Measurement of the cascade time of ∑ in liquid helium

In a study of ∑⁻π⁺ production by stopped K⁻ in liquid helium, (19 ± 6)% of stopped ∑⁻ were observed to decay. This corresponds to a “cascade time” of 28 ± 8 psec.     

The determination of technetium-99 in seawater and marine algae

Technetium-99 is preconcentrated from acidified seawater containing a trace of bromine by adsorbing it as the pertechnetate ion on the anion exchanger Duolite A101D. After elution with 4 M nitric acid, it is purified from other radionuclides by scavenging with hydrous iron(III) oxide and extracting from 5 M sodium hydroxide medium into methyl ethyl ketone. The organic phase is then evaporated and technetium is electrodeposited from oxalic acid medium onto a bronze disc and counted with a low background β-counter. Overall recovery is > 90% and the precision is ±0.2 pCi l^-1 at a technetium level of 0.6–1.0 pCi l^-1. Concentrations of the radionuclide in the central Irish Sea were found to lie in the range 0.4–2 pCi l^-1. The same analytical scheme can be used for determining the element in nitric acid digests of marine algae.     

Approximations and the spectral properties of measure-preserving group actions

This paper presents some extensions and applications of the method of approximations of ergodic theory (see [6]). Two notions of approximation are defined which are applicable to arbitrary σ-finite-measure-preserving group actions (see §1). Building upon results of [2], [13] and [6], the speeds of such approximations are related to the questions of spectral multiplicity, spectral type and ergodicity (see §3). For the result on spectral multiplicity, there is first established a general result concerning the spectral decomposition of unitary representations (see §2). The last section is devoted to applications—chiefly to certain classes of cylinder transformations which arise in connection with irregularity of distribution (see [12]). These transformations provide examples (on infinite measure spaces) of approximations of all finite multiplicities. The method of approximations is shown to be a natural tool for the study of their spectral properties.     

Lie superalgebras whose enveloping algebras satisfy a non-matrix polynomial identity

Let L be a Lie superalgebra with its enveloping algebra U(L) over a field F. A polynomial identity is called non-matrix if it is not satisfied by the algebra of 2×2 matrices over F. We characterize L when U(L) satisfies a non-matrix polynomial identity. We also characterize L when U(L) is Lie solvable, Lie nilpotent, or Lie super-nilpotent.     

Groups with a positive law on commutators

Let p be a prime number and let G be a finitely generated group that is residually a finite p-group. We prove that if G satisfies a positive law on all elements of the form [a,b][c,d]ⁱ, a,b,c,d∈G and i?0, then the entire derived subgroup G^′ satisfies a positive law. In fact, G^′ is an extension of a nilpotent group by a locally finite group of finite exponent.     

The diffraction of elastic waves by an imperfect fusion bond

We consider diffraction by a semi-infinite crack located alonga fusion interface between two differing elastic media. Twotypes of crack, namely open and partially closed cracks, areinvestigated. An open crack is modelled by a stress-free contactboundary condition and a partially closed crack is modelledby a spring contact boundary condition. For the latter, thejump in the stress across the crack is assumed to be proportionalto the jump in the displacement across the crack. This situationarises in, for example, a K-weld where the fine grain of theparent material (for example, ferritic or forged austeniticsteel) is in stark contrast with the coarse-grained weld metal(for example, austenitic weld metal). In the metal weld thedirection of the grain axis varies through the metal. However,diffraction is a local phenomenon and so the austenitic steelis assumed to have a zonal axis so that it may be modelled bya transversely isotropic composite. The ferritic or forged austeniticsteel will be modelled as an isotropic material.     

Filling Length in Finitely Presentable Groups

We study the filling length function for a finite presentation of a group , and interpret this function as an optimal bound on the length of the boundary loop as a van Kampen diagram is collapsed to the basepoint using a combinatorial notion of a null-homotopy. We prove that filling length is well behaved under change of presentation of . We look at 'AD-pairs' (f,g) for a finite presentation : that is, an isoperimetric function f and an isodiametric function g that can be realised simultaneously. We prove that the filling length admits a bound of the form [g+1][log (f+1)+1] whenever (f,g) is an AD-pair for . Further we show that (up to multiplicative constants) if is an isoperimetric function ( ) for a finite presentation then ( ) is an AD-pair. Also we prove that for all finite presentations filling length is bounded by an exponential of an isodiametric function.Partially supported by NSF grant DMS-9800158Supported by EPSRC Award No. 98001683 and Corpus Christi College, Oxford.     

Algebras with Collapsing Monomials

A semigroup S is called collapsing if there exists a positiveinteger n such that for every subset of n elements in S, atleast two distinct words of length n on these letters are equalin S. In particular, S is collapsing whenever it satisfies alaw. Let U(A) denote the group of units of a unitary associativealgebra A over a field k of characteristic zero. If A is generatedby its nilpotent elements, then the following conditions areequivalent: U(A) is collapsing; U(A) satisfies some semigrouplaw; U(A) satisfies the Engel condition; U(A) is nilpotent;A is nilpotent when considered as a Lie algebra.     

The universal earthmoving equation applied to chisel plough wings

This paper compares the results of tests which examined the effect of chisel plough wing geometry on tillage forces with those predicted by the Universal Earthmoving Equation as presented in E. McKyes' book Soil Cutting and Tillage, published by Elsevier (1985). The tests were conducted in the SAIT Tillage Test Track (an outside continous soil bin which contains a sandy loam soil) and in two field soild, one sandy loam and the other a red brown earth. The tests were conducted using a range of speeds from 5 to 15 km/h and at depths of 50 and 70 mm. The tests compared the effects of varying share wing width and rake angle. The comparison of the measured and predicted draft and vertical force responses showed a good correlation between the Universal Earthmoving Equation predictions and the measured width responses, but it did not always predict the correct rake angle responses.