Partial Ovoids in Classical Finite Polar Spaces

Ovoids in finite polar spaces are related to many other objects in finite geometries. In this article, we prove some new upper bounds for the size of partial ovoids in Q ^–(2n+1,q) and W(2n+ 1,q). Further, we give a combinatorial proof for the non-existence of ovoids of H(2n +1,q ²) for n>q ³.     

Poly(dimethylaminoethylmethacrylate) hydrochloride (PDMAEM-HCl) a well behaving polycation for multilayer formation on planar surfaces

The polycation preparation of poly(dimethylaminoethylmethacrylate) hydrochloride and the multilayer formation in combination with poly(sodium 4-styrenesulphonate) as polyanion studies onto different substrates, as followed by streaming potential measurements, in situ surface plasmon resonance spectroscopy, and multi-wavelength ellipsometry, are reported. Furthermore, we studied the resulting multilayer buildup of dry surfaces by UV-Vis spectroscopy, X-ray photoelectron spectroscopy, and atomic force microscopy measurements. Thereby, the layer built up at the solid/liquid-interface could be followed and quantified at the molecular level.This revised version was published online in April 2005 with corrections to the article category.     

First carbohydrate liquid crystals of columnar structure

S, S-Dialkylacetals of aldoses, tripodal in structure and recently synthesized in large numbers by three groups, do not exhibit thermotropically a smectic, but a columnar hexagonal mesophase (Hx) as we have proved by X-ray diffraction. The molecular organization in this mesophase is comparable with a similar one known for phasmidic molecules. These various multiols, although different in stereo-chemistry, form only one type of hydrogen-bonded disc-shaped multimer. Its mesophase structure is made up of about five molecules placed in columns with a skeleton of hydrogen-bridged sugar parts surrounded by thioalkyl groups in the periphery. Since three 6-deoxy sugar dithioacetals were shown to be non-thermomesomorphic the terminal hydroxyl function is essential for this molecular arrangement which seems not to be true for missing ones in the inner part of a sugar chain, as we have found in one case.     

Transport properties of a lateral semiconductor quantum dot defined by a single connected metallic front-gate

We present studies on the electric transport in a lateral GaAs/AlGaAs quantum dot defined by a patterned single connected metallic front-gate. This gate design allows to easily couple a large number of quantum dots and therefore holds high potential in the design of new materials with tailor-made band structures based on quantum dot superlattices of controlled shape. Clear Coulomb diamond structures and well pronounced tunneling peaks observed in experiment indicate that single-electron control has been achieved. However, the dependence on electron density in the heterostructure embedding the dot, which is controlled by an additional back-gate, reveals that transport characteristics are strongly influenced supposedly by potential fluctuations in the dot and lead regions.     

On the Dynamics of the Classical Transverse Field Ising Chain

We investigate stationary and travelling wave solutions of a special lattice differential equation in one space dimension. Depending on a parameter λ, results are given on the existence, shape and stability for these kind of solutions. The analysis of travelling wave solutions leads us to a functional differential equation with both forward and backward shifts. The existence of solutions of this equation will be proved by use of the implicit function theorem. In particular, we consider kink solutions and periodic solutions.     

The homotopy limit problem for two-primary algebraic K-theory

We solve the homotopy limit problem for two-primary algebraic K-theory of fields, that is, the Quillen-Lichtenbaum conjecture at the prime 2.