Riemann-Hilbert problems for poly-Hardy space on the unit ball

In this paper, we focus on a Riemann–Hilbert boundary value problem (BVP) with a constant coefficients for the poly-Hardy space on the real unit ball in higher dimensions. We first discuss the boundary behaviour of functions in the poly-Hardy class. Then we construct the Schwarz kernel and the higher order Schwarz operator to study Riemann–Hilbert BVPs over the unit ball for the poly- Hardy class. Finally, we obtain explicit integral expressions for their solutions. As a special case, monogenic signals as elements in the Hardy space over the unit sphere will be reconstructed in the case of boundary data given in terms of functions having values in a Clifford subalgebra. Such monogenic signals represent the generalization of analytic signals as elements of the Hardy space over the unit circle of the complex plane.

Development and characterization of Poly(L-lactic acid) (PLLA) platforms for bone tissue engineering

The development of scaffolds based on biomaterials is a promising strategy for Tissue Engineering and cellular regeneration. This work focuses on Bone Tissue Engineering, the aim is to develop electrically tailored biomaterials with different crystalline and electric features, and study their impacts onto cell biological behavior, so as to predict the materials output in the enhancement of bone tissue regeneration. It is accepted that bone exhibits piezoelectricity, a property that has been proved to be involved in bone growth/repair mechanism regulation. In addition electrical stimulations have been proved to influence bone growth and repair. Piezoelectric materials are therefore widely investigated for a potential use in bone tissue engineering. The main goal is the development of novel strategies to produce and employ piezoelectric biomaterials, with detailed knowledge of mechanisms involved in cell-material interaction. In the current work, poly (L-lactic) acid (PLLA), a synthetic semi-crystalline polymer, exhibiting biodegradibility, biocompatibility and piezoelectricity is studied and proposed as a promoter of enhanced tissue regeneration. PLLA has already been approved for implantation in human body by the Food and Drug Administration (FDA), and at the moment it is being used in several clinical strategies. The present study consists of first preparing films with different degrees of crystallinity and characterizing these PLLA films, in terms of surface and structural properties, and subsequently assessing the behavior of cells in terms of viability, proliferation, morphology and mineralization for each PLLA configuration. PLLA films were prepared using the solvent cast technique and submitted to different thermal treatments in order to obtain different degrees of crystallinity. Those platforms were then electrically poled, positively and negatively, by corona discharge in order to tailor their electrical properties. The cellular assays were conducted by using two different osteoblast cell lines grown directly onto the PLLA films:Human osteoblast Hob, a primary cell culture and Human osteosarcoma MG-63 cell line. This thesis gives also a comprehensive introduction to the area of Bone Tissue Engineering and provides a review of the work done in this field in the past until today, in that same field, including the one related with bone’s piezoelectricity. Then the experimental part deals with the effects of the crystallinity degrees and of the polarization in terms of surface properties and cellular bio assays. Three different degrees of crystallinity, and three different polarization conditions were prepared; which results in 9 different configurations under investigation.