We present a new ‘elementary’ proof of the irrationality of ζ(3) based on some recent ‘hypergeometric’ ideas of Yu. Nesterenko, T. Rivoal, and K. Ball, and on Zeilberger’s algorithm of creative telescoping. A question of an arithmetic nature of the values of Riemann’s zeta function

We prove that a certain family of flat surfaces in genus 3 does not fulfill Veech’s Dichotomy. These flat surfaces provide uncountably many minimal but nonergodic directions. The conditions on this family are a combinatorical one and an irrationality condition. The Arnoux-Yoccoz surface fulfills this conditions.

This yields an irrationality criterion (which is the basic tool for proving the irrationality of specific numbers), and Liouville extended it into a transcendence criterion. The proof by Liouville involves the irreducible polynomial f ∈ Z[X] of the given irrational algebraic number α. Since α is algebraic, there exists an irreducible polynomial f ∈ Z[X] such that f(α) = 0. Let d be the degree o...

This study examined the association among interpersonal relationships, irrational beliefs, and life satisfaction. Twenty-eight psychotherapy clients and 207 college undergraduates completed measures of interpersonal relations (Outcome Questionnaire; Lambert et al., 1996), irrationality (Rational Behavior Inventory; Shorkey & Whiteman, 1977), and life satisfaction (The Satisfaction with Life Sca...

The Ratio-Bias phenomenon, observed by psychologist Seymour Epstein and colleagues, is a systematic manifestation of irrationality. When offered a choice between two lotteries, individuals consistently choose the lottery with the greater number of potential successes, even when it offers a smaller probability of success. In the current study, we conduct experiments to confirm this phenomenon an...

Economic models of animal behaviour assume that decision-makers are rational, meaning that they assess options according to intrinsic fitness value and not by comparison with available alternatives. This expectation is frequently violated, but the significance of irrational behaviour remains controversial. One possibility is that irrationality arises from cognitive constraints that necessitate ...

The present paper proposes an integrative account of social forms of practical irrationality and corresponding disruptions of individual and group-level emotion regulation (ER). I will especially focus on disruptions in ER by means of collaborative agential and doxastic akrasia. I begin by distinguishing mutual, communal and collaborative forms of akrasia. Such a taxonomy seems all the more nee...