A variational approach to define robustness for parametric multiobjective optimization problems

In contrast to classical optimization problems, in multiobjective optimization several objective functions are considered at the same time. For these problems, the solution is not a single optimum but a set of optimal compromises, the so-called Pareto set. In this work, we consider multiobjective optimization problems that additionally depend on an external parameter ${\lambda \in \mathbb{R}}$ , so-called parametric multiobjective optimization problems. The solution of such a problem is given by the λ-dependent Pareto set. In this work we give a new definition that allows to characterize λ-robust Pareto points, meaning points which hardly vary under the variation of the parameter λ. To describe this task mathematically, we make use of the classical calculus of variations. A system of differential algebraic equations will turn out to describe λ-robust solutions. For the numerical solution of these equations concepts of the discrete calculus of variations are used. The new robustness concept is illustrated by numerical examples.     

Trapping of a Highly Reactive Oxoiron(IV) Complex in the Catalytic Epoxidation of Olefins by Hydrogen Peroxide

The generation of a nonheme oxoiron(IV) intermediate, [(cyclam)Fe^IV(O)(CH₃CN)]²⁺ ( 2 ; cyclam=1,4,8,11‐tetraazacyclotetradecane), is reported in the reactions of [(cyclam)Fe^II]²⁺ with aqueous hydrogen peroxide (H₂O₂) or a soluble iodosylbenzene (sPhIO) as a rare example of an oxoiron(IV) species that shows a preference for epoxidation over allylic oxidation in the oxidation of cyclohexene. Complex 2 is kinetically and catalytically competent to perform the epoxidation of olefins with high stereo‐ and regioselectivity. More importantly, 2 is likely to be the reactive intermediate involved in the catalytic epoxidation of olefins by [(cyclam)Fe^II]²⁺ and H₂O₂. In spite of the predominance of the oxoiron(IV) cores in biology, the present study is a rare example of high‐yield isolation and spectroscopic characterization of a catalytically relevant oxoiron(IV) intermediate in chemical oxidation reactions.     

Switching from "absorption within transparency" to "transparency within transparency" in an electromagnetically induced absorption dominated transition

The absorption of a resonant coupling laser driving a closed degenerate two-level system in an atomic cesium beam was investigated as a function of the detuning of a second laser probing the same transition. The measurements were performed for four different polarization combinations of the two laser beams. Except for the beams of counterrotating polarizations all coupling-laser absorption profiles showed "absorption within transparency," i.e., the absorption in the region around the two-photon resonance was smaller than the absorption corresponding to the one-photon transition induced by the coupling laser, and an extra absorption peak was observed on this curve at the two-photon resonance. With regard to the beams of counterrotating polarizations we observed a switch from absorption within transparency to "transparency within transparency" when the probe-laser power exceeded the constant coupling-laser power. In other words, the cesium ensemble became mostly transparent to the coupling-laser beam at the two-photon resonance.     

Isometric embeddings into Heisenberg groups

We study isometric embeddings of a Euclidean space or a Heisenberg group into a higher dimensional Heisenberg group, where both the source and target space are equipped with an arbitrary left-invariant homogeneous distance that is not necessarily sub-Riemannian. We show that if all infinite geodesics in the target are straight lines, then such an embedding must be a homogeneous homomorphism. We discuss a necessary and certain sufficient conditions for the target space to have this ‘geodesic linearity property’, and we provide various examples.     

Recent developments and challenges of biocatalytic processes in the pharmaceutical industry

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Phenanthrene-fused boron-dipyrromethenes as bright long-wavelength fluorophores

A new class of boron-dipyrromethene (BDP or BODIPY) dyes was obtained by phenanthrene fusion to the beta-pyrrole positions, absorbing in the wavelength range of important laser sources. Despite a 'propeller-like' distorted structure in the crystalline state, the chromophore absorbs (log epsilon > or = 5) and fluoresces (Phif > or = 0.8) strongly and can be easily turned into a fluorescence light-up probe. Incorporation into latex beads produces bright and photostable single-dye and F?rster Resonance Energy Transfer (FRET) particles for microscopy applications.     

Cymantrene conjugation modulates the intracellular distribution and induces high cytotoxicity of a cell-penetrating peptide

The conjugation of cymantrene CpMn(CO)(3) to cell-penetrating peptide hCT(18-32)-k7 alters the intracellular distribution in MCF-7 cells compared to the unmodified peptide, as visualized by fluorescence microscopy, and leads to an increased nuclear accumulation; the peptide and cymantrene compound themselves are not toxic, but the bioconjugate shows a significant cytotoxicity with an IC(50) value of 36 micromol l(-1).     

Synthesis of 6H-indolo[2,3-b]quinoxaline-N-glycosides and their cytotoxic activity against human ceratinocytes (HaCaT)

N-glycosides of 6H-indolo[2,3-b]quinoxalines were prepared and structurally characterized. The synthesis relies on the cyclocondensation of isatine-N-glycosides with 1,2-diaminobenzenes. Some products exhibit weak cytotoxic activity against human ceratinocytes (HaCaT).