Periodicity and Quasi-Periodicity for Super-Integrable Hamiltonian Systems

Classical trajectories are calculated for two Hamiltonian systems with ring shaped potentials. Both systems are super-integrable, but not maximally super-integrable, having four globally defined single valued integrals of motion each. All finite trajectories are quasi-periodical; they become truly periodical if a commensurability condition is imposed on an angular momentum component

Review of periodical articles

[First Paragraph] There is only one true city, wrote St Augustine, and it is not of this world. The pessimistic Christian response to the fall of Rome in AD 410, epitomized in Augustine's City of God, affected the development of the later medieval city to a degree which has yet, even now, to be fully appreciated. In the Christian city of the Middle Ages the divinity was normally confined to the sanctuaries of his churches, whose topographical prominence and harmonious proportions made manifest an otherwise hidden spiritual order. Outside the cloister gates, disorder reigned: a general lack of planning revealed the meaninglessness of the outward, secular life. This dichotomy between an inner world of spirit and a public world of transient matter was embodied in the recurrent tensions between spiritual and secular space which ran as a motif throughout the history of medieval towns. Modern studies which have emphasized (not, of course, without reason) the secular political and economic power of ecclesiastical institutions in the medieval city have perhaps distracted attention unduly from the real differences of ethos which, within the town, distinguished religious space from that of the surrounding lay world

Magazine sales promotion : a dynamic response analysis

This paper studies the impact and effectiveness of a type of non-price promotion often used in the European periodical magazines industry to stimulate sales, in which a value pack is sold containing the magazine issue plus another product. Magazines are sold simultaneously with and without promotion at different prices, and promotions are serialized by fractioning the additional product across different issues of the magazine. We find that promoted magazines contemporarily cannibalize non-promoted sales; but this loss is compensated by a medium term increase of non-promoted sales. These results show that this sales promotion strategy is an effective way to diminish the decline rate of periodical sales