Towards peptide-substituted titanocene anticancer drugs

An alkyne-substituted fulvene was transformed via hydridolithiation followed by transmetallation with titanium tetrachloride into bis-[p-(prop-2-ynyloxy)-benzyl-cyclopentadienyl] titanium(IV) dichloride. Single crystals of this titanocene derivative could be obtained and the structure determined by X-ray diffraction. It showed that this compound crystallises in the space group C2/c with four molecules in the monoclinic cell. The alkyne-substituted titanocene dichloride derivative was then subject to a copper-catalysed azide-alkyne cycloaddition with its azide-functionalised methylester-protected phenylalanine reaction partner in order to form a linking triazole. This reaction was performed under anhydrous conditions employing a dichloromethane/acetonitrile solvent mixture with copper(I) iodide and 2,6-lutidine as the catalyst system. Under these conditions the adduct between the protein mimic and the titanocene was formed without hydrolysing the titanium dichloride moiety.     

Non-Algebraic Quadrature Domains

It is well known that, in the plane, the boundary of any quadrature domain (in the classical sense) coincides with the zero set of a polynomial. We show, by explicitly constructing some four-dimensional examples, that this is not always the case. This confirms, in dimension 4, a conjecture of the second author. Our method is based on the Schwarz potential and involves elliptic integrals of the third kind.     

A nonlinear superposition principle and multibump solutions of periodic Schrödinger equations

In an abstract setting we prove a nonlinear superposition principle for zeros of equivariant vector fields that are asymptotically additive in a well-defined sense. This result is used to obtain multibump solutions for two basic types of periodic stationary Schrödinger equations with superlinear nonlinearity. The nonlinear term may be of convolution type. If the superquadratic term in the energy functional is convex, our results also apply in certain cases if 0 is in a gap of the spectrum of the Schrödinger operator.     

Light extraction via leaky modes in organic light emitting devices

Display and illumination technology require light sources with angular independent emission behaviour. Conversely, a strongly angular dependent spectral emission can be desirable for other applications in information technology or spectroscopy. In order to elucidate the potential of organic light-emitting devices (OLEDs) for the latter fields, we performed experimental and numerical studies of the angular dependent emission characteristics of cavity like OLEDs. The light generated in the organic multilayer structure and guided in leaky modes was coupled out by a prism. Here, a semitransparent gold anode, acting as a hole injection layer, was used to enhance the coupling of leaky modes guided inside the OLED to external modes (Kretschmann configuration). The observed light emission was strongly angle dependent, with the spectral emission peak of the device shifting from a wavelength of 680 nm to 500 nm as the angle is varied between 20° and 70° with respect to the normal of the substrate plane. Also, the emitted light shows a high degree of polarization. The observed behaviour can be predicted quantitatively by simulations, which are based on the transfer matrix formalism.     

Vertex Algebras, Lie Algebras, and Superstrings

We construct Lie algebras from vertex superalgebras and study their structure. They are sometimes generalized Kac–Moody algebras. In some special cases we can calculate the multiplicities of the roots.     

On real Paley-Wiener theorems for certain integral transforms

We prove real Paley-Wiener theorems for the (inverse) Jacobi transform, characterising the space of L²-functions whose image under the Jacobi transform are (smooth) functions with compact support.