102 research outputs found

    Boundedness, compactness and Schatten-class membership of weighted composition operators

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    The boundedness and compactness of weighted composition operators on the Hardy space H2{\mathcal H}^2 of the unit disc is analysed. Particular reference is made to the case when the self-map of the disc is an inner function. Schatten-class membership is also considered; as a result, stronger forms of the two main results of a recent paper of Gunatillake are derived. Finally, weighted composition operators on weighted Bergman spaces A2α(D)\mathcal{A}^2 \alpha(\mathbb{D}) are considered, and the results of Harper and Smith, linking their properties to those of Carleson embeddings, are extended to this situation.Comment: 12 page

    Weighted composition operators on the Dirichlet space: boundedness and spectral properties

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    Boundedness of weighted composition operators W u,φ acting on the classical Dirichlet space D as W u,φ f=u(f∘φ) is studied in terms of the multiplier space associated to the symbol φ , i.e., M(φ)={u∈D:W u,φ is bounded on D} . A prominent role is played by the multipliers of the Dirichlet space. As a consequence, the spectrum of W u,φ in D whenever φ is an automorphism of the unit disc is studied, extending a recent work of Hyvärinen et al. (J. Funct. Anal. 265:1749–1777, 2013) to the context of the Dirichlet space

    A Mathematical Model of Liver Cell Aggregation In Vitro

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    The behavior of mammalian cells within three-dimensional structures is an area of intense biological research and underpins the efforts of tissue engineers to regenerate human tissues for clinical applications. In the particular case of hepatocytes (liver cells), the formation of spheroidal multicellular aggregates has been shown to improve cell viability and functionality compared to traditional monolayer culture techniques. We propose a simple mathematical model for the early stages of this aggregation process, when cell clusters form on the surface of the extracellular matrix (ECM) layer on which they are seeded. We focus on interactions between the cells and the viscoelastic ECM substrate. Governing equations for the cells, culture medium, and ECM are derived using the principles of mass and momentum balance. The model is then reduced to a system of four partial differential equations, which are investigated analytically and numerically. The model predicts that provided cells are seeded at a suitable density, aggregates with clearly defined boundaries and a spatially uniform cell density on the interior will form. While the mechanical properties of the ECM do not appear to have a significant effect, strong cell-ECM interactions can inhibit, or possibly prevent, the formation of aggregates. The paper concludes with a discussion of our key findings and suggestions for future work

    Characterization of bone repair in rat femur after treatment with calcium phosphate cement and autogenous bone graft

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    <p>Abstract</p> <p>Background</p> <p>In this study, the biocompatibility, stability and osteotransductivity of a new cement based on alpha-tricalcium phosphate (alpha-TCP) were investigated in a bone repair model using a rat model.</p> <p>Methods</p> <p>The potential of alpha-TCP on bone repair was compared to autogenous bone grafting, and unfilled cavities were used as negative control. Surgical cavities were prepared and designated as test (T), implanted with alpha-TCP blocks; negative control (C - ), unfilled; and positive control (C + ), implanted with autogenous bone graft. Results were analyzed on postoperative days three, seven, 14, 21 and 60.</p> <p>Results</p> <p>The histological analyses showed the following results. Postoperative day three: presence of inflammatory infiltrate, erythrocytes and proliferating fibroblasts in T, C - and C + samples. Day seven: extensive bone neoformation in groups T and C + , and beginning of alpha-TCP resorption by phagocytic cells. Days 14 and 21: osteoblastic activity in the three types of cavities. Day 60: In all samples, neoformed bone similar to surrounding bone. Moderate interruption on the ostectomized cortical bone.</p> <p>Conclusions</p> <p>Bone neoformation is seen seven days after implantation of alpha-TCP and autogenous bone. Comparison of C - with T and C + samples showed that repair is faster in implanted cavities; on day 60, control groups presented almost complete bone repair. Alpha-TCP cement presents biocompatibility and osteotransductivity, besides stability, but 60 days after surgery the cavities were not closed.</p

    Biodegradable polyurethane for fused deposition modelling

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    Fused Deposition Modelling (FDM) is used to build prototypes from a CAD model using thermoplastic polymer filament. At present, bioresorbable filaments are not commercially available, however, some work has been reported in the literature (Hutmacher et al., 1999), where poly-(e-caprolactone), (PCL) was used as a filament and scaffolds were made for tissue engineering. CSIRO has recently developed a versatile range of biodegradable polyurethanes2 for tissue engineering applications. This work has been extended in order to optimise materials with properties suitable for FDM technologies
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