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

Rank expectations, feedback and social hierarchies

We develop and test experimentally a theoretical model of the role of self-esteem, generated by private feedback regarding relative performance, on the behavior of agents working on an effort provision task for a flat wage. Agents work harder and expect to rank better when they are told they may learn their ranking, relative to cases when they are told feedback will not be provided. Individuals who learn that they have ranked better than expected decrease their output but expect an even better rank in the future, while those who were told they ranked worse than expected increase their output and at the same time lower their rank expectations going forward. These effects are stronger in earlier rounds of the task, while subjects learn how they compare to their peers. This rank hierarchy is established early on, and remains relatively stable afterwards. Private relative rank information helps create a ratcheting effect in the group's average output, which is mainly due to the fight for dominance at the top of the hierarchy. Hence, in environments where monetary incentives are weak, moral hazard may be mitigated by providing feedback to agents regarding their relative performance, and by optimally choosing the reference peer group.rankings, incentives, feedback, moral hazard, intrinsic motivation, ego utility, self-esteem

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

Experimental Limits on Primordial Black Hole Dark Matter from the First Two Years of Kepler Data

We present the analysis on our new limits of the dark matter (DM) halo consisting of primordial black holes (PBHs) or massive compact halo objects (MACHOs). We present a search of the first two years of publicly available Kepler mission data for potential signatures of gravitational microlensing caused by these objects, as well as an extensive analysis of the astrophysical sources of background error. These include variable stars, flare events, and comets or asteroids which are moving through the Kepler field. We discuss the potential of detecting comets using the Kepler lightcurves, presenting measurements of two known comets and one unidentified object, most likely an asteroid or comet. After removing the background events with statistical cuts, we find no microlensing candidates. We therefore present our Monte Carlo efficiency calculation in order to constrain the PBH DM with masses in the range of 2 x 10^-9 solar masses to 10^-7 solar masses. We find that PBHs in this mass range cannot make up the entirety of the DM, thus closing a full order of magnitude in the allowed mass range for PBH DM.Comment: 12 pages, 6 figure