The mm-weak core inverse

Since the day the core inverse has been known in a paper of Bakasarly and Trenkler, it has been widely researched. So far, there are four generalizations of this inverse for the case of matrices of an arbitrary index, namely, the BT inverse, the DMP inverse, the core-EP inverse and the WC inverse. In this paper we introduce a new type of generalized inverse for a matrix of arbitrary index to be called $m$-weak core inverse which generalizes the core-EP inverse, the WC inverse, and therefore the core inverse. We study several properties and characterizations of the $m$-weak core inverse by using matrix decompositions

Solving an open problem about the G-Drazin partial order

[EN] G-Drazin inverses and the G-Drazin partial order for square matrices have been both recently introduced by Wang and Liu. They proved the following implication: If A is below B under the G-Drazin partial order, then any G-Drazin inverse of B is also a G-Drazin inverse of A. However, this necessary condition could not be stated as a characterization and the validity (or not) of the converse implication was posed as an open problem. In this paper, this problem is completely solved. It is obtained that the converse, in general, is false, and a form to construct counterexamples is provided. It is also proved that the converse holds under an additional condition (which is also necessary) as well as for some special cases of matrices.Partially supported by Universidad Nacional de Río Cuarto (Grant PPI 18/C472), CONICET (Grant PIP 112-201501-00433CO), and by ANPCyT (Grant PICT 2018-03492) Partially supported by Universidad Nacional de La Pampa, Facultad de Ingeniería (Grant Resol. Nro. 155/14) Partially supported by Ministerio de Economía, Industria y Competitividad of Spain (Grant Red de Excelencia MTM2017-90682-REDT), and by Universidad Nacional del Sur of Argentina (Grant 24/L108)Ferreyra, DE.; Lattanzi, M.; Levis, FE.; Thome, N. (2020). Solving an open problem about the G-Drazin partial order. The Electronic Journal of Linear Algebra. 36:55-66. http://hdl.handle.net/10251/161871S55663

The weak core inverse

[EN] In this paper, we introduce a new generalized inverse, called weak core inverse (or, in short, WC inverse) of a complex square matrix. This new inverse extends the notion of the core inverse defined by Baksalary and Trenkler (Linear Multilinear Algebra 58(6):681-697, 2010). We investigate characterizations, representations, and properties for this generalized inverse. In addition, we introduce weak core matrices (or, in short, WC matrices) and we show that these matrices form a more general class than that given by the known weak group matrices, recently investigated by H. Wang and X. Liu.In what follows, we detail the acknowledgements. D.E. Ferreyra, F.E. Levis, A.N. Priori - Partially supported by Universidad Nacional de Rio Cuarto (Grant PPI 18/C559) and CONICET (Grant PIP 112-201501-00433CO). D.E. Ferreyra F.E. Levis - Partially supported by ANPCyT (Grant PICT 201803492). D.E. Ferreyra, N. Thome -Partially supported by Universidad Nacional de La Pampa, Facultad de Ingenieria (Grant Resol. Nro. 135/19). N. Thome -Partially supported by Ministerio de Economia, Industria y Competitividad of Spain (Grant Red de Excelencia MTM2017-90682-REDT) and by Universidad Nacional del Sur of Argentina (Grant 24/L108). We would like to thank the Referees for their valuable comments and suggestions which helped us to considerably improve the presentation of the paperFerreyra, DE.; Levis, FE.; Priori, AN.; Thome, N. (2021). The weak core inverse. Aequationes Mathematicae. 95(2):351-373. https://doi.org/10.1007/s00010-020-00752-zS351373952Ben-Israel, A., Greville, T.N.E.: Generalized Inverses: Theory and Applications, 2nd edn. Springer, New York (2003)Baksalary, O.M., Trenkler, G.: Core inverse of matrices. Linear Multilinear Algebra 58(6), 681–697 (2010)Baksalary, O.M., Trenkler, G.: On a generalized core inverse. Appl. Math. Comput. 236(1), 450–457 (2014)Campbell, S.L., Meyer Jr., C.D.: Generalized Inverses of Linear Transformations. SIAM, Philadelphia (2009)Ceryan, N.: Handbook of Research on Trends and Digital Advances in Engineering Geology, Advances in Civil and Industrial Engineering. IGI Global, Hershey (2018)Chen, J.L., Mosić, D., Xu, S.Z.: On a new generalized inverse for Hilbert sapce operators. Quaest. Math. (2019). https://doi.org/10.2989/16073606.2019.1619104Cvetković-Ilić, D.S., Mosić, D., Wei, Y.: Partial orders on $$B(H)$$. Linear Algebra Appl. 481, 115–130 (2015)Djikić, M.S.: Lattice properties of the core-partial order. Banach J. Math. Anal. 11(2), 398–415 (2017)Doty, K.L., Melchiorri, C., Bonivento, C.: A theory of generalized inverses applied to robotics. Int. J. Robot. Res. 12(1), 1–19 (1993)Drazin, M.P.: Pseudo inverses in associative rings and semigroups. Am. Math. Mon. 65(7), 506–514 (1958)Ferreyra, D.E., Levis, F.E., Thome, N.: Revisiting of the core EP inverse and its extension to rectangular matrices. Quaest. Math. 41(2), 265–281 (2018)Ferreyra, D.E., Levis, F.E., Thome, N.: Maximal classes of matrices determining generalized inverses. Appl. Math. Comput. 333, 42–52 (2018)Ferreyra, D.E., Levis, F.E., Thome, N.: Characterizations of $$k$$-commutative equalities for some outer generalized inverses. Linear Multilinear Algebra 68(1), 177–192 (2020)Hartwig, R.E., Spindelböck, K.: Matrices for which $$A^*$$ and $$A^\dagger$$ conmmute. Linear Multilinear Algebra 14(3), 241–256 (1984)Liu, X., Cai, N.: High-order iterative methods for the DMP inverse. J. Math. Article ID 8175935, 6 p (2018)Malik, S., Thome, N.: On a new generalized inverse for matrices of an arbitrary index. Appl. Math. Comput. 226(1), 575–580 (2014)Malik, S., Rueda, L., Thome, N.: The class of $$m$$-EP and $$m$$-normal matrices. Linear Multilinear Algebra 64(11), 2119–2132 (2016)Manjunatha Prasad, K., Mohana, K.S.: Core EP inverse. Linear Multilinear Algebra 62(6), 792–802 (2014)Mehdipour, M., Salemi, A.: On a new generalized inverse of matrices. Linear Multilinear Algebra 66(5), 1046–1053 (2018)Mitra, S.K., Bhimasankaram, P., Malik, S.: Matrix Partial Orders, Shorted Operators and Applications, Series in Algebra, vol. 10. World Scientific Publishing Co. Pte. Ltd., Singapore (2010)Mosić, D., Stanimirović, P.S.: Composite outer inverses for rectangular matrices. Quaest. Math. (2019). https://doi.org/10.2989/16073606.2019.1671526Penrose, R.: A generalized inverse for matrices. Math. Proc. Cambr. Philos. Soc. 51(3), 406–413 (1955)Rakić, D.S., Dincić, N.C., Djordjević, D.S.: Core inverse and core partial order of Hilbert space operators. Appl. Math. Comput. 244(1), 283–302 (2014)Soleimani, F., Stanimirović, P.S., Soleymani, F.: Some matrix iterations for computing generalized inverses and balancing chemical equations. Algorithms 8(4), 982–998 (2015)Tosić, M., Cvetković-Ilić, D.S.: Invertibility of a linear combination of two matrices and partial orderings. Appl. Math. Comput. 218(9), 4651–4657 (2012)Wang, X.: Core-EP decomposition and its applications. Linear Algebra Appl. 508(1), 289–300 (2016)Wang, H., Chen, J.: Weak group inverse. Open Math. 16(1), 1218–1232 (2018)Wang, H., Liu, X.: The weak group matrix. Aequ. Math. 93(6), 1261–1273 (2019)Xiao, G.Z., Shen, B.Z., Wu, C.K., Wong, C.S.: Some spectral techniques in coding theory. Discrete Math. 87(2), 181–186 (1991)Zhou, M., Chen, J., Stanimirović, P., Katsikis, V.N., Ma, H.: Complex varying-parameter Zhang neural networks for computing core and core-EP inverse. Neural Process. Lett. 51, 1299–1329 (2020)Zhu, H.: On DMP inverses and $$m$$-EP elements in rings. Linear Multilinear Algebra 67(4), 756–766 (2019)Zhu, H., Patrício, P.: Several types of one-sided partial orders in rings. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113, 3177–3184 (2019

One sided Star and Core orthogonality of matrices

We investigate two one-sided orthogonalities of matrices, the first of which is left (right) $*$-orthogonality for rectangular matrices and the other is left (right) core-orthogonality of index $1$ matrices. We obtain some basic results for these matrices, their canonical forms, and characterizations. Also, relations between left (right) orthogonal matrices and parallel sums are investigated. Finally under these one-sided orthogonalities we explore the conditions of additivity of the Moore-Penrose inverse and the core inverse

Characterizations of k-commutative equalities for some outer generalized inverses

[EN] In this paper, we present necessary and sufficient conditions for the k-commutative equality , where X is an outer generalized inverse of the square matrix A. Also, we give new representations for core EP, DMP, and CMP inverses of square matrices as outer inverses with prescribed null space and range. In addition, we characterize the core EP inverse as the solution of a new system of matrix equations.D. E. Ferreyra F. E. Levis Partially supported by a Consejo Nacional de Investigaciones Científicas y Técnicas CONICET s Posdoctoral Research Fellowship, UNRC [grant number PPI 18/C472] and CONICET [grant number PIP 112-201501-00433CO], respectively. N. Thome Partially supported by Secretaría de Estado de Investigación, Desarrollo e Innovación Ministerio de Economía, Industria y Competitividad of Spain [grant number DGI MTM2013-43678-P and Grant Red de Excelen- cia PMTM2017-90682-REDT]. D. E. Ferreyra and N. Thome Partially supported Universidad Nacional de La Pampa (UNLPam), Facultad de Ingeniería [grant Resol. No 155/14].Ferreyra, DE.; Levis, F.; Thome, N. (2018). Characterizations of k-commutative equalities for some outer generalized inverses. Linear and Multilinear Algebra. 1-16. https://doi.org/10.1080/03081087.2018.1500994S116Baksalary, O. M., & Trenkler, G. (2010). Core inverse of matrices. Linear and Multilinear Algebra, 58(6), 681-697. doi:10.1080/03081080902778222Manjunatha Prasad, K., & Mohana, K. S. (2013). Core–EP inverse. Linear and Multilinear Algebra, 62(6), 792-802. doi:10.1080/03081087.2013.791690Malik, S. B., & Thome, N. (2014). On a new generalized inverse for matrices of an arbitrary index. Applied Mathematics and Computation, 226, 575-580. doi:10.1016/j.amc.2013.10.060Mehdipour, M., & Salemi, A. (2017). On a new generalized inverse of matrices. Linear and Multilinear Algebra, 66(5), 1046-1053. doi:10.1080/03081087.2017.1336200Malik, S. B., Rueda, L., & Thome, N. (2016). The class ofm-EPandm-normal matrices. Linear and Multilinear Algebra, 64(11), 2119-2132. doi:10.1080/03081087.2016.1139037Wang, H. (2016). Core-EP decomposition and its applications. Linear Algebra and its Applications, 508, 289-300. doi:10.1016/j.laa.2016.08.008Wang H, Chen J. Weak group inverse. Available from: http://arxiv.org/abs/1704.08403v1Wei, Y. (1998). A characterization and representation of the generalized inverse A(2)T,S and its applications. Linear Algebra and its Applications, 280(2-3), 87-96. doi:10.1016/s0024-3795(98)00008-1Rakić, D. S., Dinčić, N. Č., & Djordjević, D. S. (2014). Core inverse and core partial order of Hilbert space operators. Applied Mathematics and Computation, 244, 283-302. doi:10.1016/j.amc.2014.06.112Stanimirović, P. S., Katsikis, V. N., & Ma, H. (2016). Representations and properties of theW-Weighted Drazin inverse. Linear and Multilinear Algebra, 65(6), 1080-1096. doi:10.1080/03081087.2016.1228810Ferreyra, D. E., Levis, F. E., & Thome, N. (2017). Revisiting the core EP inverse and its extension to rectangular matrices. Quaestiones Mathematicae, 41(2), 265-281. doi:10.2989/16073606.2017.1377779Deng, C. Y., & Du, H. K. (2009). REPRESENTATIONS OF THE MOORE-PENROSE INVERSE OF 2×2 BLOCK OPERATOR VALUED MATRICES. Journal of the Korean Mathematical Society, 46(6), 1139-1150. doi:10.4134/jkms.2009.46.6.1139Wang, H., & Liu, X. (2014). Characterizations of the core inverse and the core partial ordering. Linear and Multilinear Algebra, 63(9), 1829-1836. doi:10.1080/03081087.2014.97570

Spectral and localization properties of the Dirichlet wave guide with two concentric Neumann discs

Bound states of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width $d$ are investigated. We impose the Neumann boundary condition on the two concentric windows of the radii $a$ and $b$ located on the opposite walls and the Dirichlet boundary condition on the remaining part of the boundary of the strip. We prove that such a system exhibits discrete eigenvalues below the essential spectrum for any $a,b>0$. When $a$ and $b$ tend to the infinity, the asymptotic of the eigenvalue is derived. A comparative analysis with the one-window case reveals that due to the additional possibility of the regulating energy spectrum the anticrossing structure builds up as a function of the inner radius with its sharpness increasing for the larger outer radius. Mathematical and physical interpretation of the obtained results is presented; namely, it is derived that the anticrossings are accompanied by the drastic changes of the wave function localization. Parallels are drawn to the other structures exhibiting similar phenomena; in particular, it is proved that, contrary to the two-dimensional geometry, at the critical Neumann radii true bound states exist.Comment: 25 pages, 7 figure

Spectral properties of a short-range impurity in a quantum dot

The spectral properties of the quantum mechanical system consisting of a quantum dot with a short-range attractive impurity inside the dot are investigated in the zero-range limit. The Green function of the system is obtained in an explicit form. In the case of a spherically symmetric quantum dot, the dependence of the spectrum on the impurity position and the strength of the impurity potential is analyzed in detail. It is proven that the confinement potential of the dot can be recovered from the spectroscopy data. The consequences of the hidden symmetry breaking by the impurity are considered. The effect of the positional disorder is studied.Comment: 30 pages, 6 figures, Late

Propiedades emulsificantes y espumantes de las proteínas de harina de cacahuate (Arachis hypogaea Lineau)

The functional properties of proteins present in peanut (Arachis hypogaea Lineau) flour were studied. The influence of the pH and protein solubility on emulsifying and foaming properties of peanut flour was evaluated. The isoelectric point (Ip) of these proteins was found at the pH of 4,0; and the isoelectric region between pH 3,0 and 5,0. The evaluated surface properties decreased in the isolectric region. The emulsifying activity and time stability (30 and 120 minutes) significantly decreased at the pI; the emulsifying stability at the temperature of 80°C decreased in all the isoelectric region until the pH of 6,0. The foaming activity had the best values at the pH of 2,0. The correlation between protein solubility and surface properties were more significant for emulsifying properties than for foaming properties.Se estudiaron las propiedades funcionales de las proteínas presentes en la harina de cacahuate (Arachis hypogaea Lineau). Fue evaluada la influencia que tienen el pH y la solubilidad proteica sobre las propiedades emulsificantes y espumantes de las proteínas de harina de cacahuate. El punto isoeléctrico (pI) de estas proteínas se encuentra a pH 4,0; mientras que la región isoeléctrica está entre los valores de pH de 3,0 y 5,0. Las propiedades de superficie evaluadas disminuyeron en la región isoeléctrica, siendo que la actividad emulsificante y la estabilidad emulsificante en los tiempos de 30 y 120 minutos disminuyeron fuertemente en el pI; las estabilidades emulsificantes en relación a la temperatura (80 ºC) diminuyeron en toda la región isoeléctrica extendiéndose hasta el pH 6,0. La actividad espumante mostró sus mejores valores a pH 2,0. Las correlaciones entre la solubilidad protéica y las propiedades de superficie fueron más importantes para las propiedades emulsificantes que para las espumantes

Socioeconomic inequalities in low birth weight risk before and during the COVID-19 pandemic in Argentina: A cross-sectional study

Background: The coronavirus disease 2019 (COVID-19) pandemic may have exacerbated existing socioe- conomic inequalities in health. In Argentina, public hospitals serve the poorest uninsured segment of the population, while private hospitals serve patients with health insurance. This study aimed to assess whether socioeconomic inequalities in low birth weight (LBW) risk changed during the first wave of the COVID-19 pandemic. Methods: This multicenter cross-sectional study included 15929 infants. A difference-in-difference (DID) analysis of socioeconomic inequalities between public and private hospitals in LBW risk in a pandemic cohort (March 20 to July 19, 2020) was compared with a prepandemic cohort (March 20 to July 19, 2019) by using medical records obtained from ten hospitals. Infants were categorized by weight as LBW < 2500 g, very low birth weight (VLBW) < 1500 g and extremely low birth weight (ELBW) < 1000 g. Log binomial regression was performed to estimate risk differences with an interaction term representing the DID estimator. Covariate-adjusted models included potential perinatal confounders. Findings: Of the 8437 infants in the prepandemic cohort, 4887 (57 ? 9%) were born in public hospitals. The pandemic cohort comprised 7492 infants, 4402 (58 ? 7%) of whom were born in public hospitals. The DID estimators indicated no differences between public versus private hospitals for LBW risk ( −1 ? 8% [95% CI −3 ? 6, 0 ? 0]) and for ELBW risk ( −0 ? 1% [95% CI −0 ? 6, 0 ? 3]). Significant differences were found between public versus private hospitals in the DID estimators ( −1 ? 2% [95% CI, −2 ? 1, −0 ? 3]) for VLBW risk. The results were comparable in covariate-adjusted models. Interpretation: In this study, we found evidence of decreased disparities between public and private hos- pitals in VLBW risk. Our findings suggest that measures that prioritize social spending to protect the most vulnerable pregnant women during the pandemic contributed to better birth outcomes. Funding: No funding was secured for this study.Fil: Cuestas, Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Investigaciones en Ciencias de la Salud. Universidad Nacional de Córdoba. Instituto de Investigaciones en Ciencias de la Salud; ArgentinaFil: Gómez Flores, Martha E.. Gobierno de la Provincia de Buenos Aires. Hospital Doctor Ramón Carrillo; ArgentinaFil: Charras, María D.. Gobierno de la Provincia de Buenos Aires. Hospital Doctor Ramón Carrillo; ArgentinaFil: Peyrano, Alberto J.. Hospital Materno Provincial Dr. Raúl Felipe Lucini; ArgentinaFil: Montenegro, Clara. Hospital Materno Provincial Dr. Raúl Felipe Lucini; ArgentinaFil: Sosa Boye, Ignacio. No especifíca;Fil: Burgos, Verónica. Universidad Católica de Córdoba. Facultad de Medicina. Clínica Universitaria Reina Fabiola; ArgentinaFil: Giusti, Graciela. Clínica y Maternidad del Sol; ArgentinaFil: Espósito, Mario. Clínica y Maternidad del Sol; ArgentinaFil: Blanco Pool, Silvyana S.. Hospital Misericordia Nuevo Siglo ; Gobierno de la Provincia de Cordoba; ArgentinaFil: Gurevich, Debora P.. Hospital Misericordia Nuevo Siglo ; Gobierno de la Provincia de Cordoba; ArgentinaFil: Ahumada, Luis A.. Hospital Misericordia Nuevo Siglo ; Gobierno de la Provincia de Cordoba; ArgentinaFil: Pontoriero, Ricardo D.. Hospital Misericordia Nuevo Siglo ; Gobierno de la Provincia de Cordoba; ArgentinaFil: Rizzotti, Alina. Hospital Privado Universitario de Córdoba; ArgentinaFil: Bas, José I.. Hospital Privado Universitario de Córdoba; ArgentinaFil: Vaca, María B.. Hospital Universitario de Maternidad y Neonatología; ArgentinaFil: Miranda, María J.. Hospital Universitario de Maternidad y Neonatología; ArgentinaFil: Ferreyra, Mirta E.. Hospital Misericordia Nuevo Siglo ; Gobierno de la Provincia de Cordoba; ArgentinaFil: Moreno, Gabriela C.. Gobierno de la Provincia de Buenos Aires. Hospital Doctor Ramón Carrillo; ArgentinaFil: Pedicino, Héctor. Hospital Italiano; ArgentinaFil: Rojas Rios, Melvy. Hospital Italiano; Argentin

Association between COVID-19 mandatory lockdown and decreased incidence of preterm births and neonatal mortality

Previous studies suggest a decrease in preterm births (PTB) during de coronavirus disease 2019 (COVID-19), possibly due to the effect of the mandatory lockdown. Nevertheless, other reports have been unable to confirm this finding. Most of these studies originated in high-income countries and evaluated a limited number of potential confounders, and all of them assessed a short lockdown period. In addition, an important question remains unanswered: How can we be sure that the observed changes are due to lockdown, when most of the pregnancies delivered in the lockdown period were conceived prior to it?To date there is insufficient evidence to support the notion that public health interventions during the lockdown prevent PTB . The aim of this study was to compare the incidence of PTB, neonatal mortality (NM) and stillbirths adjusted by potential confounders during the lockdown period assessing a time window of nine and a half months during which all the pregnancies analyzed in the exposed group were conceived after the lockdown, with the corresponding incidence in the previous year where all the unexposed pregnancies analyzed were conceived before the lockdown.publishedVersionFil: Cuestas, Eduardo. Universidad Nacional de Córdoba. Facultad de Ciencias Médicas; Argentina.Fil: Cuestas, Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Investigaciones en Ciencias de la Salud; Argentina.Fil: Gómez Flores, Martha E. Gobierno de la Provincia de Buenos Aires. Hospital Doctor Ramon Carrillo; Argentina.Fil: Charras, María D. Gobierno de la Provincia de Buenos Aires. Hospital Doctor Ramon Carrillo; Argentina.Fil: Peyrano, Alberto J. Hospital Materno Provincial Dr. Raúl Felipe Lucini; Argentina.Fil: Montenegro, Clara. Hospital Materno Provincial Dr. Raúl Felipe Lucini; Argentina.Fil: Sosa-Boye, Ignacio. Clínica Universitaria Reina Fabiola; Argentina.Fil: Burgos, Verónica. Clínica Universitaria Reina Fabiola; Argentina.Fil: Giusti, Graciela. Clínica y Maternidad del Sol; Argentina.Fil: Espósito, Mario. Clínica y Maternidad del Sol; Argentina.Fil: Blanco Pool, Silvyana S. Hospital Misericordia Nuevo Siglo; Argentina.Fil: Blanco Pool, Silvyana S. Sanatorio Allende; Argentina.Fil: Gurevich, Debora P. Sanatorio Allende; Argentina.Fil: Gurevich, Debora P. Hospital Misericordia Nuevo Siglo; Argentina.Fil: Ahumada, Luis A. Sanatorio Allende; Argentina.Fil: Ahumada, Luis A. Hospital Misericordia Nuevo Siglo; Argentina.Fil: Pontoriero, Ricardo D. Hospital Misericordia Nuevo Siglo; Argentina.Fil: Rizzotti, Alina. Hospital Privado Universitario de Córdoba; Argentina.Fil: Bas, José I. Hospital Privado Universitario de Córdoba; Argentina.Fil: Vaca, María B. Hospital Universitario de Maternidad y Neonatología; Argentina.Fil: Miranda, María J. Hospital Universitario de Maternidad y Neonatología; Argentina.Fil: Ferreyra, Mirta E. Sanatorio del Salvador; Argentina.Fil: Ferreyra, Mirta E. Hospital Misericordia Nuevo Siglo; Argentina.Fil: Moreno, Gabriela C. Sanatorio del Salvador; Argentina.Fil: Pedicino, Héctor. Instituto Universidad Escuela de Medicina del Hospital Italiano; Argentina.Fil: Rojas-Rios, Melvy. Instituto Universidad Escuela de Medicina del Hospital Italiano; Argentina