A LeVeque-type inequality on the ring of p-adic integers

We derive an inequality on the discrepancy of sequences on the ring of [Formula: see text]-adic integers [Formula: see text] using techniques from Fourier analysis. This is a [Formula: see text]-adic analogue of the classical LeVeque inequality on the circle group [Formula: see text]. Some applications of the inequality are also given.

Quantum E(2) groups for complex deformation parameters

We construct a family of [Formula: see text] deformations of E(2) group for nonzero complex parameters [Formula: see text] as locally compact braided quantum groups over the circle group [Formula: see text] viewed as a quasitriangular quantum group with respect to the unitary [Formula: see text]-matrix [Formula: see text] for all [Formula: see text]. For real [Formula: see text], the deformation coincides with Woronowicz’s [Formula: see text] groups. As an application, we study the braided analogue of the contraction procedure between [Formula: see text] and [Formula: see text] groups in the spirit of Woronowicz’s quantum analogue of the classic Inönü–Wigner group contraction. Consequently, we obtain the bosonization of braided [Formula: see text] groups by contracting [Formula: see text] groups.

Distributions on the circle group

In this paper, we extend the definition of a random angle and the definition of a probability distribution of a random angle. We expand P. Lévy’s researches related to wrapping the probability distributions defined on R. We determine a relation between quasi-lattice probability distributions on R and lattice probability distributions on the unit circle S. We use the Bergström identity for comparison of a convolution of probability distributions of random angles. We also prove an inverse formula for lattice probability distributions on S.

Knowledge Lies and Group Lies

This chapter is about two kinds of lies, knowledge lies and group lies, which are considered to be interestingly different from typical lies. Typically, lies are told by an individual, and they are intended to convince their addressee of a false claim. By contrast, in telling a knowledge lie, the liar does not intend to deceive the addressee into believing a false claim. Instead, the liar intends to prevent the addressees from knowing, but not necessarily from believing, some true claim. Group lies are lies that are told by a group, such as a company, a government, or your knitting circle. Group lies are unlike typical lies, because they are not straightforwardly related to lies told by individuals who are members of the lying group. For each type of lie, I give a more rigorous characterization, then discuss why this kind of lie deserves special philosophical attention, and lastly provide some critical discussion of the accounts of each type of lie that have been proposed in the philosophical literature.