Recurrence relations for Clifford algebra-valued orthogonal polynomials

The theory of orthogonal polynomials of one real or complex variable is well established as well as its generalization for the multidimensional case. Hypercomplex function theory (or Clifford analysis) provides an alternative approach to deal with higher dimensions. In this context, we study systems of orthogonal polynomials of a hypercomplex variable with values in a Clifford algebra and prove some of their properties.

Enhancement of adhesion and promotion of osteogenic differentiation of human adipose stem cells by poled electroactive poly(vinylidene fluoride)

Poly(vinylidene fluoride) (PVDF) is a biocompatible material with excellent electroactive properties. Non-electroactive α-PVDF and electroactive β-PVDF were used to investigate the substrate polarization and polarity influence on the focal adhesion size and number as well as on human adipose stem cells (hASCs) differentiation. hASCs were cultured on different PVDF surfaces adsorbed with fibronectin and focal adhesion size and number, total adhesion area, cell size, cell aspect ratio and focal adhesion density were estimated using cells expressing EGFP-vinculin. Osteogenic differentiation was also determined using a quantitative alkaline phosphatase assay. The surface charge of the poled PVDF films (positive or negative) influenced the hydrophobicity of the samples, leading to variations in the conformation of adsorbed extracellular matrix (ECM) proteins, which ultimately modulated the stem cell adhesion on the films and induced their osteogenic differentiation.