Zeta functions of a class of elliptic curves over a rational function field of characteristic two

We show how to calculate the zeta functions and the orders of Tate-Shafarevich groups of the elliptic curves with equation over the rational function field , where is a power of 2. In the range , , odd of degree , the largest values obtained for are (one case), (one case) and (three cases). We observe and discuss a remarkable pattern for the distributions of signs in the functional equation and of fudge factors at places of bad reduction. These imply strong restrictions on the precise form of the Langlands correspondence for GL over local or global fields of characteristic two.

     

The amyloid-beta (Abeta) peptide pattern in cerebrospinal fluid in Alzheimer's disease: evidence of a novel carboxyterminally elongated Abeta peptide

The patterns of amyloid beta (Abeta) peptides in human cerebrospinal fluid (CSF) and brain homogenates were studied by surface-enhanced laser desorption/ionization (SELDI) time-of-flight (TOF) mass spectrometry, and the results were compared with those obtained by Abeta-SDS-PAGE/immunoblot. Apart from the peptides known in the literature to occur in the CSF, we postulate the existence of a novel, previously not described peptide, either Abeta1-45 or Abeta2-46. This peptide was observed exclusively in a pool of samples originating from patients with AD, i.e. CSF and postmortem brain homogenates, but not in either the pooled CSF samples nor the pooled brain homogenates of the non-demented controls. Similarly to our previous results, Abeta1-42 was decreased in the CSF in AD. Expectedly, brain homogenates of the control subjects did not show the presence of Abeta peptides. Compared with Abeta-SDS-PAGE/immunoblot, SELDI-TOF enabled more precise analysis of Abeta peptides in the human material. We conclude that SELDI-TOF offers a promising tool for dementia expression pattern profiling using a minute amount of a biological sample.     

Phenomenological Modeling of Electrorheological Fluids with an Extended Casson-Model

In this paper we propose a phenomenological theory for electrorheological fluids. In general these are suspensions which undergo dramatic changes in their material properties if they are exposed to an electric field. In the context of continuum mechanics these fluids can be modeled as non-Newtonian fluids. Recalling the governing equations of rational thermodynamics and electrodynamics of moving media (Maxwell-Minkowski-equations), we derive suitable governing equations of electrorheology using essentially two assumptions concerning magnetic quantities. Furthermore we introduce a 3-dimensional nonlinear constitutive equation for the Cauchy stress tensor which is an extension of the model proposed by Ružička (see [14]). Assuming a viscometric flow, we compare the shear stress of our model with other well known models and fit the parameters by using measurements that were obtained in a rotational viscometer. Excellent agreement between model and measurements is achieved. On the basis of these results we propose a 3-dimensional model, the so-called extended Casson -model. This model is investigated further for a channel flow configuration with a homogeneous electric field. We determine analytical solutions for the electric field, the velocity and the volumetric flow rate and illustrate the velocity profiles and the predicted pressure drop. The velocity profiles are flattened compared to parabolic profiles and become more flat if the electric field increases. Received March 21, 2000     

On the arithmetic of some division algebras

During the preparation of the paper, the author has been supported by a Heisenberg grant of DFG.     

Mapping perception to action in piano practice: a longitudinal DC-EEG study

Background  

Performing music requires fast auditory and motor processing. Regarding professional musicians, recent brain imaging studies have demonstrated that auditory stimulation produces a co-activation of motor areas, whereas silent tapping of musical phrases evokes a co-activation in auditory regions. Whether this is obtained via a specific cerebral relay station is unclear. Furthermore, the time course of plasticity has not yet been addressed.     

Nuclear fluid dynamics

For energies where the mean free nucleon path is comparable to the nuclear size, there is no fast local relaxation in nuclear collective motion. Therefore, in a fluid-dynamical approach, the intrinsic energy-density functional must take the distortion of the local Fermi surface into account. This can be achieved by a dynamical Thomas Fermi method which leads to additional restoring forces for the collective modes, except for the casesL=0 andL=1 where usual hydrodynamics is sufficient.