Sentence examples for notion of dimension from inspiring English sources

Something one should not try to do is to derive a notion of dimension from an ordering relation.

1928 1930 Conflict with Karl Menger over the priority for the first correct definition of the notion of dimension.

In this article we introduce a notion of dimension of a module, to be called couniserial dimension.

Dimension theory is a branch of topology devoted to the definition and study of the notion of dimension in certain classes of topological spaces.

Either one takes the option to simply drop the notion of dimension on the basis of the argument that the concept of dimension presupposes a concept of continuity and topology and hence has no finitist meaning.

We are oriented to building up a theory of a metric measure space ( X, d, μ ) for which the notion of dimension is not equipped with μ, where d is a distance function and μ is a Borel measure.

Faced with such an inconvenience, we work on a separable metric space X equipped with a nonnegative Radon measure μ, where the notion of dimensions of X and μ does not come into play.

We show that the classical probability entropy dimension of a measure is related with diverse other notions of dimension.

Combining the notions of dimension reduction and sufficiency, sufficient dimension reduction [11, 15, 23] is used to detect a lower dimension subspace of the predictor space, such that the response variable is independent with the predictor vectors providing all the information of this subspace.

The history of dimensional analysis is reviewed, starting with the first notions of dimensions to the powerful methods of recent times.

From a unifier's point of view, one of the most interesting things about the new theory is the way it conflates the seemingly very different notions of dimensions and forces.