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...

The process that creates stereo images typically takes from 1.5 to 2 times longer than the algorithm for mono images. This paper presents a fast image-based algorithm for computing stereo images, that needs a little more time than the algorithm for mono images. The presented algorithm uses a single image with depth information (e.g. z-buffer) as an input and produces two images for left and rig...

Chen andWilliams[2]show how precomputedz-buffer hnagesfromdifferent fixedviewing positions canbe reprojected toproduceanimagefora new viewpoint. Hereimagesareprecomputedfortwigsand branchesatvariouslevelsinthehierarchical structure ofa tree,and adaptivelycombined,dependingon thepositionof thenew viewpoint.The precomputedimages containmultiplez levelstoavoidmissingpixelsinthereconstruction, subp...

This paper investigates model checking Object-Z classes via their translation to the input notation of the CSP model checker FDR. Such a translation must not only be concerned with preserving the semantics of the original specification, but also with how efficiently the resulting specification can be model checked. Hence, the paper investigates alternative translation schemes and compares how e...

OBJECTIVES To determine changes in height, weight, and BMI of extremely preterm (EPT; gestational age <28 completed weeks) survivors from birth to 18 years of age, compared with term controls. METHODS Birth, discharge, and follow-up at ages 2, 5, 8, and 18 years of consecutive EPT survivors and contemporaneous term controls born in 1991-1992 in Victoria, Australia. Weight, height, and BMI wer...