On two-dimensional parametric variational problems

Let be a two-dimensional parametric variational integral the Lagrangian F(x,z) of which is positive definite and elliptic, and suppose that is a closed rectifiable Jordan curve in . We then prove that there is a conformally parametrized minimizer of in the class of surfaces of the type of the disk B which are bounded by . An immediate consequence of this theorem is that the Dirichlet integral and the area functional have the same infima, a result whose proof usually requires a Lichtenstein-type mapping theorem or else Morrey's lemma on -conformal mappings. In addition we show that the minimizer of is H?lder continuous in B, and even in if satisfies a chord-arc condition. In Section 1 it is described how our results are related to classical investigations, in particular to the work of Morrey. Without difficulty our approach can be carried over to two-dimensional surfaces of codimension greater than one. Received July 20, 1998 / Accepted October 23, 1998     

Photodynamic effects induced by meso-tetrakis[4-(carboxymethyleneoxy)phenyl] porphyrin on isolated Sarcoma 180 ascites mitochondria.

Using mitochondria isolated from Sarcoma 180 ascites tumour in Swiss mice as a model system, we have evaluated the ability of a novel porphyrin, meso-tetrakis[4-(carboxymethyleneoxy)phenyl]porphyrin (H₂T4CPP), to induce damage on photosensitization. Oxidative damage to mitochondria, one of the primary and crucial targets of the photodynamic effect, is assessed by measuring products of lipid peroxidation such as thiobarbituric acid reactive substances (TBARS) and lipid hydroperoxides (LOOH), besides the loss of activity of the mitochondrial marker enzyme succinate dehydrogenase (SDH). Analysis of product formation, the effect of deuteration and selective inhibition by scavengers of reactive oxygen species (ROS) show that the damage observed is due mainly to singlet oxygen (¹O₂) and to a minor extent to hydroxyl radicals (^•OH). The ¹O₂ generation and triplet lifetime of this porphyrin have also been estimated. Fluorescence spectroscopy, used to ascertain the binding of this porphyrin to the mitochondrial proteins, shows a rapid association within 0–2 h and a decline thereafter. Confocal microscopy reveals intracellular localisation of this porphyrin in cells in vitro. Our overall results suggest that the porphyrin H₂T4CPP, due to its ability to bind to mitochondrial protein components and to generate ROS upon photoexcitation, may have potential applications in photodynamic therapy.     

Topological Links between Duplex DNA and a Circular DNA Single Strand

DNA nanostructures of building blocks topologically linked at a precise position can be assembled from DNA duplexes and circularized oligonucleotides with the aid of peptide nucleic acids (PNAs). Shown schematically is a linked catenane yielding an earring topological DNA label.     

Automatic parameterization of force fields for liquids by simplex optimization

In this study we demonstrate an automatic method of force field development for molecular simulations. Parameter tuning is taken as an optimization problem in many dimensions. The parameters are automatically adapted to reproduce known experimental data such as the density and the heat of vaporization. Our method is more systematic than guessing parameters and, at the same time, saves human labor in parameterization. It was applied successfully to several molecular liquids. As a test, force fields for 2-methylpentane, tetrahydrofurane, cyclohexene, and cyclohexane were developed. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1009–1017, 1999     

A model of breast carcinogenesis and recurrence after radiotherapy

Breast conserving surgery and adjuvant radiotherapy are the standard treatment of early stage breast cancer. We present simulations of a mathematical model of breast carcinogenesis and identify fields of mutated cells in the breast (formed during puberty or pregnancy) as a potential source of local recurrence after treatment with radiotherapy. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The smoothed number of Pareto-optimal solutions in bicriteria integer optimization

Mathematical Programming - A well-established heuristic approach for solving bicriteria optimization problems is to enumerate the set of Pareto-optimal solutions. The heuristics following this...