Note on a conjecture of toft

A conjecture of Toft [17] asserts that any 4-critical graph (or equivalently, every 4-chromatic graph) contains a fully odd subdivision ofK ₄. We show that if a graphG has a degree three nodev such thatG-v is 3-colourable, then eitherG is 3-colourable or it contains a fully oddK ₄. This resolves Toft's conjecture in the special case where a 4-critical graph has a degree three node, which is in turn used to prove the conjecture for line-graphs. The proof is constructive and yields a polynomial algorithm which given a 3-degenerate graph either finds a 3-colouring or exhibits a subgraph that is a fully odd subdivision ofK ₄. (A graph is 3-degenerate if every subgraph has some node of degree at most three.)     

New methods for proving the existence and stability of periodic solutions in singularly perturbed delay systems

We carry out a detailed analysis of the existence, asymptotics, and stability problems for periodic solutions that bifurcate from the zero equilibrium state in systems with large delay. The account is based on a specific meaningful example given by a certain scalar nonlinear second-order differential-difference equation that is a mathematical model of a single-circuit RCL oscillator with delay in a feedback loop.     

The effect of the external lateral electric field on the luminescence intensity of InAs/GaAs quantum dots

We report on low-temperature microphotoluminescence (μ-PL) measurements of InAs/GaAs quantum dots (QDs) exposed to a lateral external electric field. It is demonstrated that the QDs’ PL signal could be increased severalfold by altering the external and/or the internal electric field, which could be changed by an additional infrared laser. A model which accounts for a substantially faster lateral transport of the photoexcited carriers achieved in an external electric field is employed to explain the observed effects. The results obtained suggest that the lateral electric fields play a major role for the dot luminescence intensity measured in our experiment—a finding which could be used to tailor the properties of QD-based optoelectronic applications. The text was submitted by the authors in English.     

First Results of Ion Trapping in the Dresden EBIT II

Hyperfine Interactions - It is well known that many reinforced concrete structures are at risk of deterioration due to chloride ion contamination of the concrete or atmospheric carbon dioxide...     

Common luminescence intensity fluctuations of single particle and single molecules in non-conducing matrices

Optical spectroscopy in combination with wide field or confocal optical microscopy enables the investigation of single quantum objects such as organic molecules, II/VI semiconductor quantum dots and silicon nanocrystals. They all have fluctuations of luminescence intensities on time scales longer than μs in common. A comparison reveals that despite the large differences of the nature of the respective quantum objects, the intensity fluctuations are related to a slow ionisation process followed by a trapping of the photoejected charge in the non-conducing environment. Detailed aspects of the dynamics are controlled by the dielectric properties of the matrix.     

Studies on Rare-Earth/Iron and Actinide/Iron Multilayers

Hyperfine Interactions - Multilayers of Ce/Fe and U/Fe were fabricated by sputtering and studied by X-ray diffraction and reflectivity, Mössbauer spectroscopy and polarised neutron...