generalizing quasinormality

Generalizing Halfspaces Generalizing Halfspaces

Restricted-orientation convexity is the study of geometric objects whose intersection with lines from some fixed set is empty or connected. We have studied the properties of restricted-orientation convex sets and demonstrated that this notion is a generalization of standard convexity. We now describe a restricted-orientation generalization of halfspaces and explore properties of these generaliz...

Generalizing substitution

It is well known that, given an endofunctor H on a category C, the initial (A+H−)-algebras (if existing), i.e., the algebras of (wellfounded) H-terms over different variable supplies A, give rise to a monad with substitution as the extension operation (the free monad induced by the functor H). Moss [17] and Aczel, Adámek, Milius and Velebil [2] have shown that a similar monad, which even enjoys...

Generalizing Scales

Instead of considering scales to be linearly ordered structures, it is proposed that scales are better conceived of as metrics (dissimilarity matrices). Further, to be considered a scale of typological interest, there should be a significant correlation between a meaning-scale and a form-scale. This conceptualisation allows for a fruitful generalization of the concept "scale". As a hands-on exa...

Generalizing resolution

Of those things that can be estimated well in an inverse problem, which is best to estimate? Backus–Gilbert resolution theory answers a version of this question for linear (or linearized) inverse problems in Hilbert spaces with additive zero-mean errors with known, finite covariance, and no constraints on the unknown other than the data. This paper generalizes resolution: it defines the resolut...

Generalizing Halfspaces

Generalizing Halfspaces1

Restricted-orientation convexity is the study of geometric objects whose intersection with lines from some fixed set is empty or connected. We have studied the properties of restricted-orientation convex sets and demonstrated that this notion is a generalization of standard convexity. We now describe a restricted-orientation generalization of halfspaces and explore properties of these generaliz...