4,385 research outputs found
Asymptotic Behavior of Colored Jones polynomial and Turaev-Viro Invariant of figure eight knot
In this paper we investigate the asymptotic behavior of the colored Jones
polynomials and the Turaev-Viro invariants for the figure eight knot. More
precisely, we consider the -th colored Jones polynomials evaluated at
-th root of unity with a fixed limiting ratio, , of and
. We find out the asymptotic expansion formula (AEF) of the colored
Jones polynomials of the figure eight knot with close to . Nonetheless,
we show that the exponential growth rate of the colored Jones polynomials of
the figure eight knot with close to is strictly less than those with
close to . It is known that the Turaev Viro invariant of the figure
eight knot can be expressed in terms of a sum of its colored Jones polynomials.
Our results show that this sum is asymptotically equal to the sum of the terms
with close to 1. As an application of the asymptotic behavior of the
colored Jones polynomials, we obtain the asymptotic expansion formula for the
Turaev-Viro invariants of the figure eight knot. Finally, we suggest a possible
generalization of our approach so as to relate the AEF for the colored Jones
polynomials and the AEF for the Turaev-Viro invariants for general hyperbolic
knots.Comment: 40 pages, 0 figure
Accurate angle-of-arrival measurement using particle swarm optimization
As one of the major methods for location positioning, angle-of-arrival (AOA) estimation is a significant technology in radar, sonar, radio astronomy, and mobile communications. AOA measurements can be exploited to locate mobile units, enhance communication efficiency and network capacity, and support location-aided routing, dynamic network management, and many location-based services. In this paper, we propose an algorithm for AOA estimation in colored noise fields and harsh application scenarios. By modeling the unknown noise covariance as a linear combination of known weighting matrices, a maximum likelihood (ML) criterion is established, and a particle swarm optimization (PSO) paradigm is designed to optimize the cost function. Simulation results demonstrate that the paired estimator PSO-ML significantly outperforms other popular techniques and produces superior AOA estimates
An Image Forensic Scheme with Robust and Fragile Watermarking for Business Documents
This paper proposes an image forensic scheme with both robust and fragile watermarking techniques for business documents. Through a dual watermarking approach, the proposed scheme can achieve image forensics objectives of (a) identification of source; (b) authentication of documents; and (c) locating the tempered areas of documents due to attacks. An example is presented to prove the concepts of the proposed scheme.
Keywords: Image Forensics, Fragile and Robust Watermarking, Business Document
Characterization of BMO in terms of rearrangement-invariant Banach function spaces
AbstractThe atomic decomposition of Hardy spaces by atoms defined by rearrangement-invariant Banach function spaces is proved in this paper. Using this decomposition, we obtain the characterizations of BMO and Lipschitz spaces by rearrangement-invariant Banach function spaces. We also provide the sharp function characterization of the rearrangement-invariant Banach function spaces
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