A Comparison of Two Variational Methods

A discussion is given of the relation between the maximum functionaltheorem and Schwinger's variational principle, and it is shownthat the bound given by Schwinger's principle is better thanor the same as that given by the maximum functional theorem.     

Further Gurtin-type Variational Principles for Linear Initial Value Problems

Following the variational principles for linear initial valueproblems associated with the wave and heat conduction equationsdiscussed by Gurtin and Leitmann and using time convolutionsit is shown that general variational principles exist for theseproblems with sources on the boundaries and within the regionunder consideration.     

Modified Locally One Dimensional Methods for Parabolic Partial Differential Equations in Two Space Variables

In this note we consider the locally one dimensional methodas discussed in Gourlay & Mitchell (1969, 1972) and indicatehow this scheme can be used to solve accurately a parabolicpartial differential equation in two space variables.     

Methylene blue-containing silica-coated magnetic particles: a potential magnetic carrier for photodynamic therapy

We present the preparation and characterization of methylene blue-containing silica-coated magnetic particles. The entrapment of methylene blue (MB), a photodynamic therapy drug under study in our group, in the silica matrix took place during the growth of a silica layer over a magnetic core composed of magnetite nanoparticles. The resulting material was characterized by transmission electron microscopy (TEM), light scattering, and X-ray diffraction. It is composed of approximately 30 nm silica spheres containing magnetic particles of 11 +/- 2 nm and methylene blue entrapped in the silica matrix. The immobilized drug can generate singlet oxygen, which was detected by its characteristic phosphorescence decay curve in the near-infrared and by a chemical method using 1,3-diphenylisobenzofuran to trap singlet oxygen. The lifetime of singlet oxygen was determined to be 52 micros (in acetonitrile) and 3 micros (in water), with both values being in good agreement with those in the literature. The release of singlet oxygen (etaDelta) was affected by the encapsulation of MB in the silica matrix, which caused a reduction to 6% of the quantum yield of MB free in solution. The magnetization curve confirmed the superparamagnetic behavior with a reduced saturation magnetization in respect to uncoated magnetic nanoparticles, which is consistent with the presence of a diamagnetic component over the magnetite surface. The result is a single particle platform that combines therapy (photosensitizer) and diagnostic (MRI contrast agent) possibilities at the same time, as well as drug targeting.