Evaluating the Frechet derivative of the matrix exponential

LetM _n denote the space ofn×n matrices. GivenX, ZM _n define

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Influence of substitutions on asymmetric dihydroxychlorins with regard to intracellular uptake, subcellular localization and photosensitization of Jurkat cells

The search for new efficient sensitizers for photodynamic therapy (PDT) points to improve photophysical properties like absorption in the red region and singlet oxygen quantum yield as well as to control the localization of the sensitizer within the tumour cell. Depending on their physicochemical properties and their uptake mechanism, sensitizers can reach different intracellular concentrations and localize in different subcellular compartments. Moreover, the preferential localization of a sensitizer in target organelles, like mitochondria or lysosomes, could determine the cell death mechanism after PDT. This study aimed to investigate the influence of substitutions on dihydroxychlorins with regard to intracellular uptake, subcellular localization and cell death pathway. Moreover, the effect of a liposome-based delivery system was tested. The intracellular uptake was found to be strictly dependent on the sensitizer molecular structure and the means of its delivery. The most polar sensitizer in this study (compound 3) had, depending on incubation time, an intracellular concentration 2-8 times higher than the unsubstituted chlorin 1. All investigated photosensitizers localize predominantly in lysosomes but after longer incubation times weak fluorescence intensity was also detected in mitochondria and Golgi apparatus. The cell death pathway was found to be influenced by the sensitizer intracellular concentration and the applied light doses. In general, the increasing amphiphilicity of the sensitizer molecules is correlated with an increased sensitizer uptake and an increased rate of necrotic cells after irradiation.     

Synthesis of linear and starlike polymers from poly(propylene glycol) methacrylate using controlled radical polymerization

The copper‐catalyzed atom transfer radical polymerization (ATRP) of poly(propylene glycol) methacrylate (PPGM) in solution to produce linear and starlike polymers is reported, using methylethyl ketone as the solvent and a temperature of 80 °C. The ATRP system used was efficient for polymerization of the functionalized monomer without protecting hydroxyl end groups of monomer. The polymerizations were consistent with “living” or controlled processes, as revealed by the linear evolution of molecular weight with conversion. Increasing the [M]₀:[I]₀ ratio resulted in increasing molecular weights, whereas the polydispersity indices remained low (M_w/M_n < 1.4) even at high conversion. Decreasing the [CuBr]₀:[I]₀ ratio resulted in lower conversions, slightly larger polydispersities, and decreased molecular weights, likely resulting from a lower initiation efficiency. Polymers were characterized by ¹H and ¹³C NMR; molecular weights of polymers with low degrees of polymerization were estimated by end‐group analysis from ¹³C NMR spectra obtained using distortionless enhancement by polarization transfer and the gated decoupling techniques. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 40: 334–343, 2002     

Photoelectron spectroscopy of fullerene dianions C76(2-), C78(2-), and C84(2-)

We report laser photoelectron spectra of the doubly negatively charged fullerenes C(76) (2-), C(78) (2-), and C(84) (2-) at 2.33, 3.49, and 4.66 eV photon energy. From these spectra, second electron affinities and vertical detachment energies, as well as estimates for the repulsive Coulomb barriers are obtained. These results are discussed in the context of electrostatic models. They reveal that fullerenes are similar to conducting spheres, with electronic properties scaling with their size. The experimental spectra are compared with the accessible excited states of the respective singly charged product ions calculated in the framework of time dependent density functional theory.     

Splitting‐characterizations of the Papangelou process

For point processes we establish a link between integration‐by‐parts‐ and splitting‐formulas which can also be considered as integration‐by‐parts‐formulas of a new type. First we characterize finite Papangelou processes in terms of their splitting kernels. The main part then consists in extending these results to the case of infinitely extended Papangelou and, in particular, Pólya and Gibbs processes.