Repdigits as sums of three Pell numbers

In this paper, all base 10 repdigits expressible as sums of three Pell numbers are found.     

An analytic approach to the ergodic theory of a stochastic variational inequality

In an earlier work made by the first author with J. Turi (Degenerate Dirichlet Problems Related to the Invariant Measure of Elasto-Plastic Oscillators, AMO, 2008), the solution of a stochastic variational inequality modeling an elasto-perfectly-plastic oscillator has been studied. The existence and uniqueness of an invariant measure have been proven. Nonlocal problems have been introduced in this context. In this work, we present a new characterization of the invariant measure. The key finding is the connection between nonlocal PDEs and local PDEs which can be interpreted with short cycles of the Markov process solution of the stochastic variational inequality.     

Synthesis and biological evaluation of 3-aryltyramines as fragments binding to BACE-1 and BACE-2

3-Aryltyramines were prepared in one single step from tyramine and various arenediazonium salts by radical arylation. Binding as well as enzyme inhibition data of the 14 compounds do not prove true interaction with BACE-1. In contrast, with BACE-2 inhibition and binding could be confirmed indicating that 3-aryltyramines are potential starting points for a drug discovery effort.     

MRI investigation of granular interface rheology using a new cylinder shear apparatus

The rheology of granular materials near an interface is investigated through proton magnetic resonance imaging. A new cylinder shear apparatus has been inserted in the magnetic resonance imaging device, which allows the control of the radial confining pressure exerted by the outer wall on the grains and the measurement of the torque on the inner shearing cylinder. A multi-layer velocimetry sequence has been developed for the simultaneous measurement of velocity profiles in different sample zones, while the measurement of the solid fraction profile is based on static imaging of the sample. This study describes the influence of the roughness of the shearing interface and of the transverse confining walls on the granular interface rheology.