Every positive rational number has representations as Egyptian fractions (sums of reciprocals of distinct positive integers) with arbitrarily many terms and with arbitrarily large denominators. However, such representations normally use a very sparse subset of the positive integers up to the largest denominator. We show that for every positive rational there exist representations as Egyptian fr...

Persuasive technologies, used within in the domain of interactive technology, are used broadly in social contexts to encourage customers towards positive behavior change. In the context of e-commerce, persuasive technologies have already been extensively applied in the area of marketing to enhancing system credibility, however the issue of ‘persuasiveness’, and its role on positive user accepta...

We show that the positive Wiener–Hopf factor of a Lévy process with positive jumps having a rational Fourier transform is a rational function itself, expressed in terms of the parameters of the jump distribution and the roots of an associated equation. Based on this, we give the closed form of the ruin probability for a Lévy process, with completely arbitrary negatively distributed jumps, and f...

This research is defined a new neural network (NN) that depends upon positive integer parameter using the multivariate square rational Bernstein polynomials. Some theorems for this are proved, such as pointwise and uniform approximation theorems. Firstly, absolute moment function belongs to Lipschitz space estimate order of NN. Secondly, some numerical applications NN given by taking two test f...

This paper deals with the shape preserving C rational cubic interpolation. The developed rational cubic interpolating function has only one free parameter. The approximation order of rational cubic function is investigated and range of optimal error constant is determined. Moreover, positive, constrained and monotone data preserving schemes are developed. 2000 Mathematics Subject Classification...

In this paper we demonstrate the existence of Sasakian-Einstein structures on certain 2-connected rational homology 7-spheres. These appear to be the first non-regular examples of Sasakian-Einstein metrics on simply connected rational homology spheres. We also briefly describe the rational homology 7-spheres that admit regular positive Sasakian structures.

Interactions between disease dynamics and vaccinating behavior have been explored in many coupled behavior-disease models. Cognitive effects such as risk perception, framing, and subjective probabilities of adverse events can be important determinants of the vaccinating behaviour, and represent departures from the pure "rational" decision model that are often described as "bounded rationality"....

We say that a mechanism is harmless if no student can ever misreport his preferences so that he does not hurt but someone else. We consider a large class of rules which includes the Boston, the agent-proposing deferred acceptance, and the school-proposing deferred acceptance mechanisms (sDA). In this large class, the sDA happens to the unique harmless mechanism. We next provide two axiomatic ch...