Osteogenesis imperfecta (OI) is a heritable bone fragility disorder characterized by skeletal deformity and “brittle” bones. This fragility is believed to stem from a combination of bone mass deficiency and compromised bone material properties [1-3]. Poor bone quality poses major orthopaedic and rehabilitation challenges. Risk of fracture is a major consideration when prescribing activity restr...

We extend to arbitrary commutative base rings a recent result of Demeneghi that every ideal an ample groupoid algebra over field is intersection kernels induced representations from isotropy groups, with much shorter proof, by using the author's Disintegration Theorem for representations. also prove primitive kernel representation group; however, we are unable show, in general, it irreducible r...

In this paper, we characterize the (covariant) isotropy groups of free, finitely generated racks and quandles. As a consequence, show that usual inner automorphisms such quandles are precisely those “coherently extendible”. We then use result to compute global categories quandles, i.e. automorphism identity functors these categories.