Dehn filling, reducible 3-manifolds, and Klein bottles

Let be a compact, connected, orientable, irreducible 3-manifold whose boundary is a torus. We announce that if two Dehn fillings create reducible manifold and manifold containing Klein bottle, then the maximal distance is three.

     

The injected carbon impurities in intermixed GaAs/AlAs multiple quantum wells during thermal treatment

Photoluminescence (PL) measurements were performed in order to investigate the carbon impurity effects on the intermixing behavior of GaAs/AlAs multiple quantum wells (MQWs) grown by molecular beam epitaxy. The GaAs/AlAs MQWs were annealed with a carbon source in a furnace annealing system. The PL spectra show that the magnitude of the intermixing of Al and Ga induced by thermal annealing in GaAs/AlAs MQWs increases with depth. The nonuniformity of the intermixing as a function of the depth originated from the carbon impurities which were injected during thermal treatment.     

Properties of self-assembled InAs quantum dots grown by various growth techniques

The properties of self-assembled InAs quantum dots (QDs) grown by molecular beam epitaxy on GaAs substrates were investigated. The surface properties of samples were monitored by reflection high-energy electron diffraction to determine growth. Photoluminescence (PL) and transmission electron microscope (TEM) were then used to observe optical properties and the shapes of the InAs-QDs. Attempts were made to grow InAs-QDs using a variety of growth techniques, including insertion of the InGaAs strained-reducing layer (SRL) and the interruption of In flux during QD growth. The emission wavelength of InAs-QDs embedded in a pure GaAs matrix without interruption of In flux was about 1.21 μm and the aspect ratio was about 0.21. By the insertion InGaAs SRL and interruption of In flux, the emission wavelength of InAs-QDs was red shifted to 1.37 μm and the aspect ratio was 0.37. From the PL and TEM analysis, the properties of QDs were improved, particularly when interruption techniques were used.     

A sum of squares not divisible by a prime

The Ramanujan Journal - Let p be a prime. We define S(p) the smallest number k such that every positive integer is a sum of at most k squares of integers that are not divisible by p. In this...