Positive energy in general relativity

An argument is given in favor of the conjecture that an isolated system in general relativity must have nonnegative total energy.     

The symmetry of ground states under perturbation

We consider a two-body potential which has only periodic ground states and prove that it can be perturbed, by an arbitrarily small perturbation, so as to have only aperiodic ground states.Research supported in part by NSF grant MCS 78-01520-A01.     

A lattice gas model for thermohydrodynamics

The lattice gas model is extended to include a temperature variable in order to study thermohydrodynamics, the combination of fluid dynamics and heat transfer. The compressible Navier-Stokes equations are derived using a Chapman-Enskog expansion. Heat conduction and convection problems are investigated, including Bénard convection. It is shown that the usual rescaling procedure can be avoided by controlling the temperature.     

First-principles electronic structure calculations with molecular dynamics made easy

The technique of quantum molecular dynamics is reviewed, and a simplified approach based on a first-principles tight-binding implementation of local density theory is discussed. Several illustrations and applications of the theory are presented. Applying it to amorphous materials, we have developed a procedure for producing amorphous Si networks with small defect concentrations. Benchmark checks are made for atomic geometries at Si(111)-(2×1) and Si(001)-(2×1), p(2×2), and c(4×2) reconstructed surfaces. A simulation of a Scanning Tunneling Microscope tip interacting with a reconstructed surface is performed, and it is shown how the tip can alter the reconstruction of the surface. Simulation of a kinked Si(001) surface step and comparison to an unkinked step are also presented.     

A time domain analysis of wave motions in chiral materials

A time domain analysis of the equations governing wave propagation in an unbounded chiral medium is presented by a spectral family approach and by a direct eigenfunction expansion using Beltrami–Moses fields.     

Radiationless transition probabilities in muonic208Pb,232Th,and238U

The probabilities for non-radiative (n.r.) excitationsP _n.r. in the muonic nuclides²⁰⁸Pb,²³²Th, and²³⁸U have been determined from (μ^?,γγ)-measurements by comparing the intensities of muonic X-ray transitions in single and coincidence spectra. The value ofP _n.r. (3p→1s), measured for the first time, is about 90% for the actinides²³²Th and²³⁸U, but only about 8% for²⁰⁸Pb. The value ofP _n.r. (3d→1s) is found to be 10 % for²³³Th, 13% for²³⁸U, and about 4% for²⁰⁸Pb. For²⁰⁸Pb a vanishing strength of the n.r. decay of the 2p-level is found, while for²³²Th and for²³⁸U n.r. strengths of about 20% and 26%, respectively, are observed. By regarding two subcomplexes of the 2p→1s transitions leading to different mean excitation energies the n.r. transition probabilities were found to be different for²³⁸U only, 21.6% and 31.1.%, respectively.     

Prime ideals and prime radicals in near-rings

This paper investigates conditions under which a prime ideal is completely prime and conditions for which every prime ideal in a near-ring is completely prime. Various implications of these conditions are examined with respect to the associated radicals.     

Hölder continuity of the gradient of solutions of uniformly parabolic equations with conormal boundary conditions

Summary We study solutions of the conormal derivative problem for uniformly parabolic equations in divergence form. Under weak regularity hypotheses on the operator, the global Hölder continuity of the gradient of a weak solution is established. The method of proof is based on [5] and the results extend those in [7, Section V.7].Sponsored by the National Science Foundation under Grant DMS-8315545.     

A 0-stable linear multistep formulas of theα-type

The-type linear multistep formulas are a generalization of the Adams-type formulas. This paper is concerned with completely characterizing theA ₀-stability of thek-step, orderk -type formulas. Specifically, all such formulas of orders 4 or less are identified and it is shown that no-type formulas of order 5 or more exist. These theorems generalize some previous results.