On a compromise social choice correspondence

This paper analyzes the compromise social choice correspondence derived from the τ-value of digraph games. Monotonicity of this correspondence is shown. A connection between several properties of social choice correspondences based on game theoretical solutions and game theoretical properties of the underlying solutions is given. Applications to several game theoretic solutions are provided.     

Stable Ergodicity and Frame Flows

In this note we show that all diffeomorphisms close enough to the time-one map of the frame flow on certain negatively curved manifolds are ergodic. As a simple corollary we deduce that the frame flows are ergodic for all compact manifolds with curvature pinched sufficiently close to –1, thus providing results in the case of manifolds of dimension 7 or 8 which were missing from the results of Brin and Karcher.     

Microwave frequency shifting using photon acceleration

Using a Bostick Gun as a plasma source, we have been investigating the effects of a moving plasma front on the frequency of an incident R.F. signal. We have been able to measure frequency shifts of 10 MHz frequency with a 2.6 GHz signal. The density is such that the plasma frequency is well above the transmitter frequency 1.3 meters from the plasma source. No magnetic field is used.     

Quasiperiodic motions in superquadratic time-periodic potentials

It is shown that for a large class of potentials on the line with superquadratic growth at infinity and with the additional time-periodic dependence all possible motions under the influence of such potentials are bounded for all time and that most (in a precise sense) motions are in fact quasiperiodic. The class of potentials includes, as very particular examples, the exponential, polynomial and much more. This extends earlier results and gives an answer to a problem posed by Littlewood in the mid 1960's. Along the way machinery is developed for estimating the action-angle transformation directly in terms of the potential and also some apparently new identities involving singular integrals are derived.     

Initial data truncation for multivariate output of discrete-event simulations using the Kalman filter

Data truncation is a commonly accepted method of dealing with initialization bias in discrete-event simulation. An algorithm for determining the appropriate initial-data truncation point for multivariate output is proposed. The technique entails averaging across independent replications and estimating a steady-state output model in a state-space framework. A Bayesian technique called Multiple Model Adaptive Estimation (MMAE) is applied to compute a time varying estimate of the output's steady-state mean vector. This MMAE implementation features the use, in paralle, of a bank of Kalman filters. Each filter is constructed under a different assumption concerning the output's steady-state mean vector. One of the filters assumes that the steady-state mean vector is accurately reflected by an estimate, called the assumed steady-state mean vector, taken from the last half of the simulation data. As the filters process the output through the effective transient, this particular filter becomes more likely (in a Bayesian sense) to be the best filter to represent the data and the MMAE mean estimator is influenced increasingly towards the assumed steady-state mean vector. The estimated truncation point is selected when a norm of the MMAE mean vector estimate is within a small tolerance of the assumed steady-state mean vector. A Monte Carlo analysis using data from simulations of open and closed queueing models is used to evaluate the technique. The evaluation criteria include the ability to construct accurate and reliable confidence regions for the mean response vector based on the truncated sequences.     

Spherically symmetric fields in Rosen's bimetric theories of gravitation

By means of bimetric Killing vectors two spherically symmetric fields are investigated: (i) the time-dependent one in Rosen's flat-background bimetric theory; and (ii) the energy-preserving in Rosen's cosmological-background bimetric theory withk = 1. In the first case a wave behavior of the field is present. In the second case a time evolution is obtained for fields, created by insular systems of constant energy. These phenomena are typical for bimetric theories of gravitation.     

The beta decay of90g Tc and90m Tc

The level structure of⁹⁰Mo is investigated via the beta decay of^90g Tc and^90m Tc whose half-lives are measured to be 8.7±0.2 and 49.2±0.4 s, respectively. The decay properties are studied by means of beta and gamma spectroscopy techniques. The level structure of⁹⁰Mo populated in the decays of both isomers is proposed with deducedJ ^π values. Theβ-decay energies for^90g Tc and^90m Tc are 8.8±0.3 and 9.3±0.3 MeV, respectively. The structure is discussed in terms of the shell model.     

Does a generic connection depend continuously on its curvature?

For a principal bundle with semi-simple structure group over a smooth four-dimensional base manifold, the set of connections (gauge potentials)A which are uniquely determined by their curvature (field or field strength)F is generic in the set of all potentials, endowed with the WhitneyC ^∞ topology. However, the operator taking each such fieldF to its potentialA is not continuous. Partial negative results are given concerning the existence of a smaller generic set on which this operator is continuous.