Integral forms for tensor powers of the Virasoro vertex operator algebra L(12,0)L(\frac{1}{2},0) and their modules

We construct integral forms containing the conformal vector $\omega$ in certain tensor powers of the Virasoro vertex operator algebra $L(\frac{1}{2},0)$, and we construct integral forms in certain modules for these algebras. When a triple of modules for a tensor power of $L(\frac{1}{2},0)$ have integral forms, we classify which intertwining operators among these modules respect the integral forms. As an application, we explore how these results might be used to obtain integral forms in framed vertex operator algebras.Comment: 20 page

Clifford Algebras and Possible Kinematics

We review Bacry and Levy-Leblond's work on possible kinematics as applied to 2-dimensional spacetimes, as well as the nine types of 2-dimensional Cayley-Klein geometries, illustrating how the Cayley-Klein geometries give homogeneous spacetimes for all but one of the kinematical groups. We then construct a two-parameter family of Clifford algebras that give a unified framework for representing both the Lie algebras as well as the kinematical groups, showing that these groups are true rotation groups. In addition we give conformal models for these spacetimes.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Bed and Breakfast: A Canadian Airman Reflects on the Food and Quarters during the Second World War

Hollywood’s stereotyped version of an RAF fighter pilot—lounging about in a comfortable leather chair with a pint in one hand and Punch in the other—is not quite as I remember it. But what were “typical“ conditions? Using my log book and wartime letters as references, with war art to serve as illustrations, this is how I recollect RAF/RCAF living conditions during the Second World War

Non-negative integral level affine Lie algebra tensor categories and their associativity isomorphisms

For a finite-dimensional simple Lie algebra $\mathfrak{g}$, we use the vertex tensor category theory of Huang and Lepowsky to identify the category of standard modules for the affine Lie algebra $\hat{\mathfrak{g}}$ at a fixed level $\ell\in\mathbb{N}$ with a certain tensor category of finite-dimensional $\mathfrak{g}$-modules. More precisely, the category of level $\ell$ standard $\hat{\mathfrak{g}}$-modules is the module category for the simple vertex operator algebra $L_{\hat{\mathfrak{g}}}(\ell,0)$, and as is well known, this category is equivalent as an abelian category to $\mathbf{D}(\mathfrak{g},\ell)$, the category of finite-dimensional modules for the Zhu's algebra $A(L_{\hat{\mathfrak{g}}}(\ell,0))$, which is a quotient of $U(\mathfrak{g})$. Our main result is a direct construction using Knizhnik-Zamolodchikov equations of the associativity isomorphisms in $\mathbf{D}(\mathfrak{g},\ell)$ induced from the associativity isomorphisms constructed by Huang and Lepowsky in $L_{hat{\mathfrak{g}}}(\ell,0)-\mathbf{mod}$. This construction shows that $\mathbf{D}(\mathfrak{g},\ell)$ is closely related to the Drinfeld category of $U(\mathfrak{g})[[\hbar]]$-modules used by Kazhdan and Lusztig to identify categories of $\hat{\mathfrak{g}}$-modules at irrational and most negative rational levels with categories of quantum group modules.Comment: 49 page

Stimulus, effects attention and reading performance : a thesis presented in partial fulfilment of the requirements for the degree of Master of Arts in applied psychology at Massey University

This investigation reports an experimental study on the effects different stimulus characteristics have on attention and subsequent reading performance with "good" and "poor" readers. Forty subjects between the ages of eleven and eleven and a half years at the time of the study (November, 1975) were selected from a typical city school on the following criteria: (i) All subjects had to score within ±1 standard deviation of the mean on the "Henmon-Nelson Tests of Mental Ability" Group 6-9, Form A. (H.N.) (ii) Twenty of them (ten boys, ten girls) had to score between 20-30 raw score points on the "Progressive Achievement Test: Reading Comprehension" and have a Teacher rating of 3+ or 2. (iii) Twenty of them (ten boys, ten girls) had to score 18 or less raw score points on the "Progressive Achievement Test: Reading Comprehension" and have a Teacher rating of 3- or 4. These two groups were then referred to respectively as "good" and "poor" readers. Intelligence was being held constant to prevent It being an Independent variable in this study. All forty subjects were tested on the "Concealed Figures Test" (C.F.T.) which was used in the study as a measure of "attentional style". Each subject was then presented with a series of slides and his responses recorded. In the first instance six slides, containing three real and three novel animals, were presented In a typical setting. Each slide had a coloured border surrounding it. After viewing each slide (their viewing time being recorded) they were asked to select from two multiple choice questions the setting in which the animal appeared and the colour of the border. This was repeated with the same animals In atypical settings and different coloured borders. Responses to the setting were recorded as "intentional" learning while the border colour was termed "Incidental learning". Each subject was then presented with a slide containing a "mutilated" text (where the first letter of each word had been changed) on each of the animals viewed previously. Each text was presented three times - with a picture, without a picture, without a picture but surrounded by a coloured border. The "on task" time and number of word errors was recorded for each presentation. The same procedure was repeated only with a different six animals as the subjects for the text (again comprising of three novel and three real animals). "On task" time and word errors were again recorded. Finally, five slides about one novel and four real animals were presented in traditional orthography as a control measure. These were presented as text only, text and picture, text and border, text and picture and border. On analysis of the data it was found that "incidental" learning was no greater with bright coloured borders than it was with dull coloured borders. "Intentional" learning too was tested out not significantly different with novel animals or settings than it was with real animals or typical settings. On the "attentional style" test boys were found to have significantly less errors than girls (p<.005). However, predicted differences in the number correct between boys and girls, "good" and "poor" readers showed no significance on a one tailed t-test. The "on task" time of high scorers on the C.F.T, as compared with low scorers did not differ significantly in the reading of the "mutilated" texts. "Good" readers though spent less time "on task" when the text was presented with a picture than did "poor" readers (p<.05). The same significant difference existed when they were presented with a text only. However, no difference was found when they were presented with a text surrounded with a coloured border. Reading performance of "poor" readers was increased when presented with a text only as compared with a text and illustration (p<.10). A one tailed t-test also showed a significant improvement in the performance of "poor" readers when the text had a coloured border around it (p<.05). The bright colours showed a very significant improvement in reading performance of "poor" readers as compared with the text only (p<.005). Stimulus materials such as texts with a coloured border seem to assist "poor" readers in particular into focusing their attention on to the relevant cues and increase their success in reading