An approach to SU(2) gauge fields in Minkowski space-time

A reparametrization-invariant formulation of SU(2) gauge theory in Minkowski space-time is given in terms of differential forms. A map of space-time into a compact region is used and the SU(2) Maurer-Cartan forms employed to establish a convenient gauge. New solutions to the theory are presented and discussed.     

A two-compartment phosphate-doped gel phantom for localized spectroscopy.

Acrylamide gel loaded with phosphate has been used in two compartment phantoms designed to assess localized spectroscopy techniques. A chemical shift difference of 2.3 ppm was produced by changing the pH from 6 to 8.9. The 31P relaxation times were modified by doping the gels with paramagnetic ions. For a T1 of approximately 1 sec nickel doping gave a T2 of approximately 110 msec and manganese doping gave a T2 of approximately 8 msec. Gel phantoms are more robust than their liquid equivalent and are not prone to leakage. The construction of small compartments with very thin walls is possible, making this type of phantom suitable for small bore imaging/spectroscopy systems.     

Does He2 Exist?

For the electronic ground state X ¹Σ⁺_g, the potential-energy function of He₂ reported by Aziz et al. has been transformed into the form V(z), containing only eight parameters, which is more suitable for the investigation of the existence of states of discrete energy. We found no evidence that a bound vibration-rotational state of the stable diatomic molecule ³He₂ or ⁴He₂, even if rotating, can exist in the electronic ground state.     

A general saddle point result for constrained optimization

A saddle point theory in terms of extended Lagrangian functions is presented for nonconvex programs. The results parallel those for convex programs conjoined with the usual Lagrangian formulation.Sponsored in part by the Office of Naval Research under Grant No. N00014-67A-0298-0019 (NR047-004).Sponsored in part by the Office of Naval Research under Grant No. N00014-67A-0321-0003 (NR047-096).     

On the scattering of sound by a vortex ring

An analytical treatment is given of the scattering of sound by a circular vortex ring translating at low Mach number in an unbounded stationary medium. The theoretical results complement the recent numerical investigation of this problem by Kambe and Mya Oo [1].     

A superspace approach to extended conformal supergravity

Extended conformal supergravity is discussed in a superspace context.     

On the Helmholtz resonator

This paper develops the theory of the excitation of a Helmholtz resonator by external disturbances located arbitrarily close to the mouth of the resonator. The classical approach of Rayleigh is thereby extended to situations in which the disturbance at the mouth is not necessarily equivalent to a uniform, time dependent pressure perturbation. The analysis involves the derivation of the Green function of the resonator in a manner similar to that described in an earlier paper. The use of the Green function is illustrated by two examples in which the resonator is excited by a low Mach number stream of air. In the first case the air stream has a periodic large scale structure such as may be caused by a Kelvin-Helmholtz type of instability. The second example models the case of excitation by a shear layer possessing a continuous spectrum of turbulent eddies. In both of these applications the orders of magnitude of the sound pressure levels involved are illustrated for a typical resonator.     

Effects of different levels of hypercapnic hyperoxia on tumour R(2)* and arterial blood gases

The hypercapnia induced by carbogen (95% O(2)/5% CO(2)) breathing, which is being re-evaluated as a clinical radiosensitiser, causes patient discomfort and hence poor compliance. Recent preclinical and clinical studies have indicated that the CO(2) content might be lowered without compromising increased tumour oxygenation and radiosensitisation. This preclinical study was designed to see if lower levels of hypercapnia could evoke similar decreases in the transverse relaxation rate R(2)* of rodent tumours to those seen with carbogen breathing. The response of rat GH3 prolactinomas to 1%, 212% and 5% CO(2) in oxygen, and 100% O(2) breathing, was monitored by non-invasive multi-gradient echo MRI to quantify R(2)*. As the oxygenation of haemoglobin is proportional to the blood p(a)O(2) and therefore in equilibrium with tissue pO(2), R(2)* is a sensitive indicator of tissue oxygenation. Hyperoxia alone decreased R(2)* by 13%, whilst all three hypercapnic hyperoxic gases decreased R(2)* by 29%. Breathing 1% CO(2) in oxygen evoked the same decrease in R(2)* as carbogen. The DeltaR(2)* response is primarily consistent with an increase in blood oxygenation, though localised increases in tumour blood flow were also identified in response to hypercapnia. The data support the concept that levels of hypercapnia can be reduced without loss of enhanced oxygenation and hence potential radiotherapeutic benefit.