Testing the Distance-Duality Relation with a Combination of Cosmological Distance Observations

In this paper, we propose an accurate test of the distance-duality (DD) relation, $\eta=D_{L}(z)(1+z)^{-2}/D_{A}(z)=1$ (where $D_{L}$ and $D_{A}$ are the luminosity distances and angular diameter distances, respectively), with a combination of cosmological observational data of Type Ia Supernave (SNe Ia) from Union2 set and the galaxy cluster sample under an assumption of spherical model. In order to avoid bias brought by redshift incoincidence between observational data and to consider redshift error bars of both clusters and SNe Ia in analysis, we carefully choose the SNe Ia points which have the minimum acceptable redshift difference of the galaxy cluster sample ($|\Delta z|_{\rm min} =\sigma_{z, \rm SN}+\sigma_{z, \rm cluster}$). By assuming $\eta$ a constant and functions of the redshift parameterized by six different expressions, we find that there exists no conceivable evidence for variations in the DD relation concerning with observational data, since it is well satisfied within $1\sigma$ confidence level for most cases. Further considering different values of $\Delta z$ in constraining, we also find that the choosing of $\Delta z$ may play an important role in this model-independent test of the distance-duality relation for the spherical sample of galaxy clusters.Comment: 9 pages, 4 figures, 1 table. accepted for publication in Res. Astron. Astrophy

Mean Square Capacity of Power Constrained Fading Channels with Causal Encoders and Decoders

This paper is concerned with the mean square stabilization problem of discrete-time LTI systems over a power constrained fading channel. Different from existing research works, the channel considered in this paper suffers from both fading and additive noises. We allow any form of causal channel encoders/decoders, unlike linear encoders/decoders commonly studied in the literature. Sufficient conditions and necessary conditions for the mean square stabilizability are given in terms of channel parameters such as transmission power and fading and additive noise statistics in relation to the unstable eigenvalues of the open-loop system matrix. The corresponding mean square capacity of the power constrained fading channel under causal encoders/decoders is given. It is proved that this mean square capacity is smaller than the corresponding Shannon channel capacity. In the end, numerical examples are presented, which demonstrate that the causal encoders/decoders render less restrictive stabilizability conditions than those under linear encoders/decoders studied in the existing works.Comment: Accepted by the 54th IEEE Conference on Decision and Contro

Cosmology-Independent Distance Moduli of 42 Gamma-Ray Bursts between Redshift of 1.44 and 6.60

This report is an update and extension of our paper accepted for publication in ApJ (arXiv:0802.4262). Since objects at the same redshift should have the same luminosity distance and the distance moduli of type Ia supernovae (SNe Ia) obtained directly from observations are completely cosmology independent, we obtain the distance modulus of a gamma-ray burst (GRB) at a given redshift by interpolating or iterating from the Hubble diagram of SNe Ia. Then we calibrate five GRB relations without assuming a particular cosmological model, from different regression methods, and construct the GRB Hubble diagram to constrain cosmological parameters. Based upon these relations we list the cosmology-independent distance moduli of 42 GRBs between redshift of 1.44 and 6.60, with the 1-$\sigma$ uncertainties of 1-3%.Comment: 6 pages, 2 figures, 3 tables. To appear in the proceedings of "2008 Nanjing GRB conference", Nanjing, 23-27 June 200