Physical Sciences and Mathematics Commons^™

Cotorsion-Free Algebras As Endomorphism Algebras In L - The Discrete An Topological Cases., R. Gobel, Brendan Goldsmith

Articles

The discrete algebras A over a commutative ring R which can be realised as the full endomorphism algebra of a torsion-free R-module have been investigated by Dugas and Gobel under the additional set-theoretic axiom of constructibility, V = L. Many interesting results have been obtained for cotorsion-free algebras but the proofs involve rather elaborate calculations in linear algebra. Here these results are rederived in a more natural topological setting and substantial generalizations to topological algebras (which could not be handled in the previous linear algebra approach) are obtained. The results obtained are independent of the usual Zermelo-Fraenkel set theory ZFC.

On Quasi-Permutation Representations Of Finite Groups, J. M. Burns, Brendan Goldsmith, B. Hartley, R. Sandling

Articles

In [6], Wong defined a quasi-permutation group of degree n to be a finite group G of automorphisms of an n-dimensional complex vector space such that every element of G has non-negative integral trace. The terminology derives from the fact that if G is a finite group of permutations of a set ω of size n, and we think of G as acting on the complex vector space with basis ω, then the trace of an element g ∈ G is equal to the number of points of ω fixed by g. In [6] and [7], Wong studied the extent …

The Walker Endomorphism Algebra Of A Mixed Module, Brendan Goldsmith, P. Zanardo

Articles

Archimedian valuation domains R are characterised in terms of the endomorphism algebras of non-splitting mixed modules of rank 1, in the Walker category.

The Kaplansky Test Problems - An Approach Via Radicals, R. Gobel, Brendan Goldsmith

Articles

The existence of non-free, K-free Abelian groups and modules (over some non-left perfect rings R) having prescribed endomorphism algebra is established within ZFC + 0 set theory. The principal technique used exploits free resolutions of non-free R-modules X and is similar to that used previously by Griffith and Eklof; much stronger results than have been obtained heretofore are obtained by coding additional information into the module X. As a consequence we can show, inter alia, that the Kaplansky Test Problems have negative answers for strongly K,-free Abelian groups of cardinality K1 in ZFC and assuming the weak Continuum Hypothesis.

Aspects Of Gold Recovery From An Indigenous Ore, Cormac Patrick Mcnamee

Masters

This project involved the investigation into the basic electrochemistry of the thiourea-formamidine disulphide redox couple and an estimation of the formal potential, Eo1 for the couple. By carrying out optimisation experiments on the leaching of gold from an ore sample from the Avoca mine in Co. Wicklow, the optimum leaching conditions were determined for maximum gold extraction. The effects of various organic and inorganic species on the adsorption of gold onto activated carbon and modified peat were investigated with the use of factorial designed experiments. The Langmuir Isotherm model was applied to estimate the capacity of the carbon for these …

Resonant Vibrations Of The Irish Folk Harp, Patrick Healy

Other Resources

An analysis of the resonant vibration of an O’Meachair cedar and mahogany Irish folk harp is reported. A report is also made of a small number of measurements carried out on an O’Meachair spruce and maple Irish folk harp. The structure and operation of the harp is described.

The theory of small vibrations of plates and wooden boards is set out.

The system devised to measure input admittance at driving points on the harp body over a frequency range O-2 kHz is described. Tests of its linearity and out of its frequency flatness are reported.

Resonant vibrations of an isolated …

Hysteresis And Anchoring Energy In Ferroelectric Liquid Crystals, Yuri Panarin

Articles

The frequency dispersion of the coercive force of Ferroelectric Liquid Crystals (FLC) cells has been detected and examined in the range of infralow (lower than 0.1 Hz) frequencies. To clarify the low-frequency dispersion, the model has been suggested, based on the arrangement of free charges and well describing the experimental curves. The method for determination of the energy of FLC anchoring at the surface, developed on the basis of the static hysteresis loop, has been proposed. The dependence of bistability and the anchoring energy upon the orientant layer thickness has experimentally been investigated.