Classification of 3-dimensional integrable scalar discrete equations

We classify all integrable 3-dimensional scalar discrete quasilinear equations Q=0 on an elementary cubic cell of the 3-dimensional lattice. An equation Q=0 is called integrable if it may be consistently imposed on all 3-dimensional elementary faces of the 4-dimensional lattice. Under the natural requirement of invariance of the equation under the action of the complete group of symmetries of the cube we prove that the only nontrivial (non-linearizable) integrable equation from this class is the well-known dBKP-system. (Version 2: A small correction in Table 1 (p.7) for n=2 has been made.) (Version 3: A few small corrections: one more reference added, the main statement stated more explicitly.)Comment: 20 p. LaTeX + 1 EPS figur

Two-dimensional von Neumann--Wigner potentials with a multiple positive eigenvalue

International audienceBy the Moutard transformation method we construct two-dimensional Schrodinger operators with real smooth potential decaying at infinity and with a multiple positive eigenvalue. These potentials are rational functions of spatial variables and their sines and cosines

Stabilizing perovskite solar cells with modified indium oxide electron transport layer

Despite the impressive progress, the perovskite solar cells are still under the stage of laboratory research, mainly because of their inferior operational stability. To improve the device lifetime, one of the most important strategies is to eliminate the undesirable side reactions between the functional layers. In this study, we present the thermal oxidation method to yield high-quality pristine and modified indium oxide films applied as efficient electron transport layers (ETLs) for perovskite cells in a planar n-i-p configuration. The cells incorporating In2O3 as ETL material can deliver comparable efficiencies with the reference SnO2- based devices while showing much superior operational stability. We attributed the observed stabilizing effect of indium oxide to its reduced chemical activity at the interface with the perovskite absorber layer. In particular, In2O3 can hardly oxidize I- to molecular iodine on the contrary to SnO2 and TiO2 known for their photocatalytic activity. We believe that this study may provide researchers with general guidelines to develop a large variety of ETL materials for efficient yet stable perovskite cells