Physical, analytical, and numerical properties of the lattice Green's functions for the various lattices are described. Various methods of evaluating the Green's functions, which will be developed in the subsequent papers, are mentioned.

A pseudo-Nambu-Goldstone boson (pNGB) is an attractive candidate for dark matter since the current severe limits of dark matter direct detection experiments are naturally evaded by its nature. We construct a model with pNGB dark matter based on a gauged U(1) B−L symmetry, where no ad-hoc global symmetry is assumed. The model keeps natural suppression mechanism for the dark matter direct detection cross section. On the other hand, the pNGB can decay through the new high scale suppressed operators. We show that the pNGB has long enough lifetime to be a dark matter in the wide range of the parameter space of the model. The thermal relic abundance of pNGB dark matter can be fit with the observed value against the constraints on the dark matter decays from the cosmic-ray observations.

Soliton propagation along optical fibers is discussed on the basis of the modified nonlinear Schrödinger equation, which is known to be completely integrable in terms of the inverse-scattering transformation. Numerical observation of soliton propagation reveals various kinds of dynamical behavior, which cannot be accounted for by treating the nonlinear derivative term of the modified nonlinear Schrödinger equation as a perturbation term for the cubic nonlinear Schrödinger equation.

We propose a minimal model which accommodates the long-standing anomaly of muon magnetic moment based on abelian discrete flavor symmetries. The standard model is extended by scalar doublets charged under a Z n lepton flavor symmetry. In these models, a large contribution to the muon magnetic moment can be obtained by the chirality enhancement from new scalar mediated diagrams without conflicting with the flavor symmetry. Thanks to the lepton flavor symmetry, these models automatically forbid lepton flavor violation. The minimal model is based on Z 4 symmetry with only one extra scalar doublet. In this model, we show that the parameter space favored by the muon g − 2 can easily be consistent with experimental constraints and theoretical bounds such as the electroweak precision tests, lepton universality, potential stability condition and triviality bound as well as the LHC direct search mass bound. The new contributions to the muon electric dipole moment and the Higgs decay into γγ can be indirect signals of the model.

Flat hemodialysis membranes were prepared from cellulose/N-methylmorpholine-N-oxide (NMMO) solutions (dope) with different cellulose concentrations (6 -8 wt %) by using a phase-inversion method. The coagulant used was NMMO aqueous solution, of which the NMMO concentration and its temperature were varied in the range of 0 to 50 wt % and 5 to 60°C, respectively. The effects of these preparation conditions on the permeation characteristics, the ultrafiltration rate (UFR) of pure water, and sieving coefficient (SC) of dextran, were investigated. The decrease in cellulose concentration of the dope and the increases in both temperature and NMMO concentration of the coagulant gave a membrane with high UFR. Concerning the SC, the increase of the cellulose concentration and the decreases in both temperature and NMMO concentration gave a good result. Consequently, the membrane having the preferable UFR and SC as a hemodialysis membrane was obtained when the 8 wt % cellulose dope was coagulated in water at 5°C.