Since the seminal work of the Gestalt psychologists, there has been great interest in understanding what factors determine the perceptual organization of images. While the Gestaltists demonstrated the significance of grouping cues such as similarity, proximity and good continuation, it has not been well understood whether their catalog of grouping cues is complete--in part due to the paucity of...

The notion of a Γ-symmetric space is a generalization of the classical notion of a symmetric space, where a general finite abelian group Γ replaces the group Z 2. The case Γ = Z k has also been studied, from the algebraic point of view by V.Kac [10] and from the point of view of the differential geometry by Ledger, Obata [12], Kowalski [11] or Wolf-Gray [18] in terms of k-symmetric spaces. In t...

We consider Z{matrices and inverse Z{matrices, i.e. those nonsingular matrices, whose inverse is a Z{matrix. Recently Fiedler and Markham introduced a classii-cation of Z{matrices. This classiication directly leads to a classiication of inverse Z{matrices. Among all classes of Z{matrices and inverse Z{matrices the classes of M{matrices, N 0 {matrices, F 0 {matrices and inverse M{matrices, inver...

The sarcomeric Z-disc defines the lateral borders of the sarcomere and has primarily been seen as a structure important for mechanical stability. This view has changed dramatically within the last one or two decades. A multitude of novel Z-disc proteins and their interacting partners have been identified, which has led to the identification of additional functions and which have now been assign...

We investigate various aspects of the modular representation theory of Z/p × Z/p with particular focus on modules of constant Jordan type. The special modules we consider and the constructions we introduce not only reveal some of the structure of (Z/p× Z/p)-modules but also provide a guide to further study of the representation theory of finite group schemes.

Let $R$ be an associative ring with identity. An element $x in R$ is called $mathbb{Z}G$-regular (resp. strongly $mathbb{Z}G$-regular) if there exist $g in G$, $n in mathbb{Z}$ and $r in R$ such that $x^{ng}=x^{ng}rx^{ng}$ (resp. $x^{ng}=x^{(n+1)g}$). A ring $R$ is called $mathbb{Z}G$-regular (resp. strongly $mathbb{Z}G$-regular) if every element of $R$ is $mathbb{Z}G$-regular (resp. strongly $...

We derive a general formalism for constructing a four-dimensional effective action for the radion field in 5 dimensions, taking into account the possible dependence of the scale factor on the internal coordinate. First and second variations of the action with respect to the size of the extra dimension reveals two types of algebraic constraints on the combination of brane and bulk Lagrangians th...