The minimum depth d B,A of a subring B ⊆ A introduced in the work of Boltje, Danz and Külshammer 2011 is studied and compared with the tower depth of a Frobenius extension. We show that d B,A < ∞ if A is a finite-dimensional algebra and B has finite representation type. Some conditions in terms of depth and QF property are given that ensure that the modular function of a Hopf algebra restricts ...

The radiograph on this issue’s front cover demonstrates a normal image of the abdomen. It is a favourite of mine and one that I use routinely in teaching undergraduate medical students. Take a good look. You may notice a curvilinear gas density projected within the pelvis. See it? This is what a tampon looks like (figure 1). It’s a subtle finding, but once seen, the radiographic configuration i...

W constitutes a dangerous equation? There are two obvious interpretations: Some equations are dangerous if you know them, and others arc dangerous if you do not. The first category may pose danger because the secrets within its bounds open doors behind which lies terrible peril. The obvious winner in this is Einstein's iconic equation e = nic~, for it provides a measure of the enormous energy h...

As vital components of habitat for stream fishes, pools are often monitored to follow the effects of enhancement projects and natural stream processes. Variations of water depth with discharge, however, can complicate monitoring changes in the depth and volume of pools. To subtract the effect of discharge on depth in pools, residual depths can be measured. Residual depth is the difference in de...

The Southern Ocean is anomalously rich in benthos. This biodiversity is native, mostly endemic and perceived to be uniquely threatened from climateand anthropogenicallymediated invasions. Major international scientific effort throughout the last decade has revealed more connectivity than expected between fauna north and south of the worlds strongest marine barrier—the Polar Front (the strongest...

Foreground and background features are focused (or defocused) diierently in an image because corresponding objects are at diierent depths in the scene. This paper presents a novel approach for segmenting foreground and background in video images based on feature defocus. A modiied defocus measurement that distinguishes between high-contrast defocused edges and low-contrast focused edges is pres...