Relative efficiencies of estimates using patterned covariances or correlations in the multivariate normal estimation problem

Summary The relative efficiency of maximum likelihood estimates is studied when taking advantage of underlying linear patterns in the covariances or correlations when estimating covariance matrices. We compare the variances of estimates of the covariance matrix obtained under two nested patterns with the assumption that the more restricted pattern is the true state. Formulas for the asymptotic variances are given which are exact for linear covariance patterns when explicit maximum likelihood estimates exist. Several specific examples are given using complete symmetry, circular symmetry and general covariance patterns as well as an example involving a covariance matrix with a linear pattern in the correlations.     

A nuclear magnetic resonance determination of the barrier to internal rotation in phenylethane

The long-range nuclear spin-spin coupling constant between the methylene protons and the ring protons at the para position in 3,5-dibromo-phenylethane in benzene solution is consistent with a two-fold barrier of 1.2 ± 0.1 kcal/mole to rotation about the sp²-sp³ carbon-carbon bond, in agreement with thermodynamic data on phenylethane and with deductions based on hyperfine interactions in related radical anions. The low-energy conformation has a plane of symmetry, the methyl group being situated out of the aromatic plane, in disagreement with Raman depolarization data interpretations and with deductions based on proton chemical shifts.     

Squeezing in the degenerate parametric oscillator

Squeezing of the intracavity field in a degenerate parametric oscillator is calculated above threshold neglecting pump depletion. Arbitrary squeezing is in principle obtainable. We conclude that above threshold squeezing in the steady-state parametric oscillator is limited primarily by pump depletion rather than degradation by vacuum fluctuations at the mirrors. The squeezing predicted by the present calculation should be observable in an oscillator operated in a transient or pulsed mode     

Steady-state formulation of optical bistability for a Doppler-broadened medium in a Fabry-Perot

A two-level model for absorptive and dispersive bistability in a Fabry-Perot is described. Doppler broadening and the effects of atomic motion through the standing wave field are included. Numerical results illustrating saturation of the Doppler line are presented and bistable transmission characteristics are obtained for systems with varying degrees of Doppler broadening.     

Anomalous lattice parameters and hydrogen solubilities in dilute PdFe alloys

Lattice parameters for fcc $\text{Pd}$Fe alloys exhibit a maximum at X_Fe = 0.003 where X_Fe is the atom fraction Fe. In this region of alloy composition the solubility of H₂ is also a maximum. It is suggested that the “giant moments” found in this region cause the anomalous lattice expansion which in turn is the major source of the enhanced H₂ solubility.     

Thermodynamics of hydrogen solution and hydride formation in Pd-Mn alloys. 2. Ordered alloys

There are marked differences in H(2) solubilities between ordered and disordered Pd-Mn alloys with the largest difference found between the L1(2) and the disordered form of the Pd(3)Mn alloy. The thermodynamics of H(2) solution have been determined for the L1(2) form, the long-period superstructure (lps), and the disordered forms of the Pd(0.80)Mn(0.20) and Pd(0.75)Mn(0.25)(Pd(3)Mn) alloys. Relative partial molar enthalpies and entropies were determined mainly by reaction calorimetry over the range of H contents accessible from p(H)()2 approximately 10 Pa to approximately 0.3 MPa (303 K). The enthalpies for absorption of H(2) are more exothermic over most of the range of H contents for the L1(2) forms of the Pd(3)Mn and Pd(0.80)Mn(0.20) alloys than for their other forms. The reaction enthalpies are constant across a relatively wide range of H contents for the L1(2) form of the Pd(0.80)Mn(0.20) and Pd(3)Mn alloys indicating that there are two-phase coexistence regions (303 K). The H-H attractive interaction, which leads to hydride formation, is much greater for the L1(2) than for the other forms of the Pd(3)Mn alloy and for Pd itself. It has been found that the H-H interaction always decreases in magnitude and, accompanying this, the THS (terminal hydrogen solubility) always increases by alloying Pd.(1) The L1(2) ordered Pd(3)Mn alloy is an exception to this, and therefore, the generalization about THS must be restricted to disordered face centered cubic (fcc) Pd alloys.