Computational aspects of cutting-plane algorithms for geometric programming problems

This paper presents the results of computational studies of the properties of cutting plane algorithms as applied to posynomial geometric programs. The four cutting planes studied represent the gradient method of Kelley and an extension to develop tangential cuts; the geometric inequality of Duffin and an extension to generate several cuts at each iteration. As a result of over 200 problem solutions, we will draw conclusions regarding the effectiveness of acceleration procedures, feasible and infeasible starting point, and the effect of the initial bounds on the variables. As a result of these experiments, certain cutting plane methods are seen to be attractive means of solving large scale geometric programs.This author's research was supported in part by the Center for the Study of Environmental Policy, The Pennsylvania State University.     

Lattice models for liquid crystals

A problem in the theory of liquid crystals is to construct a model system which at low temperatures displays long-range orientational order, but not translational order in all directions. We present five lattice models (two two-dimensional and three three-dimensional) of hard-core particles with attractive interactions and prove (using reflection positivity and the Peierls argument) that they have orientational order at low temperatures; the two-dimensional models have no such ordering if the attractive interaction is not present. We cannot prove that these models do not have complete translational order, but their zero-temperature states are such that we are led to conjecture that complete translational order is always absent.Work of EHL supported by U.S. National Science Foundation Grant MCS 75-21684 A02. Financial assistance from the Danish Natural Science Research Council is also gratefully acknowledged.     

On the existence of optimal partially observed controls

A stochastic control problem whose dynamics are only partially observed is solved. In earlier literature it was conjectured that for such problems an optimal relaxed control exists. In this article we prove that for the problem under consideration the optimal relaxed control exists and is the weak limit of a minimizing sequence of ordinary controls. Making use of the special discrete nature of the observations and of the special form of the drift function the existence of an optimal ordinary control is derived.The general partially observed control problem is then approximated by a sequence of problems of the above form, i.e., with discrete observations. In this way the existence of an ordinary optimal control is derived for the general problem.During part of his work on this topic the author was a guest of the SFB 72 of the Deutsche Forschungsgemeinschaft of the University of Bonn.The author's work was partially supported by the Deutsche Forschungsgemeinschaft within the SFB 72 of the University of Bonn.     

Discrimination of rising and falling simulated single-formant frequency transitions: practice and transition duration effects

Two experiments evaluated discrimination of simulated single-format frequency transitions. In the first experiment, listeners received practice with trial-by-trial feedback in discriminating either rising or falling frequency transitions of three different durations (30, 60, and 120 ms). Transitions either occurred in isolation or were followed by a steady-state sound matched in frequency to the transition end point. Some improvement in discrimination over practice runs occurred for the shortest transitions. Whether performance was evaluated at the beginning or end of practice, there were no differences attributable to transition direction or to whether transitions were followed by steady-state sound. Discrimination, however, was significantly better for the longest transitions. Just noticeable differences (jnd's) for the longest transitions, measured in Hz at transition onsets, were of approximately the same magnitude as jnd's for steady-state sounds that were equal in frequency to the midpoints of the transitions. Subjects of the second experiment discriminated the longer rising and falling transitions, but did not receive extensive practice. Results of experiment 2 replicated results of experiment 1 in showing similar jnd's. Experiment 2 also showed no differences attributable to transition direction or to the presence of the steady-state sound following transitions.     

Electron paramagnetic resonance in Y1−cH1.92:Erc

We have investigated the EPR of isotopically enriched ¹⁶⁸Er³⁺ in Y_1?cH_1.92:Er_c where c = 100 and 1400 ppm, at both 1.4 and 9 GHz and between 1.5 and 50 K. Resonance lines were observed from Er³⁺ ions in both sites of cubic symmetry and sites of axial symmetry. We determine the numbers of Er³⁺ in cubic, and C_4v axial symmetry to be in the ratio 2:1. The cubic site resonance line is at g = 6.85 ± 0.07 and is attributed to a Γ₇ doublet. The linewidth has a linear thermal broadening of 3.9 ± 0.05 gauss K^-1 below circa 7 K. From the nonlinear thermal broadening above this temperature we determine the first excited state, in the cubic crystal field scheme, to be a Γ₈ at 35 ± 10 K above the Γ₇ ground state. We have investigated the origins of the (T = 0) residual linewidth for the ions in cubic symmetry, and conclude there to be a small but significant contribution due to unresolved transferred hyperfine structure from the surrounding hydrogen nuclei.     

The absorption edge technique at the Super-EBIT

High temperature Mössbauer spectroscopy has been used for studying “in situ” the phase dynamics of the silicon rich part of the binary Fe-Si system. In particular the rate and mechanism of the transformation of the so-called zeta-alpha phase of iron disilicide to the zeta-beta phase is of special interest, since there still remains uncertainty about the stability and the structure of the phase in this system which influence material properties such as compressive strength and disintegration. In the present work the phase transition from the zeta-alpha phase to the zeta-beta phase is followed by a time sequence of Mössbauer spectra recorded every three hours at a fixed temperature around 800 K. The exponential precipitation rate is analysed and the exponent calculated. Samples with differing degree of impurities have been studied and the effect of aluminium impurities on the rate of the transition will be discussed. The Debye temperature of the two phases was determined from series of Mössbauer spectra recorded at temperatures between 300 and 800 K.     

An arithmetic operator and the functions on which it is part-bounded

Approximate eigenfunctions of certain self-adjoint arithmetic operators are characterized, even when the eigenfunctions are only partially known.In memory of my friend Stan Ulam.