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).     

Analytical evaluation of three-center nuclear-attraction integrals over s-Slater orbitals for asymmetrical conformations of the centers

Analytical formulas for three-center nuclear-attraction integrals over Slater orbitals are given for any location of the three atomic centers. In the mathematical derivations the Neumann expansion has been used and new general auxiliary integrals which depend on the elliptical coordinates of one of the centers are defined. The orbital exponents within the integrals may be different.     

A new specifically designed calix[8]arene for the synthesis of functionalized, nanometric and subnanometric Pd, Pt and Ru nanoparticles

A new thioester functionalized calix[8]arene derivative is used for the synthesis of metallic Pd, Pt and Ru nanoparticles, exhibiting several interesting features such as stability and remarkable surface functionalization. Crystalline particles of very small dimensions and good dispersion have been obtained.