville operator in the resulting master equation can be reduced to blocks of $4\times 4$ matrices

Inclusive and effective bulk viscosities in the hadron gas

We estimate the temperature dependence of the bulk viscosity in a relativistic hadron gas. Employing the Green-Kubo formalism in the SMASH (Simulating Many Accelerated Strongly-interacting Hadrons) transport approach, we study different hadronic systems in increasing order of complexity. We analyze the (in)validity of the single exponential relaxation ansatz for the bulk-channel correlation function and the strong influence of the resonances and their lifetimes. We discuss the difference between the inclusive bulk viscosity of an equilibrated, long-lived system, and the effective bulk viscosity of a short-lived mixture like the hadronic phase of relativistic heavy-ion collisions, where the processes whose inverse relaxation rate are larger than the fireball duration are excluded from the analysis. This clarifies the differences between previous approaches which computed the bulk viscosity including/excluding the very slow processes in the hadron gas. We compare our final results with previous hadron gas calculations and confirm a decreasing trend of the inclusive bulk viscosity over entropy density as temperature increases, whereas the effective bulk viscosity to entropy ratio, while being lower than the inclusive one, shows no strong dependence to temperature.Comment: 23 pages, 13 figure