It is known that piecewise affine surface homeomorphisms always have measures of maximal entropy. This is easily seen to fail in the discontinuous case. Here we describe a piecewise affine, globally continuous surface map with no measure of maximal entropy.

An affine manifold is a manifold with a distinguished system of affine coordinates, namely, an open covering by charts which map homeomorphically onto open sets in an affine space E such that on overlapping charts the homeomorphisms differ by an affine automorphism of E. Some, but certainly not all, affine manifolds arise as quotients Ω/Γ of a domain in E by a discrete group Γ of affine transfo...

We consider the inverse problem of determining the twisting function in a infinite cylindrical twisted waveguide from the corresponding DN map. This problem, which is naturally linked to some inverse anisotropic conductivity problem in a straight waveguide, remains generally open, unless the twisting function is assumed to be affine. Namely we prove Lipschitz stability in the determination of a...

Let Ψ : Z → Z be an affine-linear map, and Ψ̇ be its linear part. A famous and difficult open conjecture of Dickson predicts the distribution of prime points in the affine sublattice Ψ(Z) of Z. Assuming the Gowers Inverse conjecture GI(s) and the Möbius and nilsequences conjecture MN(s) for some finite s > 1, GreenTao [GT3] verified Dickson’s conjecture for Ψ of complexity s. Let Φ : Z → Z be an...

Much local government has been utilizing a large-scale digital map using Geographic Information System (GIS). However, the maintenance and renewal of a map database need much labor and time. Moreover, the updating method of a map has not been established yet and there have been almost no successful examples. The purpose of the study is to establish a method of updating the large-scale map for l...

Abstract Let

Self-affine maps were successfully used for edge detection, image segmentation, and contour extraction. They belong to the general category of patch-based methods. Particularly, each self-affine map is defined by one pair of patches in the image domain. By minimizing the difference between these patches, the optimal translation vector of the self-affine map is obtained. Almost all image process...

Locally extended affine Lie algebras were introduced by Morita and Yoshii in [J. Algebra 301(1) (2006), 59-81] as a natural generalization of extended affine Lie algebras. After that, various generalizations of these Lie algebras have been investigated by others. It is known that a locally extended affine Lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...