686 research outputs found
Resonant-state-expansion Born approximation for waveguides with dispersion
The resonant-state expansion (RSE) Born approximation, a rigorous
perturbative method developed for electrodynamic and quantum mechanical open
systems, is further developed to treat waveguides with a Sellmeier dispersion.
For media that can be described by these types of dispersion over the relevant
frequency range, such as optical glass, I show that the perturbed RSE problem
can be solved by diagonalizing a second-order eigenvalue problem. In the case
of a single resonance at zero frequency, this is simplified to a generalized
eigenvalue problem. Results are presented using analytically solvable planar
waveguides and parameters of borosilicate BK7 glass, for a perturbation in the
waveguide width. The efficiency of using either an exact dispersion over all
frequencies or an approximate dispersion over a narrow frequency range is
compared. I included a derivation of the RSE Born approximation for waveguides
to make use of the resonances calculated by the RSE, an RSE extension of the
well-known Born approximation.Comment: BEST VERSION OF THIS ARTICL
Global offensive -alliances in digraphs
In this paper, we initiate the study of global offensive -alliances in
digraphs. Given a digraph , a global offensive -alliance in a
digraph is a subset such that every vertex outside of
has at least one in-neighbor from and also at least more in-neighbors
from than from outside of , by assuming is an integer lying between
two minus the maximum in-degree of and the maximum in-degree of . The
global offensive -alliance number is the minimum
cardinality among all global offensive -alliances in . In this article we
begin the study of the global offensive -alliance number of digraphs. For
instance, we prove that finding the global offensive -alliance number of
digraphs is an NP-hard problem for any value and that it remains NP-complete even when
restricted to bipartite digraphs when we consider the non-negative values of
given in the interval above. Based on these facts, lower bounds on
with characterizations of all digraphs attaining the bounds
are given in this work. We also bound this parameter for bipartite digraphs
from above. For the particular case , an immediate result from the
definition shows that for all digraphs ,
in which stands for the domination number of . We show that
these two digraph parameters are the same for some infinite families of
digraphs like rooted trees and contrafunctional digraphs. Moreover, we show
that the difference between and can be
arbitrary large for directed trees and connected functional digraphs
Characterization of Rate Region in Interference Channels with Constrained Power
In this paper, an -user Gaussian interference channel, where the power of
the transmitters are subject to some upper-bounds is studied. We obtain a
closed-form expression for the rate region of such a channel based on the
Perron-Frobenius theorem. While the boundary of the rate region for the case of
unconstrained power is a well-established result, this is the first result for
the case of constrained power. We extend this result to the time-varying
channels and obtain a closed-form solution for the rate region of such
channels.Comment: 21 Pages, The Conference Version is Submitted to IEEE International
Symposium on Information Theory (ISIT2007
Resonant state expansion applied to two-dimensional open optical systems
The resonant state expansion (RSE), a rigorous perturbative method in
electrodynamics, is applied to two-dimensional open optical systems. The
analytically solvable homogeneous dielectric cylinder is used as unperturbed
system, and its Green's function is shown to contain a cut in the complex
frequency plane, which is included in the RSE basis. The complex
eigenfrequencies of modes are calculated using the RSE for a selection of
perturbations which mix unperturbed modes of different orbital momentum, such
as half-cylinder, thin-film and thin-wire perturbation, demonstrating the
accuracy and convergency of the method. The resonant states for the thin-wire
perturbation are shown to reproduce an approximative analytical solution
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