25,219 research outputs found
Proportions of r-regular elements in finite classical groups
For a prime , we obtain lower bounds on the proportion of -regular
elements in classical groups and show that these lower bounds are the best
possible lower bounds that do not depend on the order of the defining field.
Along the way, we also provide new upper bounds and answer some open questions
of the first author, P\'{a}lfy and Saxl.Comment: 22 page
Science, Art and Geometrical Imagination
From the geocentric, closed world model of Antiquity to the wraparound
universe models of relativistic cosmology, the parallel history of space
representations in science and art illustrates the fundamental role of
geometric imagination in innovative findings. Through the analysis of works of
various artists and scientists like Plato, Durer, Kepler, Escher, Grisey or the
present author, it is shown how the process of creation in science and in the
arts rests on aesthetical principles such as symmetry, regular polyhedra, laws
of harmonic proportion, tessellations, group theory, etc., as well as beauty,
conciseness and emotional approach of the world.Comment: 22 pages, 28 figures, invited talk at the IAU Symposium 260 "The Role
of Astronomy in Society and Culture", UNESCO, 19-23 January 2009, Paris,
Proceedings to be publishe
Construction of Curtis-Phan-Tits system in black box classical groups
We present a polynomial time Monte-Carlo algorithm for finite simple black
box classical groups of odd characteristic which constructs all root
-subgroups associated with the nodes of the extended Dynkin
diagram of the corresponding algebraic group.Comment: 35 page
The von Neumann Model and the Early Models of General Equilibrium
The paper reconstructs the von Neumann model, comments on its salient features and critically reviews some of its generalisations. The issues related to thetreatment of consumption, decomposability and uniqueness of the rate of growth and interest will be especially scrutinised. The most prominent models of general equilibrium that appeared before or roughly at the same time as von Neumann's model will be also reviewed in the paper and compared with it. It will be demonstrated that none of them had any noticeable influence on von Neumann's model, which is genuinely distinct, ideologically free and methodologically fresh and forward-looking. It will be argued that the model can be viewed as a brilliant mathematical metaphor of some deep-rooted old vision, pertaining to the core issues of commodity production
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