On Backtracking Failure in Newton–GMRES Methods with a Demonstration for the Navier–Stokes Equations

In an earlier study of inexact Newton methods, we pointed out that certain counterintuitive behavior may occur when applying residual backtracking to the Navier–Stokes equations with heat and mass transport. Specifically, it was observed that a Newton–GMRES method globalized by backtracking (linesearch, damping) may be less robust when high accuracy is required of each linear solve in the Newton sequence than when less accuracy is required. In this brief discussion, we offer a possible explanation for this phenomenon, together with an illustrative numerical experiment involving the Navier–Stokes equations.     

Thermoreflectance of CuI

The thermoreflectance spectrum of CuI in the 4–7 eV region is reported. New structure in the $\text{E}\text{O}\text{′}$ region has been assigned to the spin-orbit split triplet between the first valence band and the second conduction band at k=0. The magnitude of the splitting indicates an inverted order in the second conduction band and a large d-state mixture in the valence band.     

Pion-nucleus inelastic scattering and charge exchange

Using a separable fixed scatterer pion-nucleon interaction and the distorted wave impulse approximation we have made predictions for medium energy pion inelastic scattering from ¹⁶O and (π^?, π⁰) charge exchange from ⁴⁸Ca. An optical potential based on the pion-nucleon interaction adopted in this work has been shown previously to provide good fits to pion-nucleus elastic scattering. After a discussion of the basic formulae, we present results of calculations for pion inelastic scattering from ¹⁶O for initial pion lab kinetic energies of 70 and 180 MeV. Because of the strong energy dependence of the pion-nucleon interaction there are qualitative differences between the predictions for the nuclear response in the momentum transfer, energy loss plane for T_π^lab = 70 and 180 MeV. At these energies, states not prominently excited by other probes are predicted to be observable. In particular, J^π = 3^? and 4^?, T = 0 states appear prominently in the excitation spectrum region at large momentum transfer. A comparison of π^? and π⁺ scattering showing the effects of the Coulomb interaction is presented. The predictions for pion single-charge exchange on ⁴⁸Ca indicate that this interaction would be useful for studying the location of the T_> states arising from the splitting of the giant dipole resonance in T ≠ 0 nuclei.     

π0 Multiplicities in π+;p interactions at 10.5 GeVc

Measurement of the π⁰ multiplicity cross sections are reported for n₀ ? 6, where n⁰ is the number of produced π⁰ particles, and for N ? 8, where N is the number of charged particles. The inclusive π⁰ cross section is 29 ± 3 mb. Values for the correlation parameters, 〈n₀〉 and 〈n₀(n₀ ? 1)〉², are also presented.     

An Interactive Method as an Aid in Solving Bicriterion Mathematical Programming Problems

In this paper, a man-machine interactive method is presented as an aid in solving the bicriterion mathematical programming problem. It is assumed that the two objective functions are real-valued functions of the decision variables which are themselves constrained to some compact and nonempty set. The overall utility function is assumed to be unknown explicitly to the decision-maker but is assumed to be a real-valued function defined on the pairs of feasible values of the objective functions and monotone non-decreasing in each argument. The decision-maker is required only to provide yes or no answers to questions regarding the desirability of increase or decrease in objective function values of solutions that he will not accept as optimal. Convergence of the method is indicated and a numerical example is presented in order to demonstrate its applicability.     

An investigation of polymorphism in MBBA by positron annihilation

The solid-state behavior of MBBA has been studied by the technique of positron lifetime measurements. The positron data support the exitence of at least two metastable forms of MBBA, one of which may be glassy.