Kramers degeneracy without eigenvectors

Wigner gave a well-known proof of Kramers degeneracy, for time reversal invariant systems containing an odd number of half-integer spin particles. But Wigner's proof relies on the assumption that the Hamiltonian has an eigenvector, and thus does not apply to many quantum systems of physical interest. This note illustrates an algebraic way to talk about Kramers degeneracy that does not appeal to eigenvectors, and provides a derivation of Kramers degeneracy in this more general context.Comment: 5 page

Disregarding the 'Hole Argument'

Jim Weatherall has suggested that Einstein's hole argument, as presented by Earman and Norton (1987), is based on a misleading use of mathematics. I argue on the contrary that Weatherall demands an implausible restriction on how mathematics is used. The hole argument, on the other hand, is in no new danger at all.Comment: 19 pages, 4 figure

Efficient Semiparametric Prediction Intervals

The construction of prediction intervals and regions and their probability content for nonlinear systems with nonparametric disturbances is considered. The semiparametric efficiency bound for estimating the probability content of a known interval (region) and estimators that attain the bound are developed. Semiparametric efficient estimation of optimal prediction intervals (regions) which either (i) maximize probability content given interval length (region area) or (ii) maximize interval length (region area) given probability content is studied. The estimated probability content of (i) is found to have the same limiting behavior as if the interval (region) were known with certainty and hence attains the semiparametric efficiency bound. Further, the estimated probability of the estimated interval (region) approximates the true coverage probability to order root-n for (i) but order smaller than root-n for (ii). A Monte Carlo experiment is conducted to compare the new predictors to competitors.

Deep sea mega-geomorphology: Progress and problems

Historically, marine geologists have always worked with mega-scale morphology. This is a consequence both of the scale of the ocean basins and of the low resolution of the observational remote sensing tools available until very recently. In fact, studies of deep sea morphology have suffered from a serious gap in observational scale. Traditional wide-beam echo sounding gave images on a scale of miles, while deep sea photography has been limited to scales of a few tens of meters. Recent development of modern narrow-beam echo sounding coupled with computer-controlled swath mapping systems, and development of high-resolution deep-towed side-scan sonar, are rapidly filling in the scale gap. These technologies also can resolve morphologic detail on a scale of a few meters or less. As has also been true in planetary imaging projects, the ability to observe phenomena over a range of scales has proved very effective in both defining processes and in placing them in proper context

Models of foreign exchange intervention: Estimation and testing

We propose a general non-linear simultaneous equations framework for the econometric analysis of models of intervention in foreign exchange markets by central banks in response to deviations of exchange rates from possibly time-varying target levels. We consider efficient estimation of possibly non-linear response functions and tests of functional form, the latter making use of the econometric literature on testing in the presence of nuisance parameters unidentified under a null hypothesis. The methodology is applied in an analysis of recent activity of the Bank of Canada with respect to the Canada-U.S. exchange ratCentral bank intervention, nonlinear simultaneous equations, time series, semiparametric methods

Generic concepts of the automated multifunctional receiver

Automated multifunctional receiver for space tracking and data acquisition network, manned space flight network, and deep space networ