A note on the growth factor in Gaussian elimination for generalized Higham matrices

The Higham matrix is a complex symmetric matrix A=B+iC, where both B and C are real, symmetric and positive definite and $\mathrm{i}=\sqrt{-1}$ is the imaginary unit. For any Higham matrix A, Ikramov et al. showed that the growth factor in Gaussian elimination is less than 3. In this paper, based on the previous results, a new bound of the growth factor is obtained by using the maximum of the condition numbers of matrixes B and C for the generalized Higham matrix A, which strengthens this bound to 2 and proves the Higham's conjecture.Comment: 8 pages, 2 figures; Submitted to MOC on Dec. 22 201

Magnetized Accretion Disks with Outflows for Changing-look AGNs

Changing-look active galactic nuclei (CL-AGNs) challenges the standard accretion theory owing to its rapid variability. Recent numerical simulations have shown that, for the sub-Eddington accretion case, the disk is magnetic pressure-dominated, thermally stable, and geometrically thicker than the standard disk. In addition, outflows were found in the simulations. Observationally, high blueshifted velocities absorption lines indicate that outflows exist in AGNs. In this work, based on the simulation results, we investigate the magnetic pressure-dominated disk, and find that the accretion timescale is significantly shorter than that of the standard thin disk. However, such a timescale is still longer than that of the CL-AGNs. Moreover, if the role of outflows is taken into account, then the accretion timescale can be even shortened. By the detailed comparison of the theoretical accretion timescale with the observations, we propose that the magnetic pressure-dominated disk incorporating outflows can be responsible for the rapid variability of CL-AGNs.Comment: 11 pages, 3 figures, accepted for publication in Ap

Magic angles in twisted bilayer graphene near commensuration: Towards a hypermagic regime

The Bistritzer-MacDonald continuum model (BM model) describes the low-energy moir\'e bands for twisted bilayer graphene (TBG) at small twist angles. We derive a generalized continuum model for TBG near any commensurate twist angle, which is characterized by complex interlayer hoppings at commensurate $AA$ stackings (rather than the real hoppings in the BM model), a real interlayer hopping at commensurate $AB/BA$ stackings, and a global energy shift. The complex phases of the $AA$ stacking hoppings and the twist angle together define a single angle parameter $\phi_0$. We compute the model parameters for the first six distinct commensurate TBG configurations, among which the $38.2^\circ$ configuration may be within experimentally observable energy scales. We identify the first magic angle for any $\phi_0$ at a condition similar to that of the BM model. At this angle, the lowest two moir\'e bands at charge neutrality become flat except near the $\boldsymbol\Gamma_M$ point and retain fragile topology but lose particle-hole symmetry. We further identify a hypermagic parameter regime centered at $\phi_0 = \pm\pi/2$ where many moir\'e bands around charge neutrality (often $8$ or more) become flat simultaneously. Many of these flat bands resemble those in the kagome lattice and $p_x$, $p_y$ 2-orbital honeycomb lattice tight-binding models.Comment: 49 pages, 22 figures, accepted by Physical Review