Displaying similar documents to “Coincidences of real-valued maps from the n-torus”

The Poulsen simplex

Joram Lindenstrauss, Gunnar Olsen, Y. Sternfeld (1978)

Annales de l'institut Fourier

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It is proved that there is a unique metrizable simplex S whose extreme points are dense. This simplex is homogeneous in the sense that for every 2 affinely homeomorphic faces F 1 and F 2 there is an automorphism of S which maps F 1 onto F 2 . Every metrizable simplex is affinely homeomorphic to a face of S . The set of extreme points of S is homeomorphic to the Hilbert space ℓ 2 . The matrices which represent A ( S ) are characterized.

A special type of triangulations in numerical nonlinear analysis.

J. M. Soriano (1990)

Collectanea Mathematica

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To calculate the zeros of a map f : Rn → Rn we consider the class of triangulations of Rn so that a certain point belongs to a simplex of fixed diameter and dimension. In this paper two types of this new class of triangulations are constructed and shown to be useful to calculate zeros of piecewise linear approximations of f.

On convergence of homogeneous Markov chains

Petr Kratochvíl (1983)

Aplikace matematiky

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Let p t be a vector of absolute distributions of probabilities in an irreducible aperiodic homogeneous Markov chain with a finite state space. Professor Alladi Ramakrishnan conjectured the following strict inequality for norms of differences p t + 2 - p t + 1 < p t + 1 - p t . In the paper, a necessary and sufficient condition for the validity of this inequality is proved, which may be useful in investigating the character of convergence of distributions in Markov chains.

A remark on Vapnik-Chervonienkis classes

Agata Smoktunowicz (1997)

Colloquium Mathematicae

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We show that the family of all lines in the plane which is a VC class of index 2 cannot be obtained in a finite number of steps starting with VC classes of index 1 and applying the operations of intersection and union. This confirms a common belief among specialists and solves a question asked by several authors.