Effect of Polymer Hydration on the Kinetic Release of Drugs: A Study of Ibuprofen and Ketoprofen in HPMC Matrices

Samples of drug/hydroxypropylmethylcellulose (HPMC) mixtures and matrices (drug/HPMC mixtures plus excipients) were allowed to equilibrate in closed chambers with defined relative humidities (RHs). Their water uptake and drug release were evaluated by differential scanning calorimetry/thermogravimetric analysis and dissolution studies, respectively. Analysis of the thermal behaviors of the drug/HPMC mixtures and of the polymer alone, as functions of RH, leads to the conclusion that most of the hydration water is retained by the polymer, and points to the occurrence of different types of hydration water, from the strongly polymer-bound water molecules at RH values up to 81%, to the almost “free water” for RH values close to 100%. In addition, application of the Korsmeyer model to the dissolution results leads to the conclusion that the rate determining dissolution processes are predominantly of the fickian type.http://www.informaworld.com/10.1081/DDC-12001820

Regularity estimates for the solution and the free boundary to the obstacle problem for the fractional Laplacian

We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem. We write an equivalent characterization as a thin obstacle problem. In this way we are able to apply local type arguments to obtain sharp regularity estimates for the solution and study the regularity of the free boundary

Decoupling of Second-Order Linear Systems by Isospectral Transformation

We consider the class of real second-order linear dynamical systems that admit real diagonal forms with the same eigenvalues and partial multiplicities. The nonzero leading coefficient is allowed to be singular, and the associated quadratic matrix polynomial is assumed to be regular. We present a method and algorithm for converting any such n-dimensional system into a set of n mutually independent second-, first-, and zeroth-order equations. The solutions of these two systems are related by a real, time-dependent, and nonlinear n-dimensional transformation. Explicit formulas for computing the 2 n× 2 n real and time-invariant equivalence transformation that enables this conversion are provided. This paper constitutes a complete solution to the problem of diagonalizing a second-order linear system while preserving its associated Jordan canonical form

A canonical form of the equation of motion of linear dynamical systems.

The equation of motion of a discrete linear system has the form of a second-order ordinary differential equation with three real and square coefficient matrices. It is shown that, for almost all linear systems, such an equation can always be converted by an invertible transformation into a canonical form specified by two diagonal coefficient matrices associated with the generalized acceleration and displacement. This canonical form of the equation of motion is unique up to an equivalence class for non-defective systems. As an important by-product, a damped linear system that possesses three symmetric and positive definite coefficients can always be recast as an undamped and decoupled system

A canonical form of the equation of motion of linear dynamical systems.

The equation of motion of a discrete linear system has the form of a second-order ordinary differential equation with three real and square coefficient matrices. It is shown that, for almost all linear systems, such an equation can always be converted by an invertible transformation into a canonical form specified by two diagonal coefficient matrices associated with the generalized acceleration and displacement. This canonical form of the equation of motion is unique up to an equivalence class for non-defective systems. As an important by-product, a damped linear system that possesses three symmetric and positive definite coefficients can always be recast as an undamped and decoupled system