An algorithm for determining copositive matrices

In this paper, we present an algorithm of simple exponential growth called COPOMATRIX for determining the copositivity of a real symmetric matrix. The core of this algorithm is a decomposition theorem, which is used to deal with simplicial subdivision of $\hat{T}^{-}=\{y\in \Delta_{m}| \beta^Ty\leq 0\}$ on the standard simplex $\Delta_m$, where each component of the vector $\beta$ is -1, 0 or 1.Comment: 15 page

Direct detonation initiation in hydrogen/air mixture: effects of compositional gradient and hotspot condition

Two-dimensional simulations are conducted to investigate the direct initiation of cylindrical detonation in hydrogen/air mixtures with detailed chemistry. The effects of hotspot condition and mixture composition gradient on detonation initiation are studied. Different hotspot pressure and composition are first considered in the uniform mixture. It is found that detonation initiation fails for low hotspot pressures and supercritical regime dominates with high hotspot pressures. Detonation is directly initiated from the reactive hotspot, whilst it is ignited somewhere beyond the nonreactive hotspots. Two cell diverging patterns (i.e., abrupt and gradual) are identified and the detailed mechanisms are analyzed. Moreover, cell coalescence occurs if many irregular cells are generated initially, which promotes the local cell growing. We also consider nonuniform detonable mixtures. The results show that the initiated detonation experiences self-sustaining propagation, highly unstable propagation, and extinction in mixtures with a linearly decreasing equivalence ratio along the radial direction respectively, i.e., 1 to 0.9, 1 to 0.5 and 1 to 0. Moreover, the hydrodynamic structure analysis shows that, for the self-sustaining detonations, the hydrodynamic thickness increases at the overdriven stage, decreases as the cells are generated, and eventually become almost constant at the cell diverging stage, within which the sonic plane shows a sawtooth pattern. However, in the detonation extinction cases, the hydrodynamic thickness continuously increases, and no sawtooth sonic plane can be observed

Auricle shaping using 3D printing and autologous diced cartilage.

ObjectiveTo reconstruct the auricle using a porous, hollow, three-dimensional (3D)-printed mold and autologous diced cartilage mixed with platelet-rich plasma (PRP).MethodsMaterialise Magics v20.03 was used to design a 3D, porous, hollow auricle mold. Ten molds were printed by selective laser sintering with polyamide. Cartilage grafts were harvested from one ear of a New Zealand rabbit, and PRP was prepared using 10 mL of auricular blood from the same animal. Ear cartilage was diced into 0.5- to 2.0-mm pieces, weighed, mixed with PRP, and then placed inside the hollow mold. Composite grafts were then implanted into the backs of respective rabbits (n = 10) for 4 months. The shape and composition of the diced cartilage were assessed histologically, and biomechanical testing was used to determine stiffness.ResultsThe 3D-printed auricle molds were 0.6-mm thick and showed connectivity between the internal and external surfaces, with round pores of 0.1 to 0.3 cm. After 4 months, the diced cartilage pieces had fused into an auricular shape with high fidelity to the anthropotomy. The weight of the diced cartilage was 5.157 ± 0.230 g (P > 0.05, compared with preoperative). Histological staining showed high chondrocyte viability and the production of collagen II, glycosaminoglycans, and other cartilaginous matrix components. In unrestricted compression tests, auricle stiffness was 0.158 ± 0.187 N/mm, similar to that in humans.ConclusionAuricle grafts were constructed successfully through packing a 3D-printed, porous, hollow auricle mold with diced cartilage mixed with PRP. The auricle cartilage contained viable chondrocytes, appropriate extracellular matrix components, and good mechanical properties.Levels of evidenceNA. Laryngoscope, 129:2467-2474, 2019

1-{1-[(2-Chloro­thia­zol-5-yl)meth­yl]-5-methyl-1H-1,2,3-triazol-4-yl}ethanone

In the title compound, C9H9ClN4OS, the two rings enclose a dihedral angle of 84.67 (11)°. Inter­molecular C—H⋯O and C—H⋯N hydrogen bonds stabilize the crystal packing