Multivariate Methods in the Development of a New Tablet Formulation: Optimization and Validation

In a previous study of the development of a tablet formulation approximately 100 excipients were characterized in screening experiments using multivariate design. Acceptable values for important responses were obtained with some of the formulations. The relationships between the properties of the excipients and the responses were evaluated using PLS. In this study additional experiments were performed in order to validate models obtained from the screening study and to find a formulation of suitable composition with desired tablet properties. A formulation with the desired disintegration time was found with the additional experiments and the agreement between observed and predicted values was fair for the tablets that did disintegrate. A limitation of this study was that tablets from four experiments did not disintegrate within the set time limit. The lack of agreement between observed and predicted values of these four experiments was probably due to the nature of one of the factors in the design. Considering the reduced experimental design the results are still encouraging.     

A note on the divergence problem arising in calculation of Green’s function for a 2D piezoelectric thin film strip containing straight line defects and free boundaries: Fourier approach for bodies of unrestricted anisotropy

In this paper we derive a set of novel formulas for computation of the Green’s function and the coupled electro-elastic fields in a 2D piezoelectric strip with free boundaries and containing a distribution of straight line defects. The strip is assumed to be of unrestricted anisotropy, but allowing piezoelectricity, and in this sense situation is more general than in the available literature where only cubic symmetry was investigated. We employ a set of already known analytic formulas for the Fourier amplitude of the Green’s function and the corresponding electro-elastic fields. The key novelty of this paper is solution for the divergence problem occurring during integration of the Fourier amplitude. This problem is caused by poles at k = 0 in various matrix components of the amplitude. From purely mathematical point of view such poles lead to quantities which do not tend to zero at infinity, and this situation is clearly unphysical. To resolve this issue it is demonstrated by means of rigorous analysis that when some additional physical conditions are imposed, physical fields exhibit regular behavior at infinity - the poles do not contribute. Nevertheless, they lead to irremovable numerical ∞ − ∞ uncertainties spreading over the whole domain of integration. This motivates us to compute exact formulas for all these poles to enable engineering calculations involving the system in question.     

A note on the divergence problem arising in calculation of Green’s function for a 2D piezoelectric thin film strip with free boundaries and containing straight line defects: Fourier approach for bodies of cubic symmetry

Analytic formulas for the Green’s function and the coupled electro-elastic fields for a 2D piezoelectric strip with free boundaries and containing a distribution of straight line defects have already been found some years ago. These formulas exploit the well-known Stroh formalism and the Fourier approach, so the result is given as the Fourier integral and therefore its numerical implementation should pose no problem. However, in this note we show that for the case of cubic symmetry this form of the Green’s function contains strong divergences, excluding possibilities of direct application of well-known numerical schemes. It is also shown that these divergences translate to divergences of the corresponding electro-elastic fields of a single defect. By means of a rigorous analysis it is demonstrated that imposing physical conditions implied by the nature of the problem all of these divergences cancel and the final, physical result exhibits expected, regular behavior at infinity. Unfortunately, although the nature of this problem is purely mathematical, it leads to irremovable numerical ∞ − ∞ uncertainties which tend to spread over the whole Fourier domain and severely impede engineering applications of the Green’s function. This motivates us to compute the exact form of all divergent terms. These novel formulas will serve as a guide when establishing numerically stable algorithms for engineering computations involving the system in question.