On explicit form of the FEM stiffness matrix for the integral fractional Laplacian on non-uniform meshes

We derive exact form of the piecewise-linear finite element stiffness matrix on general non-uniform meshes for the integral fractional Laplacian operator in one dimension, where the derivation is accomplished in the Fourier transformed space. With such an exact formulation at our disposal, we are able to numerically study some intrinsic properties of the fractional stiffness matrix on some commonly used non-uniform meshes (e.g., the graded mesh), in particular, to examine their seamless transition to those of the usual Laplacian.Comment: 7 pages, 6 figure

General mapping of one-dimensional non-Hermitian mosaic models to non-mosaic counterparts: Mobility edges and Lyapunov exponents

We establish a general mapping from one-dimensional non-Hermitian mosaic models to their non-mosaic counterparts. This mapping can give rise to mobility edges and even Lyapunov exponents in the mosaic models if critical points of localization or Lyapunov exponents of localized states in the corresponding non-mosaic models have already been analytically solved. To demonstrate the validity of this mapping, we apply it to two non-Hermitian localization models: an Aubry-Andr\'e-like model with nonreciprocal hopping and complex quasiperiodic potentials, and the Ganeshan-Pixley-Das Sarma model with nonreciprocal hopping. We successfully obtain the mobility edges and Lyapunov exponents in their mosaic models. This general mapping may catalyze further studies on mobility edges, Lyapunov exponents, and other significant quantities pertaining to localization in non-Hermitian mosaic models.Comment: 9 pages, 2 figure

4-(2-Nitro­benzene­sulfonamido)pyri­dinium trifluoro­acetate

In the title compound, C11H10N3O4S+·C2F3O2 −, the dihedral angle between the benzene ring and the pyridinium ring is 88.7 (4)°. In the crystal structure, a network of N—H⋯O, C—H⋯O and C—H⋯F hydrogen bonds links the constituent ions. One O atom of the nitro group is disordered over two positions, with site-occupancy factors of 0.57 (2) and 0.43 (2)

4-(4-Nitro­benzene­sulfonamido)pyridinium trifluoro­acetate

In the title compound, C11H10N3O4S+·C2F3O2 −, the benzene ring makes an angle of 87.3 (2)° with the pyridinium ring. The nitro group is essentially coplanar with the benzene ring. The F atoms of the CF3 group are disordered over two positions with almost equal occupancy [0.531 (12)/0.469 (12)]. The crystal structure is stabilized by N—H⋯O and C—H⋯O hydrogen bonds