We apply the theorem of Shimura and Taniyama to compute the largest abelian extension of a CM-eld E which can be obtained by evaluating E-rational automorphic functions at certain special points of Shimura varieties. Abelian class eld theory classiies the abelian extensions of a number eld k, but does not explain how to generate the elds. In his Jugendtraum, Kronecker suggested that the abelian...

in the history of philosophy, the basic role of imagination in human perception as an intermediary between sensation and intellect has been left unnoticed. imagination has often been regarded as subjective and illusory. although imagination is one of the initial faculties of the soul that has been known, its duty is described only as preservation and ideation of sensible objects in the time of ...

H Visual imagery is the invention or recreation of a perceptual experience in the absence of retinal input.The degree to which the same neural representations are involved in both visual imagery and visual perception is unclear. Previous studies have shown that visual imagery interferes with perception (Perky effect). We report here psychophysical data showing a direct facilitatory effect of vi...

University Press. All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher, except for reading and browsing via the World Wide Web. Users are not permitted to mount this file on any network servers. Introduction Like the ...

Individuals may have biased perceptions of health and safety risks. We conjecture perceptions of mortality risk from various risk measures using parametric and non-parametric methods. We investigate how risk perceptions are measured and what rational explanations can be found for these measures.

There is a popular perception that clinical judgement and evidence-based medicine are at loggerheads with each other. We examine the concepts of evidence and judgment as applied to clinical practice, and attempt to understand the reasons behind this imaginary divide.

In this paper we introduce the notion of a discrete-time negative imaginary system and we investigate its relations with discrete-time positive real system theory. In the framework presented here, discrete-time negative imaginary systems are defined in terms of a sign condition that must be satisfied in a domain of analyticity of the transfer function, in analogy with the case of discrete-time ...

We investigate a question of Cooper adjacent to the Virtual Haken Conjecture. Assuming certain conjectures in number theory, we show that there exist hyperbolic rational homology 3–spheres with arbitrarily large injectivity radius. These examples come from a tower of abelian covers of an explicit arithmetic 3–manifold. The conjectures we must assume are the Generalized Riemann Hypothesis and a ...