Robust estimation of common regression coefficients under spherical symmetry

Consider the problem of estimating the common regression coefficients of two linear regression models where the two distributions of the errors may be different and unknown. Under the spherical symmetry assumption, the paper proves the superiority of a Graybill-Deal type combined estimator and the further improvement by the Stein effect which were exhibited by Shinozaki (1978, Comm. Statist. Theory Methods, 7, 1421–1432) in the normal case. This shows the robustness of the dominations since the conditions for the dominations are independent of the errors distributions.Research supported by NSERC Grant No. A3088 and GR-5 Grant from Faculty of Graduate Studies, Carleton University, Ottawa, Canada.     

Growth of coherence by passage in quasi-ideal isoplanatic optical systems

We find the relation between moments of the object and image mutual intensity and moments of the psf of an isoplanatic optical system. This is used to relate the coherence lengths of the object and image lights with the width of the system's psf.     

Effect of source phase fluctuations on the performance of monomode fiber optic digital communication systems

Monomode optical fibers transmitting data at high rates and using sources of narrow linewidth are likely to suffer from noise due to source phase fluctuations. This effect is investigated using a simple model for phase statistics.     

Ion solvation in 3-methyl-2-oxazolidone

In continuing previous studies of the solvation behavior of electrolytes in nonaqueous media, a series of tetraalkylammonium tetraphenylborates, cesium and rubidium tetraphenylborates, tetraalkylammonium perchlorates, and tetraphenylarsonium chloride were investigated by proton magnetic resonance spectroscopy in 3-methyl-2-oxazolidone, a solvent with high dielectric constant, high polarity, and wide liquid range. In this study, as in a previous investigation, it was found that salt solutions containing the tetraphenylborate anion were found to shift the proton peaks upfield, indicating an increase in electron density around solvent protons. In this study the same effect has been noted for tetraphenylborate as well as tetraphenylarsonium ion and is attributed to the large diamagnetic anisotropy of the aromatic solute molecules which results in circulation of electrons induced by the magnetic field. This ring current causes shielding of the solvent protons, and the shielding increases as the concentration of aromatic solute increases, resulting in upfield morement of chemical shift irrespective of whether the aromatic moiety is the cation or anion.     

Statistics of integrated speckle pattern due to mixed coherent and diffused light

An approximate formula is given for the probability distribution of integrated speckle pattern that results from a mixture of coherent and diffused light. This is a modified version of a formula originally used by Horáket al. in the context of photoelectron counting theory. The modification is based on introducing a new parameter that accounts for the lack of perfect mixing between the two waves due to temporal or spatial misalignments.     

Approximate twofold photocount statistics of superposed coherent and thermal radiation with arbitrary spectrum

An approximate formula is suggested for the twofold photocounting statistics of superposed coherent and thermal light with an arbitrary spectrum, when the counting interval and the detector area are arbitrary. The approximate moment of order (2, 1) is compared to its exact value for Lorentzian light, and curves for the approximation error are given.     

XRF induced by PIXE: Comparison with radioisotope XRF

XRF induced by PIXE (XRF-PIXE) using silver as a primary target was compared with a standard radioisotope XRF system using Cd-109 as a primary exciting source, for the analysis of single-element thin standards. The sensitivity of the two methods were determined for elements from Cl to Mo. XRF is found to be more sensitive for elements from Cl to Mn, whereas XRF-PIXE is found to be more suitable for elements from Fe to Mo. Both techniques can be considered as complementary to each other.     

Dispersion-independent high-visibility quantum interference in ultrafast parametric down-conversion

We demonstrate the effective removal of intrinsic distinguishability between entangled-photon pairs in femtosecond spontaneous parametric down-conversion. High-visibility quantum interference is recovered (an increase to 96% from 17%) while preserving the high photon-flux density associated with the use of long nonlinear crystals. This new technique is expected to serve as a basic component in the preparation of multiphoton entangled states.     

Experimental demonstration of three mutually orthogonal polarization states of entangled photons

Linearly polarized classical light can be expressed in a vertical and a horizontal component. Geometrically rotating vertically polarized light by 90 degrees will convert it to the orthogonal horizontal polarization. We have experimentally generated a two-photon state of light which evolves into an orthogonal state upon geometrical rotation by 60 degrees. Rotating this state by an additional 60 degrees will yield a state which is mutually orthogonal to the first two states. Generalizing this procedure, one can generate N+1 mutually orthogonal N-photon states that cyclicly evolve from one to another upon a geometric rotation by 180/(N+1) degrees.