The solution to the initial value problem for the ultradiscrete Somos-4 and 5 equations (Mathematical structures of integrable systems, its deepening and expansion)

Mathematical structures of integrable systems, its deepening and expansion. September 9-11, 2019. edited by Takao Suzuki. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.We propose a method to solve the initial value problem for the ultradiscrete Somos-4 and Somos-5 equations by expressing terms in the equations as convex polygons and regarding max-plus algebras as those on polygons

Vertex operator for the non-autonomous ultradiscrete KP equation

We propose an ultradiscrete analogue of the vertex operator in the case of the ultradiscrete KP equation--several other ultradiscrete equations--which maps N-soliton solutions to N+1-soliton ones.Comment: 9 page

Solutions to the ultradiscrete Toda molecule equation expressed as minimum weight flows of planar graphs

We define a function by means of the minimum weight flow on a planar graph and prove that this function solves the ultradiscrete Toda molecule equation, its B\"acklund transformation and the two dimensional Toda molecule equation. The method we employ in the proof can be considered as fundamental to the integrability of ultradiscrete soliton equations.Comment: 14 pages, 10 figures Added citations in v

Global stability for a discrete SIS epidemic model with immigration of infectives

Abstract. In this paper, we propose a discrete-time SIS epidemic model which is derived from continuous-time SIS epidemic models with immigration of infectives by the backward Euler method. For the discretized model, by applying new Lyapunov function techniques, we establish the global asymptotic stability of the disease-free equilibrium for R 0 ≤ 1 and the endemic equilibrium for R 0 > 1, where R 0 is the basic reproduction number of the continuous-time model. This is just a discrete analogue of continuous SIS epidemic model with immigration of infectives

Observation of band crossings protected by nonsymmorphic symmetry in the layered ternary telluride Ta3SiTe6

We have performed angle-resolved photoemission spectroscopy of layered ternary telluride Ta3SiTe6 which is predicted to host nodal lines associated with nonsymmorphic crystal symmetry. We found that the energy bands in the valence-band region show Dirac-like dispersions which present a band degeneracy at the R point of the bulk orthorhombic Brillouin zone. This band degeneracy extends one-dimensionally along the whole SR high-symmetry line, forming the nodal lines protected by the glide mirror symmetry of the crystal. We also observed a small band splitting near EF which supports the existence of hourglass-type dispersions predicted by the calculation. The present results provide an excellent opportunity to investigate the interplay between exotic nodal fermions and nonsymmorphic crystal symmetry.Comment: 6 pages, 4 figure

Practical analysis of 3-D dynamic nonlinear magnetic field using time-periodic finite element method

A practical 3-D finite element method using edge elements for analyzing stationary nonlinear magnetic fields with eddy currents in electric apparatus, in which the flux interlinking the voltage winding is given, has been proposed. The method is applied to the analysis of magnetic fields in the Epstein frame </p