Non-separating 2-factors of an even-regular graph

For a 2-factor F of a connected graph G, we consider G−F, which is the graph obtained from G by removing all the edges of F. If G−F is connected, F is said to be a non-separating 2-factor. In this paper we study a sufficient condition for a 2r-regular connected graph G to have such a 2-factor. As a result, we show that a 2r-regular connected graph G has a non-separating 2-factor whenever the number of vertices of G does not exceed 2r²+r.     

Three-dimensional dynamic optical manipulation by combining a diffractive optical element and a spatial light modulator

Since the introduction of computer-controlled spatial light modulators (SLMs), holographic optical tweezers have become an important tool for dynamic parallel optical manipulation. In this paper we clarify the usefulness of a new configuration for optical trapping that creates light patterns using the combination of a diffractive optical element (DOE) and an SLM. This configuration not only enables the use of the higher part of the SLM’s diffraction efficiency curve, because a simple hologram can be chosen for the SLM, but also achieves three-dimensional dynamic optical manipulation over a large spatial range. By switching blaze-like holograms displayed on the SLM, we demonstrated simultaneous transportation of three 6-μm-diameter polystyrene beads over a range of 90 μm in the vertical direction and 37.5 μm in the horizontal direction. Compared with the same manipulation executed using only the SLM, the range of this method is extended four-fold in the vertical direction and three-fold in the horizontal direction.     

Inorganic–Organic Hybrid Nanoparticles with Biocompatible Calcium Phosphate Thin Shells for Fluorescence Enhancement

Polymeric micelles consisting of asymmetric triblock copolymers were successfully used for fabrication of robust hybrid nanoparticles with highly biocompatible calcium phosphate shells. The hydrophobic polystyrene core encapsulates hydrophobic fluorescent dyes such as Nile red. The anionic polyacrylic acid provides the site for the mineralization reaction of calcium phosphate. The polyethylene glycol corona stabilizes the hybrid nanoparticles. Fluorescent dyes can be used as imaging agents for determining the location of the nanoparticles and to give an observable indication of drug delivery, while the calcium phosphate shell can enhance the fluorescence of the encapsulated dye.     

Highly enantioselective synthesis of α-(perfluoroalkyl)amines via hydrogenation of enamide precursors in the presence of chiraphos-rhodium catalyst

Highly (up to 99% ee) enantio-enriched perfluoroalkyl amines can be synthesized by the perfluoroalkylation of nitriles with Lewis acidic perfluoroalkyl titanate reagents and catalytic asymmetric hydrogenation with the chiraphos-Rh catalyst of the resultant perfluoroalkyl enamides via base-mediated tautomerization.