whenever this limit exists. Here Σk(r) ≡ ∂Bn r (0)/Γk denotes the Euclidean sphere of radius r in the k-th conical end of M , all suband superscripts refer to the standard Euclidean coordinates on Rn, ν is the Euclidean exterior unit normal to Σk(r), and dA is the Euclidean area measure. Bartnik [1] and Chruściel [2] discovered sharp conditions on the decay rate of Φ∗g − g0 ensuring that the li...

A double-Gaussian model and the Schmidt modes are found for the biphoton wave function characterizing spontaneous parametric down-conversion with the degenerate collinear phase-matching of the type I and with a pulsed pump. The obtained results are valid for all durations of the pump pulses, short, long and intermediately long.

In the present paper, we propose a new definition of discrete parabolas, the so-called arithmetic discrete parabolas. We base our approach on a non-constant thickness function and characterized the 0connected and 1-connected parabolas in terms of thickness function. This results extend the well-known characterization of the κ-connectedness of arithmetic discrete lines, depending on the norm ‖ ·...

We describe a Bayesian estimation method for measurement of both range and surface orientation using a laser range finder. The method not only provides more accurate estimates of range for dark surfaces that are difficult to measure, but also simultaneously provides estimates of surface normals. This paper describes our efforts for a commercially available sensor, the laser rangefinder Acuity A...

In this paper we study regularity and free boundary regularity, below the continuous threshold, for the p Laplace equation in Lipschitz and C domains. To formulate our results we let Ω ⊂ R be a bounded Lipschitz domain with constant M . Given p, 1 < p < ∞, w ∈ ∂Ω, 0 < r < r0, suppose that u is a positive p harmonic function in Ω ∩ B(w, 4r), that u is continuous in Ω̄ ∩ B̄(w, 4r) and u = 0 on ∆(w,...

Some Definitions and Notations. In this section α : [0, L] → R will denote a curve in R that is parametrized by arclength and is of class C, k ≥ 2. We recall that the unit tangent to α at s is defined by −→t (s) := α′(s). (That it is a unit vector is just the definition of α being parametrized by arclength.) The curvature of α is the non-negative real-valued function k : [0, L] → R defined by k...

Analytical formulas are derived for the average intensity, the root-mean-square (rms) angular width, and the M2-factor of Laguerre-Gaussian correlated Schell-model (LGCSM) beam propagating in non-Kolmogorov turbulence. The influence of the beam and turbulence parameters on the LGCSM beam is numerically calculated. It is shown that the quality of the LGCSM beam can be improved by choo...

‹ Propose – Image rendering method • Surface normal, spectral reflectance, reflection model parameters • Using multi-band camera with six spectral channels • Acquired with different illumination directions • Developed chromatic adaptation transform • Producing the full color images on a monitor 3 3 / 15 / 15