Two-dimensional gratings-based phase-contrast imaging using a conventional x-ray tube

A Talbot-Lau interferometer using two-dimensional gratings and a conventional x-ray tube has been used to investigate a phase-contrast imaging technique that is sensitive to phase gradients in two orthogonal directions. Fourier analysis of Moiré fringe patterns was introduced to obtain differential phase images and scattering images from a single exposure. Two-dimensional structures of plastic phantoms and characteristic features of soft tissue were clearly obtained at 17.5 keV. The phase-stepping technique was also examined to investigate the spatial resolution of different phase retrieval methods. In the presented setup we found that the choice of phase retrieval method made little difference in image blur, and a large effective source size was found to give a high intensity in the image plane.     

Semilinear hyperbolic systems violating the null condition

We consider systems of semilinear wave equations in three space dimensions with quadratic nonlinear terms not satisfying the null condition. We prove small data global existence of the classical solution under a new structural condition related to the weak null condition. For two-component systems satisfying this condition, we also observe a new kind of asymptotic behavior: Only one component is dissipated and the other one behaves like a non-trivial free solution in the large time.     

Iron-Catalyzed Biomimetic Dimerization of Tryptophan-Containing Peptides

Biomimetic oxidative dimerization of tryptophan derivatives in aqueous media with oxygen as a bulk oxidant catalyzed by an iron octacarboxy phthalocyanine complex was established. The discovery of the extremely active iron catalyst enables aerobic enzyme-mimetic oxidation to be performed in a flask. This method was applicable to the oxidative dimerization of a wide range of tryptophan derivatives, including various dipeptides and oligopeptides, with remarkable functional-group tolerance without the protection of the amino acid residues. Furthermore, oxidative dimerization of tryptophan derivatives bearing dioxopiperazine units enabled the convergent total synthesis of five natural pyrroloindole compounds and unnatural congeners. The established chemical method provides facile access to a broad range of dimerized peptides with a unique scaffold to link two turn structures, which will serve as a powerful tool to create new small- and medium-sized-molecules as drug candidates.