Let f be a number-theoretic function. A finite set X of natural numbers is called f -large if card(X) ≥ f(min(X)). Let PHf be the Paris Harrington statement where we replace the largeness condition by a corresponding f -largeness condition. We classify those functions f for which the statement PHf is independent of first order (Peano) arithmetic PA. If f is a fixed iteration of the binary lengt...

It has been proposed that the ability to perform joint weak measurements on postselected systems would allow us to study quantum paradoxes. These measurements can investigate the history of those particles that contribute to the paradoxical outcome. Here we experimentally perform weak measurements of joint (i.e., nonlocal) observables. In an implementation of Hardy's paradox, we weakly measure ...

Since the pioneer work of Demikhov (1962), Staudacher, Bellinazzo, and Pulin (1950), and Juvenelle, Citret, Wiles, and Stewart (1951), the possibilities and problems of lung transplantation have received increasing attention, and indeed homotransplantation has already been attempted in man (Hardy, Webb, Dalton, and Walker, 1963b; Magovern and Yates, 1964). Before transplantation of a lung becom...

Free interpolation in Hardy spaces is caracterized by the well-known Carleson condition. The result extends to Hardy-Orlicz spaces contained in the scale of classical Hardy spaces H, p > 0. For the Smirnov and the Nevanlinna classes, interpolating sequences have been characterized in a recent paper in terms of the existence of harmonic majorants (quasi-bounded in the case of the Smirnov class)....

OBJECTIVES This cross-sectional study was performed in order to elucidate the relationship of musculoskeletal complaints with age, gender and physically demanding work in the Netherlands. METHODS Questionnaire data of male (n = 36756) and female (n = 7730) employees, gathered as part of periodical occupational health surveys among active workers in the Netherlands, were stratified for age, ge...