3,798 research outputs found
On Minimal Spectral Factors with Zeroes and Poles lying on Prescribed Region
In this paper, we consider a general discrete-time spectral factorization
problem for rational matrix-valued functions. We build on a recent result
establishing existence of a spectral factor whose zeroes and poles lie in any
pair of prescribed regions of the complex plane featuring a geometry compatible
with symplectic symmetry. In this general setting, uniqueness of the spectral
factor is not guaranteed. It was, however, conjectured that if we further
impose stochastic minimality, uniqueness can be recovered. The main result of
his paper is a proof of this conjecture.Comment: 14 pages, no figures. Revised version with minor modifications. To
appear in IEEE Transactions of Automatic Contro
On the existence of a solution to a spectral estimation problem \emph{\`a la} Byrnes-Georgiou-Lindquist
A parametric spectral estimation problem in the style of Byrnes, Georgiou,
and Lindquist was posed in \cite{FPZ-10}, but the existence of a solution was
only proved in a special case. Based on their results, we show that a solution
indeed exists given an arbitrary matrix-valued prior density. The main tool in
our proof is the topological degree theory.Comment: 6 pages of two-column draft, accepted for publication in IEEE-TA
D-branes and extended characters in SL(2,R)/U(1)
We present a detailed study of D-branes in the axially gauged SL(2,R)/U(1)
coset conformal field theory for integer level k. Our analysis is based on the
modular bootstrap approach and utilizes the extended SL(2,R)/U(1) characters
and the embedding of the parafermionic coset algebra in the N=2 superconformal
algebra. We propose three basic classes of boundary states corresponding to
D0-, D1- and D2-branes. We verify that these boundary states satisfy the Cardy
consistency conditions and discuss their physical properties. The D0- and
D1-branes agree with those found in earlier work by Ribault and Schomerus using
different methods (descent from the Euclidean AdS3 model). The D2-branes are
new. They are not, in general, space-filling but extend from the asymptotic
circle at infinity up to a circular boundary at some distance from the tip of
the cigar.Comment: 61 pages, 1 figure, 1 table; v2 typos corrected, added a subsection
with comments on B-type class 3 boundary states; v3 more typos corrected,
version to appear in NP
Analysis of new direct sampling indicators for far-field measurements
This article focuses on the analysis of three direct sampling indicators
which can be used for recovering scatterers from the far-field pattern of
time-harmonic acoustic measurements. These methods fall under the category of
sampling methods where an indicator function is constructed using the far-field
operator. Motivated by some recent work, we study the standard indicator using
the far-field operator and two indicators derived from the factorization
method. We show the equivalence of two indicators previously studied as well as
propose a new indicator based on the Tikhonov regularization applied to the
far-field equation for the factorization method. Finally, we give some
numerical examples to show how the reconstructions compare to other direct
sampling methods
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