A spin-statistics theorem for composites containing both electric and magnetic charges

The present paper states and proves an asymptotic spin-statistics theorem for composites consisting of electrically and magnetically charged particles. We work in the framework of a nonrelativistic theory, taking as the classical configuration space aU(1) bundle over the space of physical configurations, and as the quantum hilbert space the homogeneous square integrable functions on that bundle. The theorems are proved using a formalism we develop here for treating gauge spaces —U(1) bundles with connections; in particular, two products related to tensor products of vector bundles prove to be extremely useful in displaying the structure of the gauge spaces that naturally arise in this theory.Supported in part by the National Science Foundation under grant number PHY 77-07111Supported in part by the National Science Foundation under grant number PHY 78-24275     

Facile growth of monolayer MoS<Subscript>2</Subscript> film areas on SiO<Subscript>2</Subscript>

Areas of single-layer MoS₂ film can be prepared in a tube furnace without the need for temperature control. The films were characterized by means of Raman spectroscopy, photoluminescence, low-energy electron diffraction and microscopy, and X-ray photoelectron spectroscopy and mapping. Transport measurements show n-doped material with a mobility of 0.26 cm² V^-1 s^-1.     

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.     

4-Dimensional black holes from Kaluza-Klein theories

In this paper we consider generalizations in 4 dimensions of the Einstein-Maxwell equations which typically arise from Kaluza-Klein theories. We specify conditions such that stationary solutions lead to non-linear-models for symmetric spaces. Using both this group theoretic structure and some properties of harmonic maps we are able to generalize many of the known existence and uniqueness theorems for black holes in Einstein-Maxwell theory to this more general setting.     

Optimal design of an optical lens

We wish to construct an optimal optical lens, in the sense that it focuses all rays from a given source onto a given focal point. The construction can be reduced mathematically to a global study of a system of two nonlinear functional differential equations. We prove that this system has precisely two analytic solutions.     

Continual measurements in the spacetime formation of nonrelativistic quantum mechanics

We study the nature and effects of some continual measurements in nonrelativistic quantum mechanics, a concept introduced by R. P. Feynman in his path integral formulation of quantum mechanics. We prove the existence in various senses of mathematically rigorous objects formally equivalent to the path integrals associated with such measurements, by means of both a limiting definition and more general techniques; and we derive some quantitative results concerning the effects on the wave-function and the numerical value of certain associated probabilities.     

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.     

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.