Invariance under outer inverses

We shall use the minus partial order combined with Pierce’s decomposition to derive the class of outer inverses for idempotents, units and group invertible elements. Subsequently we show, for matrices over a field F, that the triplet BA^ C is invariant under all choices of outer inverses of A if and only if B= 0 or C= 0.FCT - Fundação para a Ciência e a Tecnologia (UID-MAT-00013/2013)info:eu-repo/semantics/publishedVersio

Moore-Penrose invertibility in involutory rings: the case aa+=bb+

In this article, we consider Moore-Penrose invertibility in rings with a general involution. Given two von Neumann regular elements a, b in a general ring with an arbitrary involution, we aim to give necessary and sufficient conditions to aa† = bb†. As a special case, EP elements are considered.Fundação para a Ciência e a Tecnologia (FCT)POCT

Further properties on the core partial order and other matrix partial orders

This paper carries further the study of core partial order initiated by Baksalary and Trenkler [Core inverse of matrices, Linear Multilinear Algebra. 2010;58:681-697]. We have extensively studied the core partial order, and some new characterizations are obtained in this paper. In addition, simple expressions for the already known characterizations of the minus, the star (and one-sided star), the sharp (and one-sided sharp) and the diamond partial orders are also obtained by using a Hartwig-Spindelbck decomposition.This author was partially supported by Ministry of Education of Spain [grant number DGI MTM2010-18228] and by Universidad Nacional de La Pampa, Argentina, Facultad de Ingenieria [grant number Resol. No 049/11].Malik, SB.; Rueda, LC.; Thome, N. (2014). Further properties on the core partial order and other matrix partial orders. Linear and Multilinear Algebra. 62(12):1629-1648. https://doi.org/10.1080/03081087.2013.839676S162916486212Mitra, S. K., & Bhimasankaram, P. (2010). MATRIX PARTIAL ORDERS, SHORTED OPERATORS AND APPLICATIONS. SERIES IN ALGEBRA. doi:10.1142/9789812838452Baksalary, J. K., & Hauke, J. (1990). A further algebraic version of Cochran’s theorem and matrix partial orderings. Linear Algebra and its Applications, 127, 157-169. doi:10.1016/0024-3795(90)90341-9Baksalary, O. M., & Trenkler, G. (2010). Core inverse of matrices. Linear and Multilinear Algebra, 58(6), 681-697. doi:10.1080/03081080902778222Baksalary, J. K., Baksalary, O. M., & Liu, X. (2003). Further properties of the star, left-star, right-star, and minus partial orderings. Linear Algebra and its Applications, 375, 83-94. doi:10.1016/s0024-3795(03)00609-8Groβ, J., Hauke, J., & Markiewicz, A. (1999). Partial orderings, preorderings, and the polar decomposition of matrices. Linear Algebra and its Applications, 289(1-3), 161-168. doi:10.1016/s0024-3795(98)10108-8Mosić, D., & Djordjević, D. S. (2012). Reverse order law for the group inverse in rings. Applied Mathematics and Computation, 219(5), 2526-2534. doi:10.1016/j.amc.2012.08.088Patrício, P., & Costa, A. (2009). On the Drazin index of regular elements. Open Mathematics, 7(2). doi:10.2478/s11533-009-0015-6Rakić, D. S., & Djordjević, D. S. (2012). Space pre-order and minus partial order for operators on Banach spaces. Aequationes mathematicae, 85(3), 429-448. doi:10.1007/s00010-012-0133-2Tošić, M., & Cvetković-Ilić, D. S. (2012). Invertibility of a linear combination of two matrices and partial orderings. Applied Mathematics and Computation, 218(9), 4651-4657. doi:10.1016/j.amc.2011.10.052Hartwig, R. E., & Spindelböck, K. (1983). Matrices for whichA∗andA†commute. Linear and Multilinear Algebra, 14(3), 241-256. doi:10.1080/03081088308817561Baksalary, O. M., Styan, G. P. H., & Trenkler, G. (2009). On a matrix decomposition of Hartwig and Spindelböck. Linear Algebra and its Applications, 430(10), 2798-2812. doi:10.1016/j.laa.2009.01.015Mielniczuk, J. (2011). Note on the core matrix partial ordering. Discussiones Mathematicae Probability and Statistics, 31(1-2), 71. doi:10.7151/dmps.1134Meyer, C. (2000). Matrix Analysis and Applied Linear Algebra. doi:10.1137/1.978089871951

The one-sided inverse along an element in semigroups and rings

The concept of the inverse along an element was introduced by Mary in 2011. Later, Zhu et al. introduced the one-sided inverse along an element. In this paper, we first give a new existence criterion for the one-sided inverse along a product and characterize the existence of Moore–Penrose inverse by means of one-sided invertibility of certain element in a ring. In addition, we show that a∈ S † ⋂ S # if and only if (a∗a)k is invertible along a if and only if (aa∗)k is invertible along a in a ∗ -monoid S, where k is an arbitrary given positive integer. Finally, we prove that the inverse of a along aa ∗ coincides with the core inverse of a under the condition a∈ S { 1 , 4 } in a ∗ -monoid S.FCT - Fuel Cell Technologies Program(CXLX13-072)This research was supported by the National Natural Science Foundation of China (No. 11371089), the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20120092110020), the Natural Science Foundation of Jiangsu Province (No. BK20141327) and the Foundation of Graduate Innovation Program of Jiangsu Province (No. KYZZ15-0049).info:eu-repo/semantics/publishedVersio

A weak group inverse for rectangular matrices

[EN] In this paper, we extend the notion of weak group inverse to rectangular matrices (called WweightedWGinverse) by using the weighted core EP inverse recently investigated. This new generalized inverse also generalizes the well-known weighted group inverse given by Cline and Greville. In addition, we give several representations of the W-weighted WG inverse, and derive some characterizations and properties.First author was partially supported by UNRC (Grant PPI 18/C472) and CONICET (Grant PIP 112-201501-00433CO). Third author was partially supported by Ministerio de Economia, Industria y Competitividad of Spain (Grants DGI MTM2013-43678-P and Red de Excelencia MTM2017-90682-REDT).Ferreyra, DE.; Orquera, V.; Thome, N. (2019). A weak group inverse for rectangular matrices. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 113(4):3727-3740. https://doi.org/10.1007/s13398-019-00674-9S372737401134Ben-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, 681–697 (2010)Baksalary, O.M., Trenkler, G.: On a generalized core inverse. Appl. Math. Comput. 236, 450–457 (2014)Bajodah, A.H.: Servo-constraint generalized inverse dynamics for robot manipulator control design. Int. J. Robot. Autom. 25, (2010). https://doi.org/10.2316/Journal.206.2016.1.206-3291Campbell, S.L., Meyer Jr., C.D.: Generalized Inverses of Linear transformations. SIAM, Philadelphia (2009)Cline, R.E., Greville, T.N.E.: A Drazin inverse for rectangular matrices. Linear Algebra Appl. 29, 53–62 (1980)Dajić, A., Koliha, J.J.: The weighted g-Drazin inverse for operators. J. Aust. Math. Soc. 2, 163–181 (2007)Doty, K.L., Melchiorri, C., Bonivento, C.: A theory of generalized inverses applied to robotics. Int. J. Rob. Res. 12, 1–19 (1993)Drazin, M.P.: Pseudo-inverses in associate rings and semirings. Am. Math. Mon. 65, 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, 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)Gigola, S., Lebtahi, L., Thome, N.: The inverse eigenvalue problem for a Hermitian reflexive matrix and the optimization problem. J. Comput. Appl. Math. 291, 449–457 (2016)Hartwig, R.E.: The weighted $$*$$ ∗ -core-nilpotent decomposition. Linear Algebra Appl. 211, 101–111 (1994)Kirkland, S.J., Neumann, M.: Group inverses of M-matrices and their applications. Chapman and Hall/CRC, London (2013)Malik, S., Thome, N.: On a new generalized inverse for matrices of an arbitrary index. Appl. Math. Comput. 226, 575–580 (2014)Male $${{\check{\rm s}}}$$ s ˇ ević, B., Obradović, R., Banjac, B., Jovović, I., Makragić, M.: Application of polynomial texture mapping in process of digitalization of cultural heritage. arXiv:1312.6935 (2013). Accessed 14 June 2018Manjunatha Prasad, K., Mohana, K.S.: Core EP inverse. Linear Multilinear Algebra 62, 792–802 (2014)Mehdipour, M., Salemi, A.: On a new generalized inverse of matrices. Linear Multilinear Algebra 66, 1046–1053 (2018)Meng, L.S.: The DMP inverse for rectangular matrices. Filomat 31, 6015–6019 (2017)Mosić, D.: The CMP inverse for rectangular matrices. Aequaetiones Math. 92, 649–659 (2018)Penrose, R.: A generalized inverse for matrices. Proc. Cambrid. Philos. Soc. 51, 406–413 (1955)Soleimani, F., Stanimirović, P.S., Soleymani, F.: Some matrix iterations for computing generalized inverses and balancing chemical equations. Algorithms 8, 982–998 (2015)Xiao, G.Z., Shen, B.Z., Wu, C.K., Wong, C.S.: Some spectral techniques in coding theory. Discrete Math. 87, 181–186 (1991)Wang, H.: Core-EP decomposition and its applications. Linear Algebra Appl. 508, 289–300 (2016)Wang, H., Chen, J.: Weak group inverse. Open Math. 16, 1218–1232 (2018)Wei, Y.: A characterization for the $$W$$ W -weighted Drazin inverse and a Crammer rule for the $$W$$ W -weighted Drazin inverse solution. Appl. Math. Comput. 125, 303–310 (2002

Deception in context: coding nonverbal cues, situational variables and risk of detection

There are many situations in which deception may arise and understanding the behaviors associated with it are compounded by various contexts in which it may occur. This paper sets out a coding protocol for identifying cues to deception and reports on three studies, in which deception was studied in different contexts. The contexts involved manipulating risks (i.e., probability) of being detected and reconnaissance, both of which are related to terrorist activities. Two of the studies examined the impact of changing the risks of deception detection, whilst the third investigated increased cognitive demand of duplex deception tasks including reconnaissance and deception. In all three studies, cues to deception were analyzed in relation to observable body movements and subjective impressions given by participants. In general, the results indicate a pattern of hand movement reduction by deceivers, and suggest the notion that raising the risk of detection influences deceivers? behaviors. Participants in the higher risk condition displayed increased negative affect (found in deceivers) and tension (found in both deceivers and truth-tellers) than those in lower risk conditions

Magnesium intake and colorectal cancer risk in the Netherlands Cohort Study

Energy-adjusted magnesium intake was nonsignificantly inversely related to risk of colorectal cancer (n=2328) in the Netherlands Cohort Study on Diet and Cancer that started in 1986 (n=58 279 men and 62 573 women). Statistically significant inverse trends in risk were observed in overweight subjects for colon and proximal colon cancer across increasing quintiles of magnesium uptake (P-trend, 0.05 and 0.02, respectively). Although an overall protective effect was not afforded, our results suggest an effect of magnesium in overweight subjects, possibly through decreasing insulin resistance

HIV Drug Resistance (HIVDR) in Antiretroviral Therapy-Naïve Patients in Tanzania Not Eligible for WHO Threshold HIVDR Survey Is Dramatically High

The World Health Organization (WHO) has recommended guidelines for a HIV drug resistance (HIVDR) survey for resource-limited countries. Eligibility criteria for patients include age below 25 years in order to focus on the prevalence of transmitted HIVDR (tHIVDR) in newly-infected individuals. Most of the participating sites across Africa have so far reported tHIVDR prevalences of below 5%. In this study we investigated whether the rate of HIVDR in patients <25 years is representative for HIVDR in the rest of the therapy-naïve population. HIVDR was determined in 88 sequentially enrolled ART-naïve patients from Mwanza, Tanzania (mean age 35.4 years). Twenty patients were aged <25 years and 68 patients were aged 25-63 years. The frequency of HIVDR in the study population was 14.8% (95%; CI 0.072-0.223) and independent of NVP-resistance induced by prevention of mother-to-child transmission programs. Patients >25 years had a significantly higher HIVDR frequency than younger patients (19.1%; 95% CI 0.095-0.28) versus 0%, P = 0.0344). In 2 out of the 16 patients with HIVDR we found traces of antiretrovirals (ARVs) in plasma. ART-naïve patients aged over 25 years exhibited significantly higher HIVDR than younger patients. Detection of traces of ARVs in individuals with HIVDR suggests that besides transmission, undisclosed misuse of ARVs may constitute a significant factor in the generation of the observed high HIVDR rate. The current WHO tHIVDR survey that is solely focused on the transmission of HIVDR and that excludes patients over 25 years of age may therefore result in substantial underestimation of the prevalence of HIVDR in the therapy-naïve population. Similar studies should be performed also in other areas to test whether the so far reported optimistic picture of low HIVDR prevalence in young individuals is really representative for the rest of the ART-naïve HIV-infected population

A critical realist evaluation of a music therapy intervention in palliative care

BACKGROUND: Music therapy is increasingly used as an adjunct therapy to support symptom management in palliative care. However, studies to date have paid little attention to the processes that lead to changes in patient outcomes. To fill this gap, we examined the processes and experiences involved in the introduction of music therapy as an adjunct complementary therapy to palliative care in a hospice setting in the United Kingdom (UK). METHODS: Using a realistic evaluation approach, we conducted a qualitative study using a variety of approaches. These consisted of open text answers from patients (n = 16) on how music therapy helped meet their needs within one hospice in Northern Ireland, UK. We also conducted three focus groups with a range of palliative care practitioners (seven physicians, seven nursing staff, two social workers and three allied health professionals) to help understand their perspectives on music therapy's impact on their work setting, and what influences its successful implementation. This was supplemented with an interview with the music therapist delivering the intervention. RESULTS: Music therapy contains multiple mechanisms that can provide physical, psychological, emotional, expressive, existential and social support. There is also evidence that the hospice context, animated by a holistic approach to healthcare, is an important facilitator of the effects of music therapy. Examination of patients' responses helped identify specific benefits for different types of patients. CONCLUSIONS: There is a synergy between the therapeutic aims of music therapy and those of palliative care, which appealed to a significant proportion of participants, who perceived it as effective