Given the positive integers m,n, solving the well known symmetric Diophantine equation xm+kyn=zm+kwn, where k is a rational number, is a challenge. By computer calculations, we show that for all integers k from 1 to 500, the Diophantine equation x6+ky3=z6+kw3 has infinitely many nontrivial (y≠w) rational solutions. Clearly, the same result holds for positive integers k whose cube-free part is n...

this paper seeks to trace some of the roots and problems of the rational view of innovation. concentrating primarily upon product innovation, we point out that the eighteenth century notion of social progress in the light of reason has gradually given an enormous impetus to a rational view of product innovation in modern organizations. we summarize several decades of research into management of...

Poetry is meant to express the emotions and thoughts often found difficult to state or even to put into prose. This clinician has dedicated his professional life to the rational treatment of epilepsy - for he understands only too well the consequences of varied interventions over a forty-year course of his own epilepsy. This poem is meant to remind other clinicians that quality of life may not ...

A rational evaluation by insurance medical directors of an applicant for life or health insurance requires not only adequate information from a prospective insuree, but current knowledge concerning a common genetic disorder such as genetic hemochromatosis (GH), and the routine use of an appropriate screening test for GH of all applicants. Such an evaluation could make a vital difference in prog...

This paper aims to explore the role of questions in communication in a group of cooperative rational agents. Using epistemic representation of questions proposed in [6] we employ the framework of public announcement logic to explore the flow of information in the process of asking and replying questions in a group. We show that some of the erotetic notions we introduce nicely correspond to the ...

We show through a number of examples how it is possible to express beliefs of agents and communication among agents by employing a rst-order logic language with metalogical facilities. We argue that (i) such a language is suitable to characterise rational agents in diierent application areas, and (ii) the interplay between metalogical reasoning and diierent modalities of communications allows u...

‘Concern Alignment in Conversations’ project aims, through empirical examinations of real-life conversations, to establish a theoretical and descriptive framework to capture discourse structures and underlying rational and affective processes in human-human joint planning interactions at dialogue act exchange level. Concern alignment model has been developed to address convergent negotiation fo...

We consider the problem of coordinating the behavior of multiple self-interested agents. It involves constraint optimization problems that often can only be solved by local search algorithms. Using local search poses problems of incentivecompatibility and individual rationality. We thus define a weaker notion of bounded-rational incentive-compatibility where manipulation is made impossible with...