On a Certain Subalgebra of Uq(sl^2)U_q(\widehat{\mathfrak{sl}}_2) Related to the Degenerate qq-Onsager Algebra

In [Kyushu J. Math. 64 (2010), 81-144, arXiv:0904.2889], it is discussed that a certain subalgebra of the quantum affine algebra $U_q(\widehat{\mathfrak{sl}}_2)$ controls the second kind TD-algebra of type I (the degenerate $q$-Onsager algebra). The subalgebra, which we denote by $U'_q(\widehat{\mathfrak{sl}}_2)$, is generated by $e_0^+$, $e_1^\pm$, $k_i^{\pm1}$ $(i=0,1)$ with $e^-_0$ missing from the Chevalley generators $e_i^\pm$, $k_i^{\pm1}$ $(i=0,1)$ of $U_q(\widehat{\mathfrak{sl}}_2)$. In this paper, we determine the finite-dimensional irreducible representations of $U'_q(\widehat{\mathfrak{sl}}_2)$. Intertwiners are also determined

Numerical homogenization of dual-phase steel by nonlinear conjugate gradient method (Recent developments on inverse problems for partial differential equations and their applications)

A numerical method is proposed to solve a cell problem for numerical homogenization of composite material, all of whose phases are homogeneous isotropic and whose deformations follow the elastoplastic constitutive law of Hencky's total strain theory

L1521E: A Starless Core in the Early Evolutionary Stage ?

We have studied the physical and chemical properties of a quiescent starless core L1521E with various molecular lines. It is found that there exists a compact dense core traced by the H^13CO^+, HN^13C, CCS, and HC_3N lines; their distributions have a single peak at the same position. The core radius is as small as 0.031 pc, whereas the H_2 density at the peak position is as high as (1.3-5.6)times10^5 cm^-3. Although the density is high enough to excite the inversion transitions of NH_3, these lines are found to be very faint in L1521E. The distributions of NH_3 and CCS seem to be different from those of well-studied starless cores, L1498 and L1544, where the distribution of CCS shows a shell-like structure while that of NH_3 is concentrated at the center of the core. Abundances of carbon-chain molecules are higher in L1521E than the other dark cloud cores, and especially those of sulfur-bearing molecules C_nS are comparable to the cyanopolyyne peak of TMC-1. Our results suggest that L1521E would be in a very early stage of physical and chemical evolution.Comment: 10 pages, 3 EPS figures, uses aaspp4.sty and epsf.sty, AAS LaTeX macros v4.0, The Astrophysical Journal, in pres

CIP methods for hyperbolic system with variable and discontinuous coefficient

We propose a multi-moment method for one-dimensional hyperbolic equations with smooth coefficient and piecewise constant coefficient. The method is entirely based on the backward characteristic method and uses the solution and its derivative as unknowns and cubic Hermite interpolation for each computational cell. The exact update formula for solution and its derivative is derived and used for an efficient time integration. At points of discontinuity of wave speed we define a piecewise cubic Hermite interpolation based on immersed interface method. The method is extended to the one-dimensional Maxwell's equations with variable material properties.Comment: 19 page

Core Challenge 2023: Solver and Graph Descriptions

This paper collects all descriptions of solvers and ISR instances submitted to CoRe Challenge 2023.Comment: arXiv admin note: text overlap with arXiv:2208.02495, arXiv:2207.1395