Effectiveness of Walker's Cancellation Theorem

Walker's Cancellation theorem for abelian groups tells us that if $A$ is finitely generated and $G$ and $H$ are such that $A \oplus G \cong A \oplus H$, then $G \cong H$. Michael Deveau showed that the theorem can be effectivized, but not uniformly. In this paper, we expand on Deveau's initial analysis to show that the complexity of uniformly outputting an index of an isomorphism between $G$ and $H$, given indices for $A$, $G$, $H$, the isomorphism between $A \oplus G$ and $A \oplus H$, and the rank of $A$, is $\mathbf{0'}$.Comment: 12 page

Self-Induced Quasistationary Magnetic Fields

The interaction of electromagnetic radiation with temporally dispersive magnetic solids of small dimensions may show very special resonant behaviors. The internal fields of such samples are characterized by magnetostatic-potential scalar wave functions. The oscillating modes have the energy orthogonality properties and unusual pseudo-electric (gauge) fields. Because of a phase factor, that makes the states single valued, a persistent magnetic current exists. This leads to appearance of an eigen-electric moment of a small disk sample. One of the intriguing features of the mode fields is dynamical symmetry breaking

A Cognitive Information Theory of Music: A Computational Memetics Approach

This thesis offers an account of music cognition based on information theory and memetics. My research strategy is to split the memetic modelling into four layers: Data, Information, Psychology and Application. Multiple cognitive models are proposed for the Information and Psychology layers, and the MDL best-fit models with published human data are selected. Then, for the Psychology layer only, new experiments are conducted to validate the best-fit models. In the information chapter, an information-theoretic model of musical memory is proposed, along with two competing models. The proposed model exhibited a better fit with human data than the competing models. Higher-level psychological theories are then built on top of this information layer. In the similarity chapter, I proposed three competing models of musical similarity, and conducted a new experiment to validate the best-fit model. In the fitness chapter, I again proposed three competing models of musical fitness, and conducted a new experiment to validate the best-fit model. In both cases, the correlations with human data are statistically significant. All in all, my research has shown that the memetic strategy is sound, and the modelling results are encouraging. Implications of this research are discussed

Some comparative aspects of specific implement in Scots law.

SIGLEAvailable from British Library Document Supply Centre- DSC:D90377 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

The dynamics of hairpin vortices in a laminar boundary layer

+177hlm.;24c

Methods for systematic generation of Liapunov functions /part one/

Review of Liapunov stability theory as applied to stability analysis on nonlinear control systems - methods for generation of Liapunov function