Closed-loop equilibrium strategies for general time-inconsistent optimal control problems

In this paper we introduce a general framework for time-inconsistent optimal control problems. We characterize the closed-loop equilibrium strategy in both the integral and point wise forms with the newly developed methodology. We recover and improve the results of some well-known models, including the classical optimal control, Bjork et al. (2017), He and Jiang(2020), and Yong (2012) models, and reveal some interesting aspects that appear for the first time in the literature. We illustrate the usefulness of the model and the results by a number of examples in dynamic portfolio selection, including mean-variance with state-dependent risk aversion, investment/consumption with non-exponential discounting, and utility-deviation-risk with coupled terminal state and expected terminal state

Phase diagram and optical conductivity of the one-dimensional spinless Holstein model

The effects of quantum lattice fluctuations on the Peierls transition and the optical conductivity in the one-dimensional Holstein model of spinless fermions have been studied by developing an analytical approach, based on the unitary transformation method. We show that when the electron-phonon coupling constant decreases to a finite critical value the Peierls dimerization is destroyed by the quantum lattice fluctuations. The dimerization gap is much more reduced by the quantum lattice fluctuations than the phonon order parameter. The calculated optical conductivity does not have the inverse-square-root singularity but have a peak above the gap edge and there exists a significant tail below the peak. The peak of optical-conductivity spectrum is not directly corresponding to the dimerized gap. Our results of the phase diagram and the spectral-weight function agree with those of the density matrix renormalization group and the exact diagonalization methods.Comment: 9 pages, 4 figures include

Investigation of topographical stability of the concave and convex Self-Organizing Map variant

We investigate, by a systematic numerical study, the parameter dependence of the stability of the Kohonen Self-Organizing Map and the Zheng and Greenleaf concave and convex learning with respect to different input distributions, input and output dimensions

Sub-TeV proton beam generation by ultra-intense laser irradiation of foil-and-gas target

A two-phase proton acceleration scheme using an ultra-intense laser pulse irradiating a proton foil with a tenuous heavier-ion plasma behind it is presented. The foil electrons are compressed and pushed out as a thin dense layer by the radiation pressure and propagate in the plasma behind at near the light speed. The protons are in turn accelerated by the resulting space-charge field and also enter the backside plasma, but without the formation of a quasistationary double layer. The electron layer is rapidly weakened by the space-charge field. However, the laser pulse originally behind it now snowplows the backside-plasma electrons and creates an intense electrostatic wakefield. The latter can stably trap and accelerate the pre-accelerated proton layer there for a very long distance and thus to very high energies. The two-phase scheme is verified by particle-in-cell simulations and analytical modeling, which also suggests that a 0.54 TeV proton beam can be obtained with a 10(23) W/cm(2) laser pulse. (C) 2012 American Institute of Physics. [doi:10.1063/1.3684658]Physics, Fluids & PlasmasSCI(E)EI0ARTICLE2null1

Permutable entire functions satisfying algebraic differential equations

It is shown that if two transcendental entire functions permute, and if one of them satisfies an algebraic differential equation, then so does the other one.Comment: 5 page

Electric Field Effect in Diluted Magnetic Insulator Anatase Co:TiO2

An external electric field induced reversible modulation of room temperature magnetic moment is achieved in an epitaxial and insulating thin film of dilutely cobalt-doped anatase TiO2. This first demonstration of electric field effect in any oxide based diluted ferromagnet is realized in a high quality epitaxial heterostructure of PbZr0.2Ti0.8O3/Co:TiO2/SrRuO3 grown on (001) LaAlO3. The observed effect, which is about 15% in strength in a given heterostructure, can be modulated over several cycles. Possible mechanisms for electric field induced modulation of insulating ferromagnetism are discussed.Comment: 14 pages, 4 figure