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Magnitudes of numbers influence numerical inequality judgments of people. Do symbols representing numbers also affect numerical inequality judgments? To answer the question, I manipulated digit similarity in two-digit number comparison tasks. During the experiment, the participants took part in two comparison tasks – the judging-larger task and the judging-smaller task. Given pairs of two-digit numbers, the participants were required to make numerical inequality judgments (judging larger or judging smaller). To investigate the effect of digit similarity, two kinds of number pairs were used. Two-digit number pairs consisting of same-digits numbers (e.g., 21 – 12) and two-digit number pairs consisting of different-digits numbers (e.g., 21 – 30) were presented at random. The participants needed more time to compare the same-digits number pairs than the different-digits pairs. The result was independent of the findings in number comparison studies such as the numerical-distance effect (Moyer & Landauer, 1967) and the unit-decade compatibility effect (Nuerk, Weger, & Willmes, 2001). The present study poses challenge to the current theories of two-digit number comparison. / Thesis (Master, Psychology) -- Queen's University, 2009-09-02 11:59:06.647

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There is no abstract available for this dissertation.

Our aim in this work is to produce equations for curves of genus 2 whose Jacobians have real multiplication (RM) by $\mathbb{Q}(\sqrt{5})$, and to examine the conjecture that any abelian surface with RM by $\mathbb{Q}(\sqrt{5})$ is isogenous to a simple factor of the Jacobian of a modular curve $X_0(N)$ for some $N$. To this end, we review previous work in this area, and are able to use a criterion due to Humbert in the last century to produce a family of curves of genus 2 with RM by $\mathbb{Q}(\sqrt{5})$ which parametrizes such curves which have a rational Weierstrass point. We proceed to give a calculation of the $\mbox{\ell}$-adic representations arising from abelian surfaces with RM, and use a special case of this to determine a criterion for the field of definition of RM by $\mathbb{Q}(\sqrt{5})$. We examine when a given polarized abelian surface $A$ defined over a number field $k$ with an action of an order $R$ in a real field $F$, also defined over $k$, can be made principally polarized after $k$-isogeny, and prove, in particular, that this is possible when the conductor of $R$ is odd and coprime to the degree of the given polarization. We then give an explicit description of the moduli space of curves of genus 2 with real multiplication by $\mathbb{Q}(\sqrt{5})$. From this description, we are able to generate a fund of equations for these curves, employing a method due to Mestre.