A note on a conjecture concerning rank one perturbations of singular M-matrices

A conjecture from a paper by J. Bierkens and A.C.M. Ran concerning the location of eigenvalues of rank one perturbations of singular M-matrices is shown to be false in dimension four and higher, but true for dimension two, as well as for dimension three with an additional condition on the perturbation.Comment: 12 pages, 3 figure

Global properties of eigenvalues of parametric rank one perturbations for unstructured and structured matrices

General properties of eigenvalues of $A+\tau uv^*$ as functions of \tau\in\Comp or \tau\in\Real or \tau=\e^{\ii\theta} on the unit circle are considered. In particular, the problem of existence of global analytic formulas for eigenvalues is addressed. Furthermore, the limits of eigenvalues with $\tau\to\infty$ are discussed in detail. The following classes of matrices are considered: complex (without additional structure), real (without additional structure), complex $H$-selfadjoint and real $J$-Hamiltonian

The scattering of a cylindrical invisibility cloak: reduced parameters and optimization

We investigate the scattering of 2D cylindrical invisibility cloaks with simplified constitutive parameters with the assistance of scattering coefficients. We show that the scattering of the cloaks originates not only from the boundary conditions but also from the spatial variation of the component of permittivity/permeability. According to our formulation, we propose some restrictions to the invisibility cloak in order to minimize its scattering after the simplification has taken place. With our theoretical analysis, it is possible to design a simplified cloak by using some peculiar composites like photonic crystals (PCs) which mimic an effective refractive index landscape rather than offering effective constitutives, meanwhile canceling the scattering from the inner and outer boundaries.Comment: Accepted for J. Phys.

Self-Organized Criticality in Compact Plasmas

Compact plasmas, that exist near black-hole candidates and in gamma ray burst sources, commonly exhibit self-organized non-linear behavior. A model that simulates the non-linear behavior of compact radiative plasmas is constructed directly from the observed luminosity and variability. The simulation shows that such plasmas self organize, and that the degree of non-linearity as well as the slope of the power density spectrum increase with compactness. The simulation is based on a cellular automaton table that includes the properties of the hot (relativistic) plasmas, and the magnitude of the energy perturbations. The plasmas cool or heat up, depending on whether they release more or less than the energy of a single perturbation. The energy release depends on the plasmas densities and temperatures, and the perturbations energy. Strong perturbations may cool the previously heated plasma through shocks and/or pair creation. New observations of some active galactic nuclei and gamma ray bursters are consistent with the simulationComment: 9 pages, 5 figures, AASTeX, Submitted to ApJ

Curve classes on irreducible holomorphic symplectic varieties

We prove that the integral Hodge conjecture holds for 1-cycles on irreducible holomorphic symplectic varieties of K3 type and of Generalized Kummer type. As an application, we give a new proof of the integral Hodge conjecture for cubic fourfolds.Comment: 15 page

Equivalence after extension and Schur coupling do not coincide on essentially incomparable Banach spaces

In 1994, H. Bart and V. É. Tsekanovskii posed the question whether the Banach space operator relations matricial coupling (MC), equivalence after extension (EAE) and Schur coupling (SC) coincide, leaving only the implication EAE/MC => SC open. Despite several affirmative results, in this paper we show that the answer in general is no. This follows from a complete description of EAE and SC for the case that the operators act on essentially incomparable Banach spaces, which also leads to a new characterisation of the notion of essential incomparability. Concretely, the forward shift operators $U$ on $\ell$$^p$ and $V$ on $\ell$$^p$, for $1 ≤ p, q ≤ \infty, p ≠ q$, are EAE but not SC. As a corollary, SC is not transitive. Under mild assumptions, given $U$ and $V$ that are Atkinson or generalised invertible and EAE, we give a concrete operator $W$ that is SC to both $U$ and $V$, even if $U$ and $V$ are not SC themselves. Some further affirmative results for the case where the Banach spaces are isomorphic are also obtained

One dimensional Coulomb-like problem in deformed space with minimal length

Spectrum and eigenfunctions in the momentum representation for 1D Coulomb potential with deformed Heisenberg algebra leading to minimal length are found exactly. It is shown that correction due to the deformation is proportional to square root of the deformation parameter. We obtain the same spectrum using Bohr-Sommerfeld quantization condition.Comment: 11 pages, typos corrected, references adde

A Toeplitz-like operator with rational matrix symbol having poles on the unit circle: Invertibility and Riccati equations

This paper is a continuation of the work on unbounded Toeplitz-like operators T_\Om with rational matrix symbol \Om initiated in Groenewald et. al (Complex Anal. Oper. Theory 15, 1(2021)), where a Wiener-Hopf type factorization of \Om is obtained and used to determine when T_\Om is Fredholm and compute the Fredholm index in case T_\Om is Fredholm. Due to the high level of non-uniqueness and complicated form of the Wiener-Hopf type factorization, it does not appear useful in determining when T_\Om is invertible. In the present paper we use state space methods to characterize invertibility of T_\Om in terms of the existence of a stabilizing solution of an associated nonsymmetric discrete algebraic Riccati equation, which in turn leads to a pseudo-canonical factorization of \Om and concrete formulas of T_\Om^{-1}.Comment: 19 page

Novel frataxin isoforms may contribute to the pathological mechanism of friedreich ataxia

This is an open-access article, free of all copyright, and may be freely reproduced, distributed, transmitted, modified, built upon, or otherwise used by anyone for any lawful purpose. The work is made available under the Creative Commons CC0 public domain dedication.Friedreich ataxia (FRDA) is an inherited neurodegenerative disease caused by frataxin (FXN) deficiency. The nervous system and heart are the most severely affected tissues. However, highly mitochondria-dependent tissues, such as kidney and liver, are not obviously affected, although the abundance of FXN is normally high in these tissues. In this study we have revealed two novel FXN isoforms (II and III), which are specifically expressed in affected cerebellum and heart tissues, respectively, and are functional in vitro and in vivo. Increasing the abundance of the heart-specific isoform III significantly increased the mitochondrial aconitase activity, while over-expression of the cerebellum-specific isoform II protected against oxidative damage of Fe-S cluster-containing aconitase. Further, we observed that the protein level of isoform III decreased in FRDA patient heart, while the mRNA level of isoform II decreased more in FRDA patient cerebellum compared to total FXN mRNA. Our novel findings are highly relevant to understanding the mechanism of tissue-specific pathology in FRDA.This work was supported by the intramural program of the National Institute of Child Health and Human Development, National Institutes of Health, and in part by Friedreich ataxia research association; by the National Nature Science Foundation of China (NSFC) (No. 31071085), by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, and by State Key Laboratory of Pharmaceutical Biotechnology (No. ZZYJ-SN-201006). Zvonimir Marelja was supported by a grant from the Studienstiftung des Deutschen Volkes and by Deutscher Akademischer Austauschdienst scholarship. Additional support was obtained from the Deutsche Forschungsgemeinschaft Grant SL1171/5-3