The minimal-length paradigm, a possible implication of quantum gravity at low energies, is commonly understood as phenomenological modification Heisenberg's uncertainty relation. We show that this equivalent to cut-off in the space conjugate position representation, i.e. wave numbers, which does not necessarily correspond momentum space. This result generalized several dimensions and noncommuta...

To date, there are few large-scale studies that have examined the relationship between duration of abstinence and cognitive functioning in polysubstance-dependent individuals. Existing large-scale studies of polysubstance abusers have reported only minimal recovery of cognitive functioning with abstinence [Arch. Gen. Psychiatry 35 (1978) 1063]. The goal of this study is to test whether length o...

If there are multiple images corresponding to one set of line sums, it is interesting to reconstruct an image with a special property. In order to find reconstructions that look rather like a real object, two special properties in particular are often imposed on the reconstructions. The first is connectivity of the points with value one in the picture [6, 8, 28]. The second is hv-convexity : if...

We define the length of a semigroup presentation and related ideas. Theoretical results and bounds are presented, gained while investigating the lengths of groups defined by semigroup presentations. Minimal length semigroup presentations are obtained in certain cases. AMS Mathematics Subject Classification (2000): 20F05, 20M05

We consider binary abelian codes of length pq where p and q are prime rational integers under some restrictive hypotheses. In this case, we determine the idempotents generating minimal codes and either the respective weights or bounds of these weights. We give examples showing that these bounds are attained in some cases.