Decomposability problem on branched coverings

Given a branched covering of degree d between closed surfaces, it determines a collection of partitions of d, the branch data. In this work we show that any branch data are realized by an indecomposable primitive branched covering on a connected closed surface N with chi(N) <= 0. This shows that decomposable and indecomposable realizations may coexist. Moreover, we characterize the branch data of a decomposable primitive branched covering. Bibliography: 20 titles.

A FREE BOUNDARY ISOPERIMETRIC PROBLEM IN HYPERBOLIC 3-SPACE BETWEEN PARALLEL HOROSPHERES

We investigate the isoperimetric problem of finding the regions of prescribed volume with minimal boundary area between two parallel horospheres in hyperbolic 3-space (the part of the boundary contained in the horospheres is not included). We reduce the problem to the study of rotationally invariant regions and obtain the possible isoperimetric solutions by studying the behavior of the profile curves of the rotational surfaces with constant mean curvature in hyperbolic 3-space. We also classify all the connected compact rotational surfaces M of constant mean curvature that are contained in the region between two horospheres, have boundary partial derivative M either empty or lying on the horospheres, and meet the horospheres perpendicularly along their boundary.

New classes of spatial central configurations for the n+3-body problem

In this paper, we show the existence of new families of spatial central configurations for the n + 3-body problem, n >= 3. We study spatial central configurations where n bodies are at the vertices of a regular n-gon T and the other three bodies are symmetrically located on the straight line that is perpendicular to the plane that contains T and passes through the center of T. The results have simple and analytic proofs. (c) 2010 Elsevier Ltd. All rights reserved.

Stacked central configurations for the spatial six-body problem

In this paper we show the existence of three new families of stacked spatial central configurations for the six-body problem with the following properties: four bodies are at the vertices of a regular tetrahedron and the other two bodies are on a line connecting one vertex of the tetrahedron with the center of the opposite face. (c) 2009 Elsevier B.V. All rights reserved.

The importance of protoporphyrin IX efflux for ALA-PDT dosimetry

One of the major advances in PDT is the use of 5-aminolevulinic acid (ALA) to induce the production of an enclogenous photosensitizer inside the cells using intracellular enzymatic pathways. ALA is the first intermediate in heme biosynthesis and a precursor of the protoporphyrin IX (PpIX). When activated by light, this efficient photosensitizer accumulated in the target cells can produce cytotoxicity. The aim of this study was to find the best conditions for cell killing using ALA to temporarily increase the concentration of PpIX in two cell lines. It was shown that a considerable efflux of synthesized PpIX occurs. Since this efflux is time-dependent, it is essential to know the optimum time for irradiation after ALA administration. So, the efflux of PpIX from the cells is an important parameter to be considered for ALA-PDT dosimetry.