Observability Inequalities by Internal Observation and Their Applications

By means of a Carleman estimate, we obtain several observability inequalities by internal observation for hyperbolic equations with lower-order terms. Also, we apply our observability results to an exact controllability problem and an inverse wave source problem.     

Covering vertices of a graph by k disjoint cycles

Let d, k and n be three integers with k3, d4k−1 and n3k. We show that if d(x)+d(y)d for each pair of nonadjacent vertices x and y of a graph G of order n, then G contains k vertex-disjoint cycles converting at least min{d,n} vertices of G.     

Sonochemical preparation of composite nanoparticles of Au/gamma-Fe2O3 and magnetic separation of glutathione

We prepared Au/gamma-Fe2O3 composite nanoparticles by sonochemically reducing Au(III) ions employing no stabilizer in the aqueous solution to form stable Au nanoparticles and allowing them to attach onto the surface of gamma-Fe2O3 particles with an average size of 21 nm. Size of the formed Au nanoparticle depended on the initial concentration of Au(III) ions. The number of the Au nanoparticles, supported on each gamma-Fe2O3 particle was controlled by changing the relative amounts of Au(III) ions and gamma-Fe2O3 particles. The composite nanoparticles exhibited a high affinity with glutathione, a tripeptide with mercapto group so that separation and manipulation of glutathione in aqueous solutions could be performed by application of external magnetic field. Because the surfaces of the Au nanoparticles were not shielded by any stabilizers, or naked, sonochemically prepared Au/gamma-Fe2O3 composite nanoparticles seemed to show stronger affinity to the glutathione than those by the radiochemical method.     

PEO-based composite lithium polymer electrolyte, PEO-BaTiO3-Li(C2F5SO2)2N

Polyethylene oxide (PEO) based polymer electrolytes with BaTiO₃ as filler and Li(C₂F₅SO₂)₂N as salt have been examined in lithium polymer batteries. The aluminum disolution potential in PEO-Li(C₂F₅SO₂)₂N was estimated to be 4.1 V vs. Li/Li⁺ at 80 °C, which was compared to that of 3.8 V vs. Li/Li⁺ in PEO-Li(CF₃SO₂)₂N. The electrical conductivity of the system was measured as a function of O/Li ratio. The highest conductivity was observed in O/Li=8. The conductivity was 1.65×10⁻³ S/cm at 80 °C and 1.5×10⁻⁵ S/cm at 25 °C. The interfacial resistance of Li/polymer electrolyte/Li annealed at 80 °C for 15 days was lower than 100 Ωcm². Paper presented at the 8th EuroConference on Ionics, Carvoeiro, Algarve, Portugal, Sept. 16 – 22, 2001.     

Achievement of a 920-MHz high resolution NMR

We have developed a 920-MHz NMR system and performed the proton NMR measurement of H(2)O and ethylbenzene using the superconducting magnet operating at 21.6 T (920 MHz for proton), which is the highest field produced by a superconducting NMR magnet in the persistent mode. From the NMR measurements, it is verified that both homogeneity and stability of the magnet have a specification sufficient for a high resolution NMR.