93 research outputs found
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
Improved bounds and new techniques for Davenport-Schinzel sequences and their generalizations
Let lambda_s(n) denote the maximum length of a Davenport-Schinzel sequence of
order s on n symbols. For s=3 it is known that lambda_3(n) = Theta(n alpha(n))
(Hart and Sharir, 1986). For general s>=4 there are almost-tight upper and
lower bounds, both of the form n * 2^poly(alpha(n)) (Agarwal, Sharir, and Shor,
1989). Our first result is an improvement of the upper-bound technique of
Agarwal et al. We obtain improved upper bounds for s>=6, which are tight for
even s up to lower-order terms in the exponent. More importantly, we also
present a new technique for deriving upper bounds for lambda_s(n). With this
new technique we: (1) re-derive the upper bound of lambda_3(n) <= 2n alpha(n) +
O(n sqrt alpha(n)) (first shown by Klazar, 1999); (2) re-derive our own new
upper bounds for general s; and (3) obtain improved upper bounds for the
generalized Davenport-Schinzel sequences considered by Adamec, Klazar, and
Valtr (1992). Regarding lower bounds, we show that lambda_3(n) >= 2n alpha(n) -
O(n), and therefore, the coefficient 2 is tight. We also present a simpler
version of the construction of Agarwal, Sharir, and Shor that achieves the
known lower bounds for even s>=4.Comment: To appear in Journal of the ACM. 48 pages, 3 figure
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
Decomposition of Geometric Set Systems and Graphs
We study two decomposition problems in combinatorial geometry. The first part
deals with the decomposition of multiple coverings of the plane. We say that a
planar set is cover-decomposable if there is a constant m such that any m-fold
covering of the plane with its translates is decomposable into two disjoint
coverings of the whole plane. Pach conjectured that every convex set is
cover-decomposable. We verify his conjecture for polygons. Moreover, if m is
large enough, we prove that any m-fold covering can even be decomposed into k
coverings. Then we show that the situation is exactly the opposite in 3
dimensions, for any polyhedron and any we construct an m-fold covering of
the space that is not decomposable. We also give constructions that show that
concave polygons are usually not cover-decomposable. We start the first part
with a detailed survey of all results on the cover-decomposability of polygons.
The second part investigates another geometric partition problem, related to
planar representation of graphs. The slope number of a graph G is the smallest
number s with the property that G has a straight-line drawing with edges of at
most s distinct slopes and with no bends. We examine the slope number of
bounded degree graphs. Our main results are that if the maximum degree is at
least 5, then the slope number tends to infinity as the number of vertices
grows but every graph with maximum degree at most 3 can be embedded with only
five slopes. We also prove that such an embedding exists for the related notion
called slope parameter. Finally, we study the planar slope number, defined only
for planar graphs as the smallest number s with the property that the graph has
a straight-line drawing in the plane without any crossings such that the edges
are segments of only s distinct slopes. We show that the planar slope number of
planar graphs with bounded degree is bounded.Comment: This is my PhD thesi
A Terrestrial Multiple-Receiver Radio Link Experiment at 10.7 GHz - Comparisons of Results with Parabolic Equation Calculations
This work presents the results of a terrestrial multiple-receiver radio link experiment at 10.7 GHz. Results are shown in the form of the power levels recorded at several antennas attached to a receiving mast. Comparisons of the measurement data with theoretical predictions using a parabolic equation technique show that, due to the complex propagation environment of the troposphere in terms of the refractive index of air, closer agreement between measurements and simulations can be achieved during periods of standard refractive conditions
A Mode-Matching Technique for Analysis of Scattering by Periodic Comb Surfaces
Numerical techniques for calculating electromagnetic fields within three-dimensional surfaces are computationally intensive. Therefore, this paper presents the application of a mode-matching technique developed for analyzing electromagnetic scattering from periodic comb surfaces illuminated by a plane wave. A set of linear equations has been developed to calculate mode coefficients of the field distribution for both E- and H-polarized incident waves. Analysis is performed for two cases where the comb thickness is either infinitely thin or of a finite thickness. The technique is shown to accurately predict both field intensities within the near-field of the periodic surface and far-field scattering patterns. Results are compared to those obtained using the finite integration techniques (FIT) implemented in CST Microwave Studio. Furthermore, numerical results are compared to measurements of an aluminum prototype. Additional far-field scattering measurements using a bi-static system provide additional confidence in CST simulations and the mode-matching methods presented here
Every Large Point Set contains Many Collinear Points or an Empty Pentagon
We prove the following generalised empty pentagon theorem: for every integer
, every sufficiently large set of points in the plane contains
collinear points or an empty pentagon. As an application, we settle the
next open case of the "big line or big clique" conjecture of K\'ara, P\'or, and
Wood [\emph{Discrete Comput. Geom.} 34(3):497--506, 2005]
Planar Point Sets Determine Many Pairwise Crossing Segments
We show that any set of points in general position in the plane
determines pairwise crossing segments. The best previously known
lower bound, , was proved more than 25 years ago by
Aronov, Erd\H os, Goddard, Kleitman, Klugerman, Pach, and Schulman. Our proof
is fully constructive, and extends to dense geometric graphs.Comment: A preliminary version to appear in the proceedings of STOC 201
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