R-matrix for a geodesic flow associated with a new integrable peakon equation

We use the r-matrix formulation to show the integrability of geodesic flow on an $N$-dimensional space with coordinates $q_k$, with $k=1,...,N$, equipped with the co-metric $g^{ij}=e^{-|q_i-q_j|}\big(2-e^{-|q_i-q_j|}\big)$. This flow is generated by a symmetry of the integrable partial differential equation (pde) $m_t+um_x+3mu_x=0, m=u-\alpha^2u_{xx}$ (\al is a constant). This equation -- called the Degasperis-Procesi (DP) equation -- was recently proven to be completely integrable and possess peakon solutions by Degasperis, Holm and Hone (DHH[2002]). The isospectral eigenvalue problem associated with the integrable DP equation is used to find a new $L$-matrix, called the Lax matrix, for the geodesic dynamical flow. By employing this Lax matrix we obtain the $r$-matrix for the integrable geodesic flow.Comment: This paper has some crucial technical errors in $r$-matrix formula derivatio

Skin impedance models for transdermal drug delivery

In this paper, a study based on the different models of the skin impedance is carried out. The purpose is to examine the drug delivery method through iontophoresis, which relies on active transportation of the charged medication agent within an electric field. It is a kind of transdermal drug delivery method, and hence the method has to handle the variability in skin characteristics of a patient. This paper carries out a simulation study based on three different skin impedance models. ©2009 IEEE.published_or_final_versio