1. Dorosz, S., Abubacker, S., Masala, N., Jay, G., Schmidt TA. Cartilage Boundary Lubricating Ability of Full-Length Human Recombinant PRG4 – Alone and in Combination with Hyaluronan. March 28-31, 2015. Las Vegas, NV. 2. Al-Sharif A., Schmidt T., Jay G., Elsaid K. Lubricin/Proteoglycan-4 Inhibits Proinflammatory Cytokine Induced Synoviocyte Proliferation via CD44-Interaction. Orthopedic Researc...

Building on the abstract notion of prolongation developed in [10], the theory of iterative Hasse-Schmidt rings and schemes is introduced, simultaneously generalising difference and (Hasse-Schmidt) differential rings and schemes. This work provides a unified formalism for studying difference and differential algebraic geometry, as well as other related geometries. As an application, Hasse-Schmid...

A new criterion for selective reorthogonalization in the Gram-Schmidt procedure is given. We establish its comportment in presence of rounding errors when the criterion is used with modified Gram-Schmidt algorithm and show counter-example matrices which prove that standard criteria are not always valid. Experimentally, our criterion is fine also for the classical Gram-Schmidt algorithm with reo...

We consider a family of vector and operator norms which we refer to as Schmidt norms. We show that these norms have several uses in quantum information theory – they can be used to help classify k-positive linear maps (and hence entanglement witnesses), they are useful for approaching the problem of finding non-positive partial transpose bound entangled Werner states, they are related to the qu...

Definition 1. Given a vector |v〉 ∈ H, by a Schmidt decomposition across the (i, i + 1) cut we shall mean a decomposition |v〉 = ∑j=1 λj|aj〉|bj〉 with {|aj〉} (respectively {|bj〉} ) a family of orthonormal vectors of H[1,i] (respectively H[i+1,n]) and with λj ≥ λj+1 > 0 for all 1 ≤ j ≤ D. The vectors |aj〉 will be called the left Schmidt vectors across that cut, and the vectors |bj〉 the right Schmid...