We have generalized the ABCD propagation law, Q(2) = (AQ(1) + B)/(CQ(1) + D), for an optical system by introducing a generalized complex radius of curvature Q for a general optical beam. The real part of 1/Q is related to the mean radius of curvature of the wave front, while the imaginary part is related to the second moment of the amplitude of the beam.

We present two results characterizing minimizers of the LTV functional F (u) ≡ ∫ |∇u|dx+λ ∫ |u−f |dx; u, f : R → R. If we restrict to u = χΣ and f = χΩ, Σ,Ω ∈ R, the LTV functional reduces to E(Σ) = Per(Σ) + λ|Σ M Ω|. We show that there is a minimizer Σ such that its boundary ∂Σ lies between the union of all balls of radius nλ contained in Ω and the corresponding union of nλ -balls in Ω . We al...

The hydrogen molecule can be used for determination of physical constants, including the proton charge radius, and for improved tests of the hypothetical long range force between hadrons, which require a sufficiently accurate knowledge of the molecular levels. In this work, we perform the first step toward a significant improvement in theoretical predictions of H2 and solve the nonrelativistic ...

Article history: Received 03 May 2012 Accepted 26 April 2013 Available online 24 May 2013 Submitted by R.A. Brualdi

In this paper, we give lower and upper bounds on the covering radius of codes over the ring R = Z2 + uZ2, where u2 = 0 with bachoc distance and also obtain the covering radius of various Repetition codes, Simplex codes of α-Type code and β-Type code. We give bounds on the covering radius for MacDonald codes of both types over R = Z2 + uZ2. MSC: 20C05, 20C07, 94A05, 94A24.

By means of lattice-Boltzmann simulations the drag force on a sphere of radius R approaching a superhydrophobic striped wall has been investigated as a function of arbitrary separation h. Superhydrophobic (perfect-slip vs. no-slip) stripes are characterized by a texture period L and a fraction of the gas area ϕ. For very large values of h/R, we recover the macroscopic formulae for a sphere movi...

Tactile dots and bars serve as tactile landmarks so that people with visual impairment can use same consumer products as those used by sighted people. However, reliable age-related data on the appropriate sizes and the shapes was not necessarily available. The purpose of this study is to evaluate influences of edge radius of curvature of tactile dots and bars on their discriminability in younge...

The class SH consists of univalent, harmonic, and sense-preserving functions f in the unit disk, ∆, such that f = h + g where h(z) = z + ∑∞ 2 akz , g(z) = ∑∞ 1 bkz . Using a technique from Clunie and Sheil-Small, we construct a family of 1-slit mappings in SH by varying ω(z) = g ′(z)/f ′(z). As ω(z) changes, the tip of the slit slides along the negative real axis from the point 0 to −1. In doin...

We propose a dynamic model for a system consisting of self-propelled agents in which the influence of an agent on another agent is weighted by geographical distance. A parameter α is introduced to adjust the influence: The smaller value of α means that the closer neighbors have a stronger influence on the moving direction. We find that there exists an optimal value of α leading to the highest d...

We study theoretically light propagations at the zigzag edge of a honeycomb photonic crystal consisting of dielectric rods in air, analogous to graphene. Within the photonic band gap of the honeycomb photonic crystal, a unimodal edge state may exist with a sharp confinement of optical fields. Its dispersion can be tuned simply by adjusting the radius of the edge rods. For the edge rods with a g...