Studying Gaussian beam is a method to investigate laser beam propagation and ABCD matrix is a fast and simple method to simulate Gaussian beam propagation in different mediums. Of the ABCD matrices studied so far, reflection and refraction matrices at various surfaces have attracted a lot of researches. However in previous work the incident beam and the principle axis of surface are in parallel...

We study first-passage properties for a particle that diffuses either inside or outside of generalized paraboloids, defined by y = a(x1 + · · ·+ xd−1) where p > 1, with absorbing boundaries. When the particle is inside the paraboloid, the survival probability S(t) generically decays as a stretched exponential, lnS ∼ −t(p−1)/(p+1), independent of the spatial dimension. For a particle outside the...

Spanish architect Antoni Gaudı́ drew on natural precedent to create fantastic organically inspired designs. This paper examines some common motifs in his works, and demonstrates how simple geometric operations can be applied to polyhedral models to achieve similar results. The importance of the partial hyperbolic paraboloid surface (or hypar) is discussed in this context. r 2007 Elsevier Ltd. Al...

For cylindrically symmetric functions dyadically supported on the paraboloid, we obtain a family of sharp linear and bilinear adjoint restriction estimates. As corollaries, we first extend the ranges of exponents for the classical linear or bilinear adjoint restriction conjectures for such functions and verify the linear adjoint restriction conjecture for the paraboloid. We also interpret the r...

Spanish architect Antoni Gaudı́ drew on natural precedent to create fantastic organically inspired designs. This paper examines some common motifs in his works, and demonstrates how simple geometric operations can be applied to polyhedral models to achieve similar results. The importance of the partial hyperbolic paraboloid surface (or hypar) is discussed in this context. r 2007 Elsevier Ltd. Al...

An open problem in affine geometry is whether an affine complete locally uniformly convex hypersurface in Euclidean (n + 1)-space is Euclidean complete for n ≥ 2. In this paper we give the affirmative answer. As an application, it follows that an affine complete, affine maximal surface in R3 must be an elliptic paraboloid.

We deal with the restriction phenomenon for the Fourier transform. We prove that each of the restriction conjectures for the sphere, the paraboloid, the elliptic hyperboloid in R implies that for the cone in R. We also prove a new restriction estimate for any surface in R locally isometric to the plane and of finite type.

The intent of this analysis is to explore the influence of thermal radiation paired with variable thermal conductivity on MHD micropolar fluid flow over an upper surface. The novelty of the present model is to consider the fluid flow along an upper horizontal surface of a paraboloid of revolution (uhspr) with the porous medium.  This physical phenomenon is described by a set of coupled...

This paper presents an algorithm to compute the bisector curve of two planar paramet-ric curves. We reduce the problem of computing a bisector curve to that of intersecting two developable surfaces. Given an input curve C (t) = (x(t); y(t)), the corresponding developable surface D C(t) is constructed symbolically as the envelope surface of a one-parameter family of tangent planes of the parabol...

Two offset IRAs are numerically modeled and analyzed. The reflector of the offset IRA is an offset portion of a paraboloid that is carved out by the intersection of the paraboloid and a cone whose apex is at the focal point of the paraboloid. A pair of conical curved plates is placed on the surface of the cone as TEM feed arms. The TEM feed arm of the first IRA is conical throughout its length ...