A flat Lorentz space form is a geodesically complete Lorentzian manifold of zero curvature. It is well known (see Auslander & Markus [3]) that such a space M may be represented as a quotient R/Γ, where R" is an ^-dimensional Minkowski space (n equals the dimension of M) and Γ is a group of Lorentz isometries acting properly discontinuously and freely on R. In particular the universal covering o...

In three experiments, observers judged the apparent extents of spatial intervals along the surface of a curved cylinder or a flat plane that was binocularly viewed in a natural, indoor environment. The observers' judgments of surface lengths were precise and reliable but were also inaccurate and subject to relatively large constant errors. These distortions differed among the observers, but the...

In this paper, we give normal forms for flat two-input control-affine systems in dimension five that admit a output depending on the state only (we call with property x-flat systems). We discuss relations of x-flatness static and dynamic feedback linearization show if system is it becomes linearizable via at most three prolongations suitably chosen control. Therefore can be, general, brought in...

It was shown by Weyl that the general static axisymmetric solution of the vacuum Einstein equations in four dimensions is given in terms of a single axisymmetric solution of the Laplace equation in three-dimensional flat space. Weyl’s construction is generalized here to arbitrary dimension D ≥ 4. The general solution of the D-dimensional vacuum Einstein equations that admits D− 2 orthogonal com...

This paper proposes a multi-dimensional framework for classifying text documents. In this framework, the concept of multidimensional category model is introduced for representing classes. In contrast with traditional flat and hierarchical category models, the multi-dimensional category model classifies each text document in a collection using multiple predefined sets of categories, where each s...