Portfolio optimization under D.C. transaction costs and minimal transaction unit constraints

This paper addresses itself to a portfolio optimization problem under nonconvex transaction costs and minimal transaction unit constraints. Associated with portfolio construction is a fee for purchasing assets. Unit transaction fee is larger when the amount of transaction is smaller. Hence the transaction cost is usually a concave function up to certain point. When the amount of transaction increases, the unit price of assets increases due to illiquidity/market impact effects. Hence the transaction cost becomes convex beyond certain bound. Therefore, the net expected return becomes a general d.c. function (difference of two convex functions). We will propose a branch-and-bound algorithm for the resulting d.c. maximization problem subject to a constraint on the level of risk measured in terms of the absolute deviation of the rate of return of a portfolio. Also, we will show that the minimal transaction unit constraints can be incorporated without excessively increasing the amount of computation.     

Chaos in Fiber-Optic Stimulated Brillouin Scattering Dependent on Pump Power, Nonlinear Refractive Index, Feedback Power, and Fiber Length

Dependence of Stokes dynamics in stimulated Brillouin scattering generated in optical fibers on the pump power, the nonlinear refractive index, the fiber length, and the feedback powers of the pump and the Stokes is numerically analyzed. The Stokes power fluctuation becomes complicated and chaotic as the nonlinear refractive index and the input pump power increase in a fiber of sufficient length. The Stokes dynamics is less complicated and the chaotic region decreases in a pump power-reflectivity domain in a short fiber. The chaotic behavior appears without regular tendency in relation to the feedback power. Taking into account the pump feedback, the chaotic region expands and some Stokes behaviors are different in the P_P-R domain graph, compared with the case with the Stokes feedback alone, although this feedback does play an essential role in Stokes dynamics.     

Nanoparticles in Emissions and Atmospheric Environment: Now and Future

Journal of Nanoparticle Research -     

The inverse scattering problem and the equivalent local potential

We examine the role of the non-locality of the potential in the two-body scattering by taking the nucleon-Σ system as an example. We employ a non-local potential for the nucleon-Σ channel which has the characteristic features of the quark model and reproduces the phase shifts of widely used local potentials. We use inverse scattering methods to obtain the equivalent local potential from the non-local potential, and show that the obtained local potential has a strong short range repulsion.     

Generalized Prikry forcing and iteration of generic ultrapowers

It is known that there is a close relation between Prikry forcing and the iteration of ultrapowers: If U is a normal ultrafilter on a measurable cardinal κ and 〈M_n, j_m,n | m ≤ n ≤ ω〉 is the iteration of ultrapowers of V by U, then the sequence of critical points 〈j_0,n(κ) | n ∈ ω〉 is a Prikry generic sequence over M_ω. In this paper we generalize this for normal precipitous filters. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spatial frequency selective reconstruction using Fourier transform holograms generated in functionalized mesogenic composites

We have demonstrated spatial frequency selective reconstruction (SFSR) of two-dimensional optical images by using functionalized mesogenic composites possessing real-time holographic capability. The two-dimensional optical image was Fourier transformed by a lens and part of the spatial frequency was brought into interference with the reference beam in the Raman-Nath regime. The SFSR images were observed in the self-diffraction patterns and we calculated the expected reconstructed images which were in good agreement with the observed images.     

Phase grating generation and optical phase conjugation in photorefractive polymer/dissolved liquid crystal composites

The orientational photorefractive properties of photorefractive mesogenic composites have been investigated by means of two-beam coupling and degenerate four-wave mixing. Photorefractive mesogenic composites, consisting of low molar mass liquid crystals, polymer, and photoconductive sensitizer, constitute novel organic materials possessing high performance photoreractivity. The refractive index change was estimated on the basis of the theory of two-beam coupling and four-wave mixing, and large index modulation of over 0.01 was obtained.