Sharp Morawetz estimates

We prove sharp Morawetz estimates — global in time with a singular weight in the spatial variables — for the linear wave, Klein-Gordon, and Schrödinger equations, for which we can characterise the maximisers. We also prove refined inequalities with respect to the angular integrability.     

Formal (4+1) Cycloaddition and Enantioselective Michael–Henry Cascade Reactions To Synthesize Spiro[4,5]decanes and Spirooxindole Polycycles

Spiro[4,5]decanes and polycyclic compounds bearing spiro[4,5]decane systems are important biofunctional molecules. Described are diastereoselective formal (4+1) cycloaddition reactions to afford oxindole-functionalized spiro[4,5]decanes and organocatalytic enantioselective Michael–Henry cascade reactions of the (4+1) cycloaddition products to generate spirooxindole polycyclic derivatives bearing the spiro[4,5]decane system. Spiro[4,5]decanes bearing oxindoles containing three stereogenic centers and spirooxindole polycycles having seven stereogenic centers, including two all-carbon chiral quaternary centers and one tetrasubstituted chiral carbon center, were obtained with high diastereo- and enantioselectivities.     

Applications of Clifford’s Geometric Algebra

We survey the development of Clifford’s geometric algebra and some of its engineering applications during the last 15 years. Several recently developed applications and their merits are discussed in some detail. We thus hope to clearly demonstrate the benefit of developing problem solutions in a unified framework for algebra and geometry with the widest possible scope: from quantum computing and electromagnetism to satellite navigation, from neural computing to camera geometry, image processing, robotics and beyond.     

Cyclization from Higher Excited States of Diarylethenes Having a Substituted Azulene Ring

The cyclization reaction of diarylethenes having an azulene ring occurs only via higher excited states. Novel diarylethenes having an azulene ring with a strong donor or acceptor were synthesized and examined in these reactions. A derivative having an electron-donating 1,3-benzodithiol-2-ylidenemethyl group at the 1-position of the azulene ring showed photochromism, whereas neither a derivative having a π-conjugated electron-donating group at the 3-position of the azulene ring nor derivatives having a π-conjugated electron-withdrawing group at the 1- or 3-position of the azulene ring showed any photochromism. The photoreactivities of these compounds were explained by calculating forces and bond orders on the excited states using density functional theory (DFT) and time-dependent (TD)-DFT.     

Preparation of dibromopyridines having -(CH2)m-SO3Na groups as monomers for new polypyridines

Dibromopyridines or dibromopyridone with -(CH₂)_m-SO₃Na group(s) has been prepared via the reactions of the corresponding dibromopyridines with -OH and -NH₂ groups with sultone. These compounds were converted into polymers with the -(CH₂)_m-SO₃H groups via organometallic polycondensation. The polymer showed proton conducting properties and high stability toward oxidation.     

Introduction of multiple γ-ray detection to charged particle activation analysis

Charged particle activation analysis (CPAA) is a rapid method with high accuracy which can analyze multi-elements simultaneously. Since multiple γ-ray detection method is expected to improve the detection efficiency and the signal-to-noise ratio, we study what design of the γ-ray detector array is the most suitable for CPAA. We take up four design candidates and investigated the responses by the radiation simulation code Geant 4. From the results, we have deduced the best design with 5 germanium detectors in close geometry. By inspecting the sensitivity in CPAA, the method is proved to be useful and applicable to 116 nuclides.