In this paper we present several proofs on the extension of M. Riesz fractional integration and di¤erentiation to the contexts of spaces of homogeneous type and measure metric spaces with non-doubling measures. 1. Introduction, some de…nitions, and a basic lemma Professor M. Ash asked me to write a survey article on some of the results that Stephen Vági and I obtained in the nineties on fractio...

Reciprocity is when wave or quantum scattering satisfies a symmetry property, connecting a scattering process with the reversed one. While reciprocity involves the interchange of source and detector, it is fundamentally different from rotational invariance, and is a generalization of time reversal invariance, occurring in absorptive media as well. Due to its presence at diverse areas of physics...

The topic of reciprocity has long played an important role in anthropology, ethnology, and sociological thinking, for instance, in the classic writings of Georg Simmel (1950), Bronislaw Malinowski (1926), Marcel Mauss (1950/1990), or Alvin Gouldner (1960). More than four decades ago, Gouldner clarified the concept and its dimensions and assumed the existence of a universal norm of reciprocity i...

Homo Reciprocans: Survey Evidence on Behavioural Outcomes This paper complements the experimental literature that has shown the importance of reciprocity for behaviour in stylized labour markets or other decision settings. We use individual measures of reciprocal inclinations in a large, representative survey, and relate reciprocity to real world labour market behaviour and life outcomes. We fi...

We investigate to what extent reciprocity, exhibited by employers and employees, lead to stable gift exchange practices in the labour contract, giving rise to noncompensating wage differentials among industries and firms. We use the concept of Sequential Reciprocity Equilibrium (Dufwenberg and Kirchsteiger 1998, 2004) to incorporate players’ preferences for reciprocity in their utility function...

This study investigated reciprocity in parent–adolescent interactions among 102 families from lower or higher socioeconomic status (SES) backgrounds. Negative behaviors between parents and adolescents were more reciprocal (strongly correlated) in higher SES than lower SES families, and this reciprocity correlated with higher family relationship quality. Lower SES families exhibited reciprocity ...