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.     

Salem numbers and L-functions

Every Salem number is the exponential of a rational multiple of the derivative at s = 0 of an Artin L-function.     

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.     

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.     

N- and P-channel transport behavior in thin film transistors based on tricyanovinyl-capped oligothiophenes

We report the structural and electrical characterization of thin films of organic semiconductor molecules consisting of an oligothiophene core capped with electron-withdrawing tricyanovinyl (TCV) groups. X-ray diffraction and atomic force microscopy of evaporated films of three different TCV-capped oligothiophenes showed that the films were highly crystalline. Electrical transport was measured in thin film transistors employing silver source and drain contacts and channel probes to correct for contact resistance. Three compounds exhibited n-channel (electron) conduction consistent with cyclic voltametry data that indicated they undergo facile reduction. Maximum electron mobilities were 0.02 cm2/V.s with an on/off current ratio of 10(6). A fourth end-capped molecule, TCV-6T-TCV, which had six thiophene rings, exhibited both p- and n-channel transport. Overall, these results confirm that substitution of oligothiophene cores with electron-withdrawing groups is a useful strategy to achieve electron-transporting materials.     

Nonequilibrium thermodynamics of spacetime

It has previously been shown that the Einstein equation can be derived from the requirement that the Clausius relation dS=deltaQ/T hold for all local acceleration horizons through each spacetime point, where is one-quarter the horizon area change in Planck units and deltaQ and T are the energy flux across the horizon and the Unruh temperature seen by an accelerating observer just inside the horizon. Here we show that a curvature correction to the entropy that is polynomial in the Ricci scalar requires a nonequilibrium treatment. The corresponding field equation is derived from the entropy balance relation dS=deltaQ/T+diS, where diS is a bulk viscosity entropy production term that we determine by imposing energy-momentum conservation. Entropy production can also be included in pure Einstein theory by allowing for shear viscosity of the horizon.