Ein allgemeiner Satz überW-Kongruenzen mit Anwendungen auf Laplacesche Zyklen,Biegungsflächen des einschaligen Hyperboloids und schiefe Weingartensche Systeme

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Untersuchungen über die als Gewebe bezeichneten Kurvennetze und über eine Reihe von Problemen,die mit der Verbiegung des gleichseitigen hyperbolischen Paraboloids zusammenhängen

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On computing of arbitrary positive integer powers for one type of even order symmetric anti-pentadiagonal matrices

In this paper, we derive the general expression of the lth power (l ∈ N) for one type of symmetric anti-pentadiagonal matrices of even order.     

The Ras dimer structure

Oncogenic mutated Ras is a key player in cancer, but despite intense and expensive approaches its catalytic center seems undruggable. The Ras dimer interface is a possible alternative drug target. Dimerization at the membrane affects cell growth signal transduction. In vivo studies indicate that preventing dimerization of oncogenic mutated Ras inhibits uncontrolled cell growth. Conventional computational drug-screening approaches require a precise atomic dimer model as input to successfully access drug candidates. However, the proposed dimer structural models are controversial. Here, we provide a clear-cut experimentally validated N-Ras dimer structural model. We incorporated unnatural amino acids into Ras to enable the binding of labels at multiple positions via click chemistry. This labeling allowed the determination of multiple distances of the membrane-bound Ras-dimer measured by fluorescence and electron paramagnetic resonance spectroscopy. In combination with protein–protein docking and biomolecular simulations, we identified key residues for dimerization. Site-directed mutations of these residues prevent dimer formation in our experiments, proving our dimer model to be correct. The presented dimer structure enables computational drug-screening studies exploiting the Ras dimer interface as an alternative drug target.

By combining the incorporation of unnatural amino acids, click chemistry, FRET and EPR distance measurements, protein modeling and biomolecular simulations, we obtained an unambiguous Ras dimer structural model and disrupt the dimer by mutagenesis.     

Über den wahren geometrischen Zusammenhang zwischen der Bianchischen Transformation der auf die Paraboloide abwickelbaren Flächen und der Bäcklundschen Transformation der Flächen von konstanter Krümmung

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Flächen mit Bertrandschen Kurven und pseudosphärische Flächen- und Strahlensysteme

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Formation of CdS nanoclusters in phase‐separated poly(2‐hydroxyethyl methacrylate)‐l‐polyisobutylene amphiphilic conetworks

Nanophase‐separated poly(2‐hydroxyethyl methacrylate)‐l‐polyisobutylene (PHEMA‐l‐PIB) amphiphilic conetworks were obtained by crosslinking α,ω‐bismethacrylate‐terminated polyisobutylene (PIB) via copolymerization with silylated 2‐hydroxyethyl methacylate, followed by the hydrolysis of the silylether groups. Morphology development of a sample containing 64% PIB was monitored by means of transmission electron microscopy (TEM), atomic force microscopy (AFM), and small‐angle X‐ray scattering. For comparison, the morphology of a sample containing 53% PIB was investigated by AFM. The dry conetworks exhibited hydrophilic and hydrophobic phases with average 8–10‐nm domain sizes and were swellable in water as well as in heptane. Swelling amphiphilic conetworks with aqueous cadmium–chloride solution followed by exposure to H₂S resulted in nanosized CdS clusters located in the amphiphilic conetworks, that is, for the first time, new inorganic–organic hybrid materials composed of CdS semiconducting nanocrystals and PHEMA‐l‐PIB amphiphilic conetworks were prepared. © 2001 John Wiley & Sons, Inc. J Polym Sci B Part B: Polym Phys 39: 1429–1436, 2001     

Rhodamine Spiroamides for Multicolor Single‐Molecule Switching Fluorescent Nanoscopy

The design, synthesis, and evaluation of new rhodamine spiroamides are described. These molecules have applications in optical nanoscopy based on random switching of the fluorescent single molecules. The new markers may be used in (co)localization studies of various objects and their (mutual) positions and shape can be determined with a precision of a few tens of nanometers. Multicolor staining, good photoactivation, a large number of emitted photons, and selective chemical binding with amino or thiol groups were achieved due to the presence of various functional groups on the rhodamine spiroamides. Rigidized sulfonated xanthene fragment fused with six‐membered rings, N,N′‐bis(2,2,2‐trifluoroethyl) groups, and a combination of additional double bonds and sulfonic acid groups with simple aliphatic spiroamide residue provide multicolor properties and improve performance of the rhodamine spiroamides in photoactivation and bioconjugation reactions. Having both essential parts of the photoswitchable assembly—the switching and the fluorescent (reporter) groups—combined in one chemical entity make this approach attractive for further development. A series of rhodamine spiroamides is presented along with characterizations of their most relevant properties for application as fluorescent probes in single‐molecule switching and localization microscopy. Optical images with resolutions on the nanometer scale illustrate the potential of the labels in the colocalization of biological objects and the two‐photon activation technique with optical sectioning.