A general framework for investigating topological actions of Z d on compact metric spaces was proposed by Boyle and Lind in terms of expansive behavior along lower dimensional subspaces of R d. Here we completely describe this expansive behavior for the class of algebraic Z d-actions given by commuting automorphisms of compact abelian groups. The description uses the logarithmic image of an alg...

Pyramidal multiresolution image representation is an ordered sequence of decreasing spatial resolution images in which each image is filtered version of its predecessor. Pyramidal representation of an image is applied in various fields of image processing: progressive image transmission used in interactive image communication over low-bandwidth channels, for image compression used in transmissi...

Laguerre geometry provides a simple approach to the design of rational curves and surfaces with rational offsets. These so-called PH curves and PN surfaces can be constructed from arbitrary rational curves or surfaces with help of a geometric transformation which describes a change between two models of Laguerre geometry. Closely related to that is their optical interpretation as anticaustics o...

Environmental Justice is a movement that was born in the early 1980s to assure fair distribution of environmental risks and benefits (Bullard 1996). In many occasions, minority communities are more affected by environmentally hazardous substances and activities than other population groups. This normally happens because they either ignore the problem or have less power to have an opinion about ...

Converging evidences have indicated that the ability to generate creative ideas could be limited by recently activated knowledge such as examples of solutions. However, neuroimaging studies have recently demonstrated that exposure to examples did not systematically lead to fixation and could on the contrary have a stimulation effect on creativity.Our hypothesis is that there are two types of ex...

It is shown that for any expansive, integer valued 2×2 matrix, there exists a (multi-)wavelet whose Fourier transform is compactly supported and smooth. A key step is showing that for almost every equivalence class of integrally similar matrices there is a representative A which is strictly expansive in the sense that there is a compact set K which tiles the plane by integer translations and su...

A general framework for investigating topological actions of Z d on compact metric spaces was proposed by Boyle and Lind in terms of expansive behavior along lower-dimensional subspaces of R d. Here we completely describe this expansive behavior for the class of algebraic Z d-actions given by commuting automorphisms of compact abelian groups. The description uses the logarithmic image of an alg...

An algebraic Z-action of entropy rank one is one for which each element has finite entropy. Using the structure theory of these actions due to Einsiedler and Lind, this paper investigates dynamical zeta functions for elements of the action. An explicit periodic point formula is obtained leading to a uniform parameterization of the zeta functions that arise in expansive components of an expansiv...

Video games, unlike traditional, non-digital games, are based on a combination of fixed rules which cannot be broken from the player position, and implied rules which are not enforced by the computer program. It is relatively common, however, for players to impose additional or alternative rules on video games, in order to refine or expand gameplay and to create new gaming experiences. This pap...