A striking feature of the traditional armchair method of philosophy is the use of imaginary examples: for instance, of Gettier cases as counterexamples to the justified true belief analysis of knowledge. The use of such examples is often thought to involve some sort of a priori rational intuition, which crude rationalists regard as a virtue and crude empiricists as a vice. It is argued here tha...

The problem of estimating the number of imaginary quadratic fields whose ideal class group has an element of order ` ≥ 2 is classical in number theory. Analogous questions for quadratic twists of elliptic curves have been the focus of recent interest. Whereas works of Stewart and Top [St-T], and of Gouvêa and Mazur [G-M] address the nontriviality of MordellWeil groups, less is known about the n...

We obtain the quasinormal modes for tensor perturbations of Gauss-Bonnet black holes in d = 5, 7, 8 dimension using third order WKB formalism. The black hole in d = 6 is not considered because of the fact that it is unstable to tensor mode perturbations. For the uncharged Gauss-Bonnet black hole the real part of the frequency increases as the GaussBonnet coupling (α) increases. The imaginary pa...

Let d1 and d2 be discriminants of distinct quadratic imaginary orders and let J(d1, d2) denote the product of differences of CM j-invariants with discriminants d1 and d2. In 1985, Gross and Zagier gave an elegant formula for the factorization of the integer J(d1, d2) in the case that d1 and d2 are relatively prime and discriminants of maximal orders. We generalize their methods and give a compl...

The aim of this research was to test empirically Elkind’s (1967, 1970, 1978) Piagetian theoretical formulation for the developmental nature of adolescent egocentrism. The contribution of this study is threefold because it includes: 1) Pubertal development (with a distinction between status and timing), which has been systematically ignored by other investigators; 2) a broad age range (11 18 yea...