1 On the so–called Pell–Fermat equation 2 1.1 Examples of simple continued fractions . . . . . . . . . . . . . 2 1.2 Existence of integer solutions . . . . . . . . . . . . . . . . . . 5 1.3 All integer solutions . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 On the group of units of Z[ √ D] . . . . . . . . . . . . . . . . . 8 1.5 Connection with rational approximation . . . . . . . . . . ....

We consider a resource allocation problem, where a rational agent has to decide how to share a limited amount of resources among different companies that might be facing financial difficulties. The objective is to minimize the total long term cost incurred by the economy due to default events. Using the framework of multiarmed restless bandits and, assuming a two-state evolution of the default ...

A memory-based collaborative system for recommending Master programs has been recently developed for University College Maastricht (UCM). Given the academic profile of a Bachelor student, the system recommends Master programs for that student based on the similarity of her profile to the profiles of the alumni students. The system is operational since September 2011 and is already popular among...

In contrast to verfication methods, such as the use of BDI (belief, desire, intention) logics, e.g., (Rao Georgetf 1993), which can be used to verify for instance commitment properties of rational agents, our agent algebra is intended to be used for more concrete properties such as safety or progress properties (deadlock freedom, fairness, ...) of more action-oriented agents. In MASs there can ...

A new method for construction of bases for general distribution spaces is developed. This method allows the freedom to prescribe the nature and properties of the basis elements. The method is deployed to the construction of bases consisting of rational functions of uniformly bounded degrees for Besov and Triebel–Lizorkin spaces of holomorphic functions in the unit disc. In turn, this is utilize...

the immortality of the rational soul is one of the most important issues of ibn sina’s philosophy and anthropology. he poses many arguments in proving this subject. ibn sina proves the immortality of rational soul by not having relation or position of the intelligible concepts, indefinite power of the rational soul in his actions as well as its needlessness to sensible faculties in some of its ...

the subject matter of this article is not to determine the priority of reason to heart or privacy of rationality to love, but find out the answers to these questions: what is role of reason and rational knowledge in attaining mystical intuitive visions? how far does the horizon of rational knowledge extend from perspective of ibn arabi? given the fact that mysticism is arena for esoteric vision...

study of the works of rumi and kierkegaard shows that both thinkers in some principles like faith and morality, faith and leap, and also in relation between devil and faith, and destiny and faith, come to a common point. both of them believe that human’s duty is to surrender to god’s will, and the devil is an obstacle against faith. they also put emphasize on the matter of leap in faith. moreov...