On the perturbation of the group generalized inverse for a class of bounded operators in Banach spaces

En este trabajo se estudia la perturbación de la inversa generalizada grupo en el ámbito de los operadores lineales y acotados sobre un espacio de Banach complejo. Se establecen, en primer lugar, caracterizaciones de los {1,2}-inversos generalizados de operadores perturbados que verifican una condición de no singularidad. Posteriormente se caracteriza la clase de operadores perturbados para los cuales existe el operador inverso grupo y verifican ciertas condiciones geométricas. Se prueba que los operadores perturbados tienen una determinada estructura de matriz 2 por 2 de operadores y se desarrolla una representación para la resolvente de tales matrices de operadores a partir de la cual se obtiene una representación para el operador inverso grupo. Este resultado extiende al contexto de operadores un resultado para matrices por bloques incluido en el libro [Campbell y Meyer, Generalized inverses of Linear Transformations, Dover, 1979] y nos proporciona una herramienta para el análisis de la perturbación. Otras aportaciones son la obtención de xpresiones explícitas para el operador inverso grupo el operador perturbado y su proyección espectral asociada al 0 y la obtención de cotas superiores para el error relativo de la inversa de Drazin y de los proyectores espectrales y un resultado de continuidad de la inversa grupo para operadores en espacios de Banach. Las aportaciones de este trabajo extienden o complementan resultados obtenidos previamente por autores sobre el mismo tema (Djordjevic, Koliha, Rakoèevic) Given a bounded operator A on a Banach space X with Drazin inverse AD and index r, we study the class of group invertible bounded operators B such that I + A(D)(B - A) is invertible and R(B) boolean AND N(A(r)) = {0}. We show that they can be written with respect to the decomposition X = R(A(r))circle plus N(A(r)) as a matrix operator, B = (B-1 B-12 B-21 B21B1-1B12), where B-1 and B-1(2) + B12B21 are invertible. Several characterizations of the perturbed operators are established, extending matrix results. We analyze the perturbation of the Drazin inverse and we provide explicit upper bounds of parallel to B-# - A(D)parallel to and parallel to BB# - A(D)A parallel to. We obtain a result on the continuity of the group inverse for operators on Banach space

Astrophysical parameters and orbital solution of the peculiar X-ray transient IGR J00370+6122

BD+6073 is the optical counterpart of the X-ray source IGR J00370+6122, a probable accretion-powered X-ray pulsar. The X-ray light curve of this binary system shows clear periodicity at 15.7 d, which has been interpreted as repeated outbursts around the periastron of an eccentric orbit. We obtained high-resolution spectra of BD+6073 at different epochs. We used the FASTWind code to generate a stellar atmosphere model to fit the observed spectrum and obtain physical magnitudes. The synthetic spectrum was used as a template for cross-correlation with the observed spectra to measure radial velocities. The radial velocity curve provided an orbital solution for the system. We have also analysed the RXTE/ASM and Swift/BAT light curves to confirm the stability of the periodicity. BD +6073 is a BN0.7 Ib low-luminosity supergiant located at an approximate distance of 3.1 kpc, in the CasOB4 association. We derive Teff=24000 K and log gc=3.0, and chemical abundances consistent with a moderately high level of evolution. The spectroscopic and evolutionary masses are consistent at the 1 sigma level with a mass of 15 solar masses. The recurrence time of the X-ray flares is the orbital period of the system. The NS is in a high eccentricity (e=0.56) orbit, and the X-ray emission is strongly peaked around orbital phase 0.2, though the observations are consistent with some level of X-ray activity happening at all orbital phases. The X-ray behaviour of IGR J00370+6122 is reminiscent of intermediate SFXTs, though its peak luminosity is rather low. The orbit is somewhat wider than those of classical persistent supergiant X-ray binaries, which, combined with the low luminosity of the mass donor, explains the low X-ray luminosity. IGR J00370+6122 will likely evolve towards a persistent supergiant system, highlighting the evolutionary connection between different classes of wind-accreting X-ray sources.Comment: Accepted for publication in A&

Expressions for the g-Drazin inverse of additive perturbed elements in a Banach algebra

AbstractWe study additive properties of the g-Drazin inverse in a Banach algebra A. In our development we derive a representation of the resolvent of a 2×2 matrix with entries in A, which is then used to find explicit expressions for the g-Drazin inverse of the sum a+b, under new conditions on a,b∈A. As an application of our results we obtain a representation for the Drazin inverse of a 2×2 complex block matrix in terms of the individual blocks, under certain conditions

Código de Lipit-Istar

Fil: González Sánchez, Carlos A. Universidad de Sevilla. Facultad de Geografía e Historia. Cátedra Historia Moderna. Sevilla, Españ

El Código de Esnuna : (dos mil años antes de Jesucristo)

Fil: González Sánchez, Carlos A. Universidad de Sevilla. Facultad de Geografía e Historia. Cátedra Historia Moderna. Sevilla, Españ

On a partial order defined by the weighted Moore Penrose inverse

The weighted Moore-Penrose inverse of a matrix can be used to define a partial order on the set of m x n complex matrices and to introduce the concept of weighted-EP matrices. In this paper we study the weighted star partial order on the set of weighted-EP matrices. In addition, some properties that relate the eigenprojection at zero with the weighted star partial order are obtained. (C) 2013 Elsevier Inc. All rights reserved.This author was partially supported by Ministry of Education of Spain (Grant DGI MTM2010-18228).Hernández, AE.; Lattanzi, MB.; Thome, N. (2013). On a partial order defined by the weighted Moore Penrose inverse. Applied Mathematics and Computation. 219(14):7310-7318. https://doi.org/10.1016/j.amc.2013.02.010S731073182191

Generalized inverses of a sum in rings

Documento submetido para revisão pelos pares. A publicar em "Bulletin of the Australian Mathematical Society". ISSN 0004-9727. 82:1 (2010) 156-164.We study properties of the Drazin index of regular elements in a ring with a unity 1. We give expressions for generalized inverses of 1 − ba in terms of generalized inverses of 1 − ab. In our development we prove that the Drazin index of 1 − ba is equal to the Drazin index of 1 − ab.Fundação para a Ciência e a Tecnologia (FCT) através do programa POCTIMinisterio de Educación y Ciencia of Spain - Project MTM2007-6723

NGC 6067: A young and massive open cluster with high metallicity

© 2017 The Authors. NGC6067 is a young open cluster hosting the largest population of evolved stars among known Milky Way clusters in the 50-150 Ma age range. It thus represents the best laboratory in our Galaxy to constrain the evolutionary tracks of 5-7M⊙ stars. We have used high-resolution spectra of a large sample of bright cluster members (45), combined with archival photometry, to obtain accurate parameters for the cluster as well as stellar atmospheric parameters.We derive a distance of 1.78 ± 0.12 kpc, an age of 90 ± 20 Ma and a tidal radius of 14.8 -3.2+6.8 arcmin. We estimate an initial mass above 5700M⊙, for a present-day evolved population of two Cepheids, two A supergiants and 12 red giants with masses ≈6M⊙. We also determine chemical abundances of Li, O, Na, Mg, Si, Ca, Ti, Ni, Rb, Y and Ba for the red clump stars. We find a supersolar metallicity, [Fe/H]=+0.19 ± 0.05, and a homogeneous chemical composition, consistent with the Galactic metallicity gradient. The presence of a Li-rich red giant, star 276 with A(Li)=2.41, is also detected. An overabundance of Ba is found, supporting the enhanced s-process. The ratio of yellow to red giants is much smaller than 1, in agreement with models with moderate overshooting, but the properties of the cluster Cepheids do not seem consistent with current Padova models for supersolar metallicity

The star partial order and the eigenprojection at 0 on EP matrices

[EN] The space of n x n complex matrices with the star partial order is considered in the first part of this paper. The class of EP matrices is analyzed and several properties related to this order are given. In addition, some information about predecessors and successors of a given EP matrix is obtained. The second part is dedicated to the study of some properties that relate the eigenprojection at 0 with the star and sharp partial orders. 2012 Elsevier Inc. All rights reserved.This paper was partially supported by Ministry of Education of Argentina (PPUA, Grant Resol. 228, SPU, 14-15-222) and by Universidad Nacional de La Pampa, Facultad de Ingenieria (Grant Resol. No 049/11).Hernández, AE.; Lattanzi, MB.; Thome, N.; Urquiza, F. (2012). The star partial order and the eigenprojection at 0 on EP matrices. Applied Mathematics and Computation. 218(21):10669-10678. https://doi.org/10.1016/J.AMC.2012.04.034S10669106782182

Some additive results on Drazin inverse

In this paper, we investigate additive results of the Drazin inverse of elements in a ring R. Under the condition ab = ba, we show that a + b is Drazin invertible if and only if aa^D(a+b) is Drazin invertible, where the superscript D means the Drazin inverse. Furthermore we find an expression of (a + b)^D. As an application we give some new representations for the Drazin inverse of a 2 × 2 block matrix.Supported by the National Natural Science Foundation of China (11361009), the Guangxi Provincial Natural Science Foundation of China (2013GXNSFAA019008), and Science Research Project 2013 of the China-ASEAN Study Center (Guangxi Science Experiment Center) of Guangxi University for Nationalities.Liu, X.; Qin, X.; Benítez López, J. (2015). Some additive results on Drazin inverse. Applied Mathematics - A Journal of Chinese Universities. 30(4):479-490. https://doi.org/10.1007/s11766-015-3333-4S479490304A Ben-Israel, T N E Greville. Generalized Inverses, Theory and Applications, 2nd edition, Springer-Verlag, 2003.S L Campbell, C D Meyer. Generalized Inverses of Linear Transformations, Pitman (Advanced Publishing Program), Boston, MA, 1979.N Castro-González, J J Koliha. Additive perturbation results for the Drazin inverse, Linear Algebra Appl, 2005, 397: 279–297.N Castro-González, E Dopazo, M F Martínez-Serrano. On the Drazin inverse of the sum of two operators and its application to operator matrices, J Math Anal Appl, 2008, 350: 207–215.N Castro-González, M F Martínez-Serrano. Expressions for the g-Drazin inverse of additive perturbed elements in a Banach algebra, Linear Algebra Appl, 2010, 432: 1885–1895.N Castro-González, J J Koliha. New additive results for the Drazin inverse, Proc Roy Soc Edinburgh Sect A, 2004, 134: 1085–1097.M Catral, D D Olesky, P van den Driessche. Block representations of the Drazin inverse of a bipartite matrix, Electron J Linear Algebra, 2009, 18: 98–107.J L Chen, G F Zhuang, Y Wei. The Drazin inverse of a sum of morphisms, Acta Math Sci Ser A Chin Ed, 2009, 29(3): 538–552.D S Cvetković-Ilić, D S Djordjević, Y Wei. Additive results for the generalized Drazin inverse in a Banach algebra, Linear Algebra Appl, 2006, 418, 53–61.D S Cvetković-Ilić. A note on the representation for the Drazin inverse of 2 × 2 block matrices, Linear Algebra Appl, 2008, 429: 242–248.C Deng. The Drazin inverses of sum and difference of idempotents, Linear Algebra Appl, 2009, 430: 1282–1291.C Deng, Y Wei. Characterizations and representations of the Drazin inverse of idempotents, Linear Algebra Appl, 2009, 431: 1526–1538.C Deng, Y Wei. New additive results for the generalized Drazin inverse, J Math Anal Appl, 2010, 370: 313–321.D S Djordjević, P S Stanimirović. On the generalized Drazin inverse and generalized resolvent, Czechoslovak Math J, 2001, 51(126): 617–634.D S Djordjević, Y Wei. Additive results for the generalized Drazin inverse, J Aust Math Soc, 2002, 73: 115–125.D S Djordjević, V Rakočević. Lectures on Generalized inverses, University of Niš, 2008.E Dopazo, M F Martínez-Serrano. Further results on the representation of the Drazin inverse of a 2 × 2 block matrices, Linear Algebra Appl, 2010, 432: 1896–1904.M P Drazin. Pseudo-inverses in associative rings and semiproup, Amer Math Monthly, 1958, 65: 506–514.R E Hartwig, G R Wang, Y Wei. Some additive results on Drazin inverse, Linear Algebra Appl, 2001, 322: 207–217.R E Hartwig, X Li, Y Wei. Representations for the Drazin inverse of a 2×2 block matrix, SIAM J Matrix Anal Appl, 2006, 27: 757–771.Y Liu, C G Cao. Drazin inverse for some partitioned matrices over skew fields, J Nat Sci Heilongjiang Univ, 2004, 24: 112–114.J Ljubisavljević, D S Cvetković-Ilić. Additive results for the Drazin inverse of block matrices and applications, J Comput Appl Math, 2011, 235: 3683–3690.C D Meyer ffixJr, N J Rose. The index and the Drazin inverse of block triangular matrices, SIAM J Appl Math, 1977, 33(1): 1–7.L Wang, H H Zhu, X Zhu, J L Chen. Additive property of Drazin invertibility of elements, arXiv: 1307.1816v1 [math.RA], 2013.H Yang, X Liu. The Drazin inverse of the sum of two matrices and its applications, J Comput Appl Math, 2011, 235: 1412–1417