Satellite signatures in SLR observations

We examine the evidence for the detection of satellite-dependent signatures in the laser range observations obtained by the UK single-photon Satellite Laser Ranging (SLR) System models of the expected observation distributions from Ajisai and Lageos are developed from the published satellite spread functions and from the characteristics of the SLR System and compared with the observations. The effects of varying return strengths are discussed using the models and by experimental observations of Ajisai, during which a range of return levels from single to multiple photons is achieved. The implications of these results for system-dependent center for mass corrections are discussed

Spectra of phase point operators in odd prime dimensions and the extended Clifford group

We analyse the role of the Extended Clifford group in classifying the spectra of phase point operators within the framework laid out by Gibbons et al for setting up Wigner distributions on discrete phase spaces based on finite fields. To do so we regard the set of all the discrete phase spaces as a symplectic vector space over the finite field. Auxiliary results include a derivation of the conjugacy classes of ${\rm ESL}(2, \mathbb{F}_N)$.Comment: Latex, 19page

SIC~POVMs and Clifford groups in prime dimensions

We show that in prime dimensions not equal to three, each group covariant symmetric informationally complete positive operator valued measure (SIC~POVM) is covariant with respect to a unique Heisenberg--Weyl (HW) group. Moreover, the symmetry group of the SIC~POVM is a subgroup of the Clifford group. Hence, two SIC~POVMs covariant with respect to the HW group are unitarily or antiunitarily equivalent if and only if they are on the same orbit of the extended Clifford group. In dimension three, each group covariant SIC~POVM may be covariant with respect to three or nine HW groups, and the symmetry group of the SIC~POVM is a subgroup of at least one of the Clifford groups of these HW groups respectively. There may exist two or three orbits of equivalent SIC~POVMs for each group covariant SIC~POVM, depending on the order of its symmetry group. We then establish a complete equivalence relation among group covariant SIC~POVMs in dimension three, and classify inequivalent ones according to the geometric phases associated with fiducial vectors. Finally, we uncover additional SIC~POVMs by regrouping of the fiducial vectors from different SIC~POVMs which may or may not be on the same orbit of the extended Clifford group.Comment: 30 pages, 1 figure, section 4 revised and extended, published in J. Phys. A: Math. Theor. 43, 305305 (2010

The resummation of inter-jet energy flow for gaps-between-jets processes at HERA

We calculate resummed perturbative predictions for gaps-between-jets processes and compare to HERA data. Our calculation of this non-global observable needs to include the effects of primary gluon emission (global logarithms) and secondary gluon emission (non-global logarithms) to be correct at the leading logarithm (LL) level. We include primary emission by calculating anomalous dimension matrices for the geometry of the specific event definitions and estimate the effect of non-global logarithms in the large $N_c$ limit. The resulting predictions for energy flow observables are consistent with experimental data.Comment: 31 pages, 4 figures, 2 table

Formation of on-site normal points

We describe our methods of fitting a smoothing function to observational range differences from a predicted orbit, by deducing corrections to the orbit in the radial and along-track directions. The method has been used on observations of a variety of satellites, and using predicted orbits computed both by numerical integration using IRV's as starting values and analytically from orbital elements. The along-track corrections to the predicted orbit have been successfully used in the form of time biases to improve subsequent predictions, and a statistical test has been devised to ensure that the range residuals may be used to form unbiased quick look normal points

Joint measurements via quantum cloning

We explore the possibility of achieving optimal joint measurements of noncommuting observables on a single quantum system by performing conventional measurements of commuting self adjoint operators on optimal clones of the original quantum system. We consider the case of both finite dimensional and infinite dimensional Hilbert spaces. In the former we study the joint measurement of three orthogonal components of a spin 1/2, in the latter we consider the case of the joint measurements of any pair of noncommuting quadratures of one mode of the electromagnetic field. We show that universally covariant cloning is not ideal for joint measurements, and a suitable non universally covariant cloning is needed.Comment: 8 page

Reconstruction of contaminant trends in a salt wedge estuary with sediment cores dated using a multiple proxy approach

The Taunton River is a partially mixed tidal estuary in southeastern Massachusetts (USA) which has received significant contaminant inputs, yet little information exists on the history of discharge and the subsequent fate of these contaminants. Three sediment cores taken along a transect were analyzed, reconstructing the spatial and temporal trends of pollution in the estuary. A combination of radiometric dating, contaminant markers, and storm layers from major hurricanes were used to establish age models and sedimentation rates. Age estimates obtained from the different dating methods compared well, establishing an accurate history of contaminant release to the estuary. Polycyclic aromatic hydrocarbons (PAHs) were present in one core at depths corresponding to the early 1860s, earlier than previously established dates of introduction. Temporal and spatial trends of Cr, Cu, Hg and Pb indicated multiple sources of varying input to the river. Polychlorinated biphenyls (PCBs) were present in each of the cores from the 1930s onward, with elevated levels still present in surficial sediments at several sites. A unique organic compound, Topanol, which was produced locally was used as a tracer to track contaminant transport in the river. Tracer data indicates that contaminants are still being transported and deposited to surficial sediments at high concentrations well after their discharge. This reconstruction demonstrates the utility of using multiple dating proxies where often the sole use of radiometric dating techniques is not an option and provides insights into the fate of contaminants discharged decades ago but continue to represent environmental risks