An extension of Fourier analysis for the n-torus in the magnetic field and its application to spectral analysis of the magnetic Laplacian

We solved the Schr{\"o}dinger equation for a particle in a uniform magnetic field in the n-dimensional torus. We obtained a complete set of solutions for a broad class of problems; the torus T^n = R^n / {\Lambda} is defined as a quotient of the Euclidean space R^n by an arbitrary n-dimensional lattice {\Lambda}. The lattice is not necessary either cubic or rectangular. The magnetic field is also arbitrary. However, we restrict ourselves within potential-free problems; the Schr{\"o}dinger operator is assumed to be the Laplace operator defined with the covariant derivative. We defined an algebra that characterizes the symmetry of the Laplacian and named it the magnetic algebra. We proved that the space of functions on which the Laplacian acts is an irreducible representation space of the magnetic algebra. In this sense the magnetic algebra completely characterizes the quantum mechanics in the magnetic torus. We developed a new method for Fourier analysis for the magnetic torus and used it to solve the eigenvalue problem of the Laplacian. All the eigenfunctions are given in explicit forms.Comment: 32 pages, LaTeX, minor corrections are mad

Accumulation of Ulva spp. (Chlorophyta) and other seaweed thalli on the shallow sea bottom of Hiroshima Bay (A preliminary survey)

広島湾奥部の大野瀬戸周辺の砂泥海底域で，小型底曳き網（ナマコ桁網）と潜水により，アオサ類等をはじめとする海藻類の堆積状況を調査した。38種の海藻・海草類が採集されたが，現存量では底曳き網による採集物の64～100％をアオサ類が占めていた。アオサ類は水深5m以浅で最も多く採集され，砂浜・干潟に連続する海底勾配の緩やかな浅海底がアオサ類の増殖帯になっていると考えられた。Biomass of Ulva spp. (Chlorophyta) causing ‘green tide’ and other seaweeds accumulated on shallow sea bottom in inner area of Hiroshima Bay was estimated by trawl-net and SCUBA surveys. Thirty-eight species of seaweed and seagrass was sampled, but Ulva spp. was dominant occupying 64-100 % in biomass of all samples. Ulva spp. was sampled most abundantly at the stations shallower than 5 m, and it was indicated that sea bottom with a gentle slope, and located offshore of sandy beaches or tidal-flats offers a suitable condition for Ulva growth

Efficacy of soft palatal augmentation prosthesis for oral functional rehabilitation in patients with dysarthria and dysphagia: a protocol for a randomised controlled trial

Introduction Palatal augmentation prosthesis (PAP) is used in patients with articulation and swallowing disorders caused by postoperative loss of tongue tissue due to tongue cancer, cerebrovascular disease sequelae and age-related hypofunction. We have previously reported a newly designed soft PAP fabricated using an thermoplastic material that is particularly appropriate for early intervention. However, the effect of soft PAP on oral function improvement remains to be elucidated. The aim of this study is to investigate whether soft PAP can improve dysarthria and dysphagia occurring as cerebrovascular disease sequelae. Methods and analysis This prospective, randomised, controlled trial will compare the immediate and training effects of rehabilitation using soft PAP with those of rehabilitation without using it. Primary outcomes are the single-word intelligibility test score and pharyngeal transit time (PTT). Secondary outcomes are tongue function (evaluated based on maximum tongue pressure, repetitions of tongue pressure and endurance of tongue pressure), articulation function (evaluated based on speech intelligibility, oral diadochokinesis, Voice-Related Quality of Life (V-RQOL)) and swallowing function (evaluated using Eating Assessment Tool-10). The study results will help determine the efficacy of Soft PAP in improving functional outcomes of word intelligibility and PTT. We hypothesised that early rehabilitation using Soft PAP would more effectively improve articulation and swallowing function compared with conventional rehabilitation without using soft PAP. Ethics and dissemination Ethical approval was obtained from the Okayama University Certified Review Board. The study findings will be published in an open access, peer-reviewed journal and presented at relevant conferences and research meetings

Shock Excitation in Narrow Line Regions Powered by AGN Outflows

Outflows in the Active Galactic Nucleus (AGN) are considered to play a key role in the host galaxy evolution through transfer of a large amount of energy. A Narrow Line Region (NLR) in the AGN is composed of ionized gas extending from pc-scales to kpc-scales. It has been suggested that shocks are required for ionization of the NLR gas. If AGN outflows generate such shocks, they will sweep through the NLR and the outflow energy will be transferred into a galaxy-scale region. In order to study contribution of the AGN outflow to the NLR-scale shock, we measure the [\ion{Fe}{2}]$\lambda12570$/[\ion{P}{2}]$\lambda11886$ line ratio, which is a good tracer of shocks, using near-infrared spectroscopic observations with WINERED (Warm INfrared Echelle spectrograph to Realize Extreme Dispersion and sensitivity) mounted on the New Technology Telescope. Among 13 Seyfert galaxies we observed, the [\ion{Fe}{2}] and [\ion{P}{2}] lines were detected in 12 and 6 targets, respectively. The [\ion{Fe}{2}]/[\ion{P}{2}] ratios in 4 targets were found to be higher than 10, which implies the existence of shocks. We also found that the shock is likely to exist where an ionized outflow, i.e., a blue wing in [\ion{S}{3}]$\lambda9533$, is present. Our result implies that the ionized outflow present over a NLR-scale region sweeps through the interstellar medium and generates a shock.Comment: Accepted for ApJ, 20 pages, 11 figure

The Japanese space gravitational wave antenna; DECIGO

DECi-hertz Interferometer Gravitational wave Observatory (DECIGO) is the future Japanese space gravitational wave antenna. DECIGO is expected to open a new window of observation for gravitational wave astronomy especially between 0.1 Hz and 10 Hz, revealing various mysteries of the universe such as dark energy, formation mechanism of supermassive black holes, and inflation of the universe. The pre-conceptual design of DECIGO consists of three drag-free spacecraft, whose relative displacements are measured by a differential Fabry– Perot Michelson interferometer. We plan to launch two missions, DECIGO pathfinder and pre- DECIGO first and finally DECIGO in 2024