On worst-case investment with applications in finance and insurance mathematics

We review recent results on the new concept of worst-case portfolio optimization, i.e. we consider the determination of portfolio processes which yield the highest worst-case expected utility bound if the stock price may have uncertain (down) jumps. The optimal portfolios are derived as solutions of non-linear differential equations which itself are consequences of a Bellman principle for worst-case bounds. They are by construction non-constant ones and thus differ from the usual constant optimal portfolios in the classical examples of the Merton problem. A particular application of such strategies is to model crash possibilities where both the number and the height of the crash is uncertain but bounded. We further solve optimal investment problems in the presence of an additional risk process which is the typical situation of an insurer

Core compressor exit stage study, 2

A total of two three-stage compressors were designed and tested to determine the effects of aspect ratio on compressor performance. The first compressor was designed with an aspect ratio of 0.81; the other, with an aspect ratio of 1.22. Both compressors had a hub-tip ratio of 0.915, representative of the rear stages of a core compressor, and both were designed to achieve a 15.0% surge margin at design pressure ratios of 1.357 and 1.324, respectively, at a mean wheel speed of 167 m/sec. At design speed the 0.81 aspect ratio compressor achieved a pressure ratio of 1.346 at a corrected flow of 4.28 kg/sec and an adiabatic efficiency of 86.1%. The 1.22 aspect ratio design achieved a pressure ratio of 1.314 at 4.35 kg/sec flow and 87.0% adiabatic efficiency. Surge margin to peak efficiency was 24.0% with the lower aspect ratio blading, compared with 12.4% with the higher aspect ratio blading

Directional photoelectric current across the bilayer graphene junction

A directional photon-assisted resonant chiral tunneling through a bilayer graphene barrier is considered. An external electromagnetic field applied to the barrier switches the transparency $T$ in the longitudinal direction from its steady state value T=0 to the ideal T=1 at no energy costs. The switch happens because the a.c. field affects the phase correlation between the electrons and holes inside the graphene barrier changing the whole angular dependence of the chiral tunneling (directional photoelectric effect). The suggested phenomena can be implemented in relevant experiments and in various sub-millimeter and far-infrared optical electronic devices.Comment: 7 pages 5 figure

Magnetic properties of nanosized diluted magnetic semiconductors with band splitting

The continual model of the nonuniform magnetism in thin films and wires of a diluted magnetic semiconductor is considered with taking into account the finite spin polarization of carriers responsible for the indirect interaction of magnetic impurities (e.g. via RKKY mechanism). Spatial distributions (across the film thickness or the wire radius) of the magnetizaton and carrier concentrations of different spin orientations, as well as the temperature dependence of the average magnetization are determined as the solution of the nonlinear integral equation

Casimir-Polder interaction between an atom and a conducting wall in cosmic string spacetime

The Casimir-Polder interaction potential is evaluated for a polarizable microparticle and a conducting wall in the geometry of a cosmic string perpendicular to the wall. The general case of the anisotropic polarizability tensor for the microparticle is considered. The corresponding force is a function of the wall-microparticle and cosmic string-microparticle distances. Depending on the orientation of the polarizability tensor principal axes the force can be either attractive or repulsive. The asymptotic behavior of the Casimir-Polder potential is investigated at large and small separations compared to the wavelength of the dominant atomic transitions. We show that the conical defect may be used to control the strength and the sign of the Casimir-Polder force.Comment: 17 pages, 3 figure

Characterization of anomalous Zeeman patterns in complex atomic spectra

The modeling of complex atomic spectra is a difficult task, due to the huge number of levels and lines involved. In the presence of a magnetic field, the computation becomes even more difficult. The anomalous Zeeman pattern is a superposition of many absorption or emission profiles with different Zeeman relative strengths, shifts, widths, asymmetries and sharpnesses. We propose a statistical approach to study the effect of a magnetic field on the broadening of spectral lines and transition arrays in atomic spectra. In this model, the sigma and pi profiles are described using the moments of the Zeeman components, which depend on quantum numbers and Land\'{e} factors. A graphical calculation of these moments, together with a statistical modeling of Zeeman profiles as expansions in terms of Hermite polynomials are presented. It is shown that the procedure is more efficient, in terms of convergence and validity range, than the Taylor-series expansion in powers of the magnetic field which was suggested in the past. Finally, a simple approximate method to estimate the contribution of a magnetic field to the width of transition arrays is proposed. It relies on our recently published recursive technique for the numbering of LS-terms of an arbitrary configuration.Comment: submitted to Physical Review

Non-minimal monopoles of the Dirac type as realization of the censorship conjecture

We discuss a class of exact solutions of a three-parameter non-minimally extended Einstein-Maxwell model, which are attributed to non-minimal magnetic monopoles of the Dirac type. We focus on the investigation of the gravitational field of Dirac monopoles for those models, for which the singularity at the central point is hidden inside of an event horizon independently on the mass and charge of the object. We obtained the relationships between the non-minimal coupling constants, for which this requirement is satisfied. As explicit examples, we consider in detail two one-parameter models: first, non-minimally extended Reissner-Nordstr\"om model (for the magnetically charged monopole), second, the Drummond-Hathrell model.Comment: 9 pages; one reference added, accepted to Phys. Rev.