Negative refraction via domain wall resonances in a homogeneous mixture of ferro- and nonmagnetic substances

We deliver the general conditions on the synthetic proportions for a homogeneous mixture of ferro- and nonmagnetic substances to become left-handed. As an alternative for left-handed metamaterials, we consider mixing ferromagnetic materials with nonmagnetic microscopic particles. In the mixture, the ferromagnetic material provides the needed permeability via domain wall resonances at high frequencies, whereas the nonmagnetic material gives the required permittivity. Using the effective medium theory, we have found that when the concentration of the nonmagnetic particles falls into a certain range, the refractive index of the mixture is negative, n < 0, which includes the double negative ( epsilon < 0 and mu < 0) and other cases ( e. g. epsilon < 0 and mu > 0). We finally give the requirements on the microscopic material properties for the ferromagnetic materials to reach the domain wall resonances at high frequencies.

Parameterizing probabilities for estimating age-composition distributions for mixture models

When estimating parameters that constitute a discrete probability distribution {pj}, it is difficult to determine how constraints should be made to guarantee that the estimated parameters { pˆj} constitute a probability distribution (i.e., pˆj>0, Σ pˆj =1). For age distributions estimated from mixtures of length-at-age distributions, the EM (expectationmaximization) algorithm (Hasselblad, 1966; Hoenig and Heisey, 1987; Kimura and Chikuni, 1987), restricted least squares (Clark, 1981), and weak quasisolutions (Troynikov, 2004) have all been used. Each of these methods appears to guarantee that the estimated distribution will be a true probability distribution with all categories greater than or equal to zero and with individual probabilities that sum to one. In addition, all these methods appear to provide a theoretical basis for solutions that will be either maximum-likelihood estimates or at least convergent to a probability distribut