Enrico Bombieri proved that the ABC Conjecture implies Roth's theorem in 1994. This paper concerns the other direction. In making use of Bombieri's and Van der Poorten's explicit formula for the coefficients of the regular continued fractions of algebraic numbers, we prove that Roth's theorem...

Enrico Bombieri proved that the ABC Conjecture implies Roth's theorem in 1994. This paper concerns the other direction. In making use of Bombieri's and Van der Poorten's explicit formula for the coefficients of the regular continued fractions of algebraic numbers, we prove that Roth's theorem...

Samuelson's (1938) weak (generalized) axiom of revealed preference- WGARP-is a minimal and appealing consistency condition of choice. We offer a rationalization of WGARP in general settings. Our main result is an exact analog of the celebrated Afriat's theorem, but for WGARP. Its ordinal...

Market participants use leveraged derivatives to gain access to equity market exposure through broker banks. Leverage and interconnectedness via overlapping portfolios of dealer banks can amplify adverse market movements, potentially causing sizeable losses. I propose a model, based on granular...

Repeated interactions provide a prominent but paradoxical hypothesis for human cooperation in one-shot interactions. Intergroup competitions provide a different hypothesis that is intuitively appealing but heterodox. We show that neither mechanism reliably supports the evolution of cooperation...

Ride-hailing applications create new challenges for governments providing transit services, but also create new opportunities to raise tax revenue. To shed light on the effect of taxing or subsidizing ride-hailing applications, we extend a pseudo-monocentric city model to include multiple...

This research investigates the Ethiopian economy's sectoral linkages. It examines the forward and backward production and total linkages of the industry with the agriculture and service sectors. The import penetration and export intensity of the agriculture-based industry and the manufacturing...

Artificial Intelligence (AI) scientists are challenged to create intelligent, autonomous agents that can make rational decisions. In this challenge, they confront two questions: what decision theory to follow and how to implement it in AI systems. This paper provides answers to these questions...

This paper argues that the natural rate of unemployment hypothesis, in which equilibrium unemployment is determined by 'structural' variables alone, is wrong: it is both implausible and inconsistent with the evidence. Instead, equilibrium unemployment is haunted by hysteresis. The curious...

The picture fuzzy set (PFS) is a powerful tool to collect and handle large amounts of uncertain assess information in a new light. In this study, we explore some distance measures for the PFSs and propose Picture fuzzy ordered weighted distance measure and Picture fuzzy hybrid weighted distance...