Closed-Form Approximation for Parallel-Plate Waveguide Coefficients

Simple closed-form formulas for calculating coefficients of modes excited in a parallel-plate waveguide illuminated by a planar wave are presented. The mode-matching technique and Green’s formula are used to arrive at a matrix-based expression for waveguide coefficients calculation. Simplified solution to this matrix is proposed to derive approximate mode coefficient formulas in closed-form for both TE and TM polarization. The results are validated by numerical simulations and show good accuracy for all incidence angles and in broad frequency range

Probability that n random points are in convex position

We show that n random points chosen independently and uniformly from a parallelogram are in convex position with probability

On mutually avoiding sets

Two finite sets of points in the plane are called mutually avoiding if any straight line passing through two points of anyone of these two sets does not intersect the convex hull of the other set. For any integer n, we construct a set of n points in general position in the plane which contains no pair of mutually avoiding sets of size more than O (n). The given bound is tight up to a constant factor, since Aronov et al. [AEGKKPS] showed a polynomial time algorithm for finding two mutually avoiding sets of size (n) in any set of n points in general position in the plane

Unit squares intersecting all secants of a square

Let S be a square of side length s > 0. We construct, for any sufficiently large s, a set of less than 1.994 s closed unit squares whose sides are parallel to those of S such that any straight line intersecting S intersects at least one square of S. It disproves L. Fejes Tòth's conjecture that, for integral s, there is no such configuration of less than 2s -1 unit squares

On the minimum number of empty polygons in planar point sets

We describe a configuration (related to Horton's constructions) of n points in general position in the plane with less than 1.8 n2 empty triangles less than 2.42 n2 empty quadrilaterals less than 1.46 n2 empty pentagons and less than n2/3 emptyhexagons. It improves the constants shown by Bárány and Füredi

Diffraction Calculations and Measurements in Millimeter Frequency Band

The paper deals with a study of diffraction on dielectric wedge (building corner) in millimeter frequency band, both theoretically and experimentally, to provide knowledge support for ray tracing/launching calculations of MWS interference issues in urban areas. The main motivation was to find balance between reasonably reliable results and necessary demands on calculation complexity and input data accuracy. Verification of Uniform Theory of Diffraction (UTD) was made both for perfectly conducting and dielectric wedge-shaped obstacle. Comparisons of theoretical results and experimental measurement at millimeter waves in anechoic chamber are presented