Convergence S-compactifications

[EN] Properties of continuous actions on convergence spaces are investigated. The primary focus is the characterization as to when a continuous action on a convergence space can be continuously extended to an action on a compactification of the convergence space. The largest and smallest such compactifications are studied.Losert, B.; Richardson, G. (2014). Convergence S-compactifications. Applied General Topology. 15(2):121-136. doi:http://dx.doi.org/10.4995/agt.2014.3156.SWORD121136152Boustique, H., Mikusinski, P., & Richardson, G. (2009). Convergence semigroup actions: generalized quotients. Applied General Topology, 10(2), 173-186. doi:10.4995/agt.2009.1731H. Boustique, P. Mikusinski and G. Richardson, Convergence semigroup categories, Appl. Gen. Topol. 11, no. 2 (2010), 67-88.J. de Vries, On the existence of G -compactifications, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 26, no. 3 (1978), 275-280.W. H. Gottschalk and G. A. Hedlund, Topological D ynamics, volume 36. American Mathematical Society, 1955.Keller, H. H. (1968). Die Limes-Uniformisierbarkeit der Limesräume. Mathematische Annalen, 176(4), 334-341. doi:10.1007/bf02052894Richardson, G. D., & Kent, D. C. (1972). Regular compactifications of convergence spaces. Proceedings of the American Mathematical Society, 31(2), 571-571. doi:10.1090/s0002-9939-1972-0286074-2D. C. Kent and G. D. Richardson, Open and proper maps between convergence spaces, Czechoslovak Mathematical Journal 23, no. 1 (1973), 15-23.D. C. Kent and G. D. Richardson, Locally compact convergence spaces, The Michigan Mathematical Journal 22, no. 4 (1975), 353-360.Kent, D. C., & Richardson, G. D. (1979). Compactifications of convergens spaces. International Journal of Mathematics and Mathematical Sciences, 2(3), 345-368. doi:10.1155/s0161171279000302E. Lowen-Colebunders, Function Classes of Cauchy Continuous Maps, M. Dekker, 1989.Preuss, G. (2002). Foundations of Topology. doi:10.1007/978-94-010-0489-3Reed, E. E. (1971). Completions of uniform convergence spaces. Mathematische Annalen, 194(2), 83-108. doi:10.1007/bf0136253

Galois Got his Gun

This paper appeals to the figure of \'Evariste Galois for investigating the gates between mathematics and their "publics." The figure of Galois draws some lines of/within mathematics for/from the outside of mathematics and these lines in turn sketch the silhouette of Galois as a historical figure. The present paper especially investigates the collective categories that have been used in various types of public discourses on Galois's work (e.g. equations, groups, algebra, analysis, France, Germany etc.). In a way, this paper aims at shedding light on the boundaries some individuals drew by getting Galois his gun. It is our aim to highlight the roles of authority some individuals (such as as Picard) took on in regard with the public figure of Galois as well as the roles such authorities assigned to other individuals (such as the mediating role assigned to Jordan as a mediator between Galois's "ideas" and the public). The boundary-works involved by most public references to Galois have underlying them a long-term tension between academic and public legitimacies in the definition of some models for mathematical lives (or mathematics personae

Dynamic problems for metamaterials: Review of existing models and ideas for further research

Metamaterials are materials especially engineered to have a peculiar physical behaviour, to be exploited for some well-specified technological application. In this context we focus on the conception of general micro-structured continua, with particular attention to piezoelectromechanical structures, having a strong coupling between macroscopic motion and some internal degrees of freedom, which may be electric or, more generally, related to some micro-motion. An interesting class of problems in this context regards the design of wave-guides aimed to control wave propagation. The description of the state of the art is followed by some hints addressed to describe some possible research developments and in particular to design optimal design techniques for bone reconstruction or systems which may block wave propagation in some frequency ranges, in both linear and non-linear fields. (C) 2014 Elsevier Ltd. All rights reserved

Mathematical models of games of chance: Epistemological taxonomy and potential in problem-gambling research

Games of chance are developed in their physical consumer-ready form on the basis of mathematical models, which stand as the premises of their existence and represent their physical processes. There is a prevalence of statistical and probabilistic models in the interest of all parties involved in the study of gambling – researchers, game producers and operators, and players – while functional models are of interest more to math-inclined players than problem-gambling researchers. In this paper I present a structural analysis of the knowledge attached to mathematical models of games of chance and the act of modeling, arguing that such knowledge holds potential in the prevention and cognitive treatment of excessive gambling, and I propose further research in this direction