Centralizer's applications to the (b, c)-inverses in rings

[EN] We give several conditions in order that the absorption law for one sided (b,c)-inverses in rings holds. Also, by using centralizers, we obtain the absorption law for the (b,c)-inverse and the reverse order law of the (b,c)-inverse in rings. As applications, we obtain the related results for the inverse along an element, Moore-Penrose inverse, Drazin inverse, group inverse and core inverse.This research is supported by the National Natural Science Foundation of China (no. 11771076 and no. 11871301). The first author is grateful to China Scholarship Council for giving him a scholarship for his further study in Universitat Politecnica de Valencia, Spain.Xu, S.; Chen, J.; Benítez López, J.; Wang, D. (2019). Centralizer's applications to the (b, c)-inverses in rings. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. 113(3):1739-1746. https://doi.org/10.1007/s13398-018-0574-0S173917461133Baksalary, O.M., Trenkler, G.: Core inverse of matrices. Linear Multilinear Algebra 58(6), 681–697 (2010)Benítez, J., Boasso, E.: The inverse along an element in rings with an involution, Banach algebras and $$C^*$$ C ∗ -algebras. Linear Multilinear Algebra 65(2), 284–299 (2017)Benítez, J., Boasso, E., Jin, H.W.: On one-sided $$(B, C)$$ ( B , C ) -inverses of arbitrary matrices. Electron. J. Linear Algebra 32, 391–422 (2017)Boasso, E., Kantún-Montiel, G.: The $$(b, c)$$ ( b , c ) -inverses in rings and in the Banach context. Mediterr. J. Math. 14, 112 (2017)Chen, Q.G., Wang, D.G.: A class of coquasitriangular Hopf group algebras. Comm. Algebra 44(1), 310–335 (2016)Chen, J.L., Ke, Y.Y., Mosić, D.: The reverse order law of the $$(b, c)$$ ( b , c ) -inverse in semigroups. Acta Math. Hung. 151(1), 181–198 (2017)Deng, C.Y.: Reverse order law for the group inverses. J. Math. Anal. Appl. 382(2), 663–671 (2011)Drazin, M.P.: Pseudo-inverses in associative rings and semigroups. Am. Math. Mon. 65, 506–514 (1958)Drazin, M.P.: A class of outer generalized inverses. Linear Algebra Appl. 436, 1909–1923 (2012)Drazin, M.P.: Left and right generalized inverses. Linear Algebra Appl. 510, 64–78 (2016)Jin, H.W., Benítez, J.: The absorption laws for the generalized inverses in rings. Electron. J. Linear Algebra 30, 827–842 (2015)Johnson, B.E.: An introduction to the theory of centralizers. Proc. Lond. Math. Soc. 14, 299–320 (1964)Ke, Y.Y., Cvetković-Ilić, D.S., Chen, J.L., Višnjić, J.: New results on $$(b, c)$$ ( b , c ) -inverses. Linear Multilinear Algebra 66(3), 447–458 (2018)Ke Y.Y., Višnjić J., Chen J.L.: One sided $$(b,c)$$ ( b , c ) -inverse in rings (2016). arXiv:1607.06230v1Liu, X.J., Jin, H.W., Cvetković-Ilić, D.S.: The absorption laws for the generalized inverses. Appl. Math. Comput. 219, 2053–2059 (2012)Mary, X.: On generalized inverse and Green’s relations. Linear Algebra Appl. 434, 1836–1844 (2011)Mary, X., Patrício, P.: Generalized inverses modulo $$\cal{H}$$ H in semigroups and rings. Linear Multilinear Algebra 61(8), 1130–1135 (2013)Mosić, D., Cvetković-Ilić, D.S.: Reverse order law for the Moore-Penrose inverse in $$C^*$$ C ∗ -algebras. Electron. J. Linear Algebra 22, 92–111 (2011)Rakić, D.S.: A note on Rao and Mitra’s constrained inverse and Drazin’s $$(b, c)$$ ( b , c ) -inverse. Linear Algebra Appl. 523, 102–108 (2017)Rakić, D.S., Dinčić, N.Č., Djordjević, D.S.: Group, Moore–Penrose, core and dual core inverse in rings with involution. Linear Algebra Appl. 463, 115–133 (2014)Wang, L., Castro-González, N., Chen, J.L.: Characterizations of outer generalized inverses. Can. Math. Bull. 60(4), 861–871 (2017)Wei, Y.M.: A characterization and representation of the generalized inverse $$A^{(2)}_{T, S}$$ A T , S ( 2 ) and its applications. Linear Algebra Appl. 280, 87–96 (1998)Xu, S.Z., Benítez, J.: Existence criteria and expressions of the $$(b, c)$$ ( b , c ) -inverse in rings and its applications. Mediterr. J. Math. 15, 14 (2018)Zhu, H.H., Chen, J.L., Patrício, P.: Further results on the inverse along an element in semigroups and rings. Linear Multilinear Algebra 64(3), 393–403 (2016)Zhu, H.H., Chen, J.L., Patrício, P.: Reverse order law for the inverse along an element. Linear Multilinear Algebra 65, 166–177 (2017)Zhu, H.H., Chen, J.L., Patrício, P., Mary, X.: Centralizer’s applications to the inverse along an element. Appl. Math. Comput. 315, 27–33 (2017)Zhu, H.H., Zhang, X.X., Chen, J.L.: Centralizers and their applications to generalized inverses. Linear Algebra Appl. 458, 291–300 (2014

Robustness analysis of discrete predictor-based controllers for input-delay systems

In this article, robustness to model uncertainties are analysed in the context of discrete predictor-based state-feedback controllers for discrete-time input-delay systems with time-varying delay, in an LMI framework. The goal is comparing robustness of predictor-based strategies with respect to other (sub)optimal state feedback ones. A numerical example illustrates that improvements in tolerance to modelling errors can be achieved by using the predictor framework.The authors are grateful for grant nos. DPI2008-06737-C02-01, DPI2008-06731-C02-01, DPI2011-27845-C02-01 and PROMETEO/2008/088 from the Spanish and Valencian governments.González Sorribes, A.; Sala, A.; García Gil, PJ.; Albertos Pérez, P. (2013). Robustness analysis of discrete predictor-based controllers for input-delay systems. International Journal of Systems Science. 44(2):232-239. https://doi.org/10.1080/00207721.2011.600469S232239442Boukas, E.-K. (2006). Discrete-time systems with time-varying time delay: Stability and stabilizability. Mathematical Problems in Engineering, 2006, 1-10. doi:10.1155/mpe/2006/42489Du, D., Jiang, B., & Zhou, S. (2008). Delay-dependent robust stabilisation of uncertain discrete-time switched systems with time-varying state delay. International Journal of Systems Science, 39(3), 305-313. doi:10.1080/00207720701805982El Ghaoui, L., Oustry, F., & AitRami, M. (1997). A cone complementarity linearization algorithm for static output-feedback and related problems. IEEE Transactions on Automatic Control, 42(8), 1171-1176. doi:10.1109/9.618250Gao, H., & Chen, T. (2007). New Results on Stability of Discrete-Time Systems With Time-Varying State Delay. IEEE Transactions on Automatic Control, 52(2), 328-334. doi:10.1109/tac.2006.890320Gao, H., Wang, C., Lam, J., & Wang, Y. (2004). Delay-dependent output-feedback stabilisation of discrete-time systems with time-varying state delay. IEE Proceedings - Control Theory and Applications, 151(6), 691-698. doi:10.1049/ip-cta:20040822Gao, H., Chen, T., & Lam, J. (2008). A new delay system approach to network-based control. Automatica, 44(1), 39-52. doi:10.1016/j.automatica.2007.04.020Garcia , P , Castillo , P , Lozano , R and Albertos , P . 2006 . Robustness with Respect to Delay Uncertainties of a Predictor Observer Based Discrete-time Controller . Proceeding of the 45th IEEE Conference on Decision and Control . 2006 . pp. 199 – 204 .Guo , Y and Li , S . 2009 . New Stability Criterion for Discrete-time Systems with Interval Time-varying State Delay . Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference . 2009 . pp. 1342 – 1347 .Hägglund, T. (1996). An industrial dead-time compensating PI controller. Control Engineering Practice, 4(6), 749-756. doi:10.1016/0967-0661(96)00065-2V.J.S. Leite, and Miranda, M.F. (2008), ‘Robust Stabilization of Discrete-time Systems with Time-varying Delay: An LMI Approach’,Mathematical Problems in Engineering, 2008, 15 pages (doi:10.1155/2008/875609)Liu, X. G., Tang, M. L., Martin, R. R., & Wu, M. (2006). Delay-dependent robust stabilisation of discrete-time systems with time-varying delay. IEE Proceedings - Control Theory and Applications, 153(6), 689-702. doi:10.1049/ip-cta:20050223Lozano, R., Castillo, P., Garcia, P., & Dzul, A. (2004). Robust prediction-based control for unstable delay systems: Application to the yaw control of a mini-helicopter. Automatica, 40(4), 603-612. doi:10.1016/j.automatica.2003.10.007Manitius, A., & Olbrot, A. (1979). Finite spectrum assignment problem for systems with delays. IEEE Transactions on Automatic Control, 24(4), 541-552. doi:10.1109/tac.1979.1102124Michiels, W., & Niculescu, S.-I. (2003). On the delay sensitivity of Smith Predictors. International Journal of Systems Science, 34(8-9), 543-551. doi:10.1080/00207720310001609057Palmor, Z.J. (1996), ‘Time-delay Compensation – Smith Predictor and Its Modifications’, inThe Control Handbook, ed. W.S. Levine, Boca Raton: CRC Press, pp. 224–237Pan, Y.-J., Marquez, H. J., & Chen, T. (2006). Stabilization of remote control systems with unknown time varying delays by LMI techniques. International Journal of Control, 79(7), 752-763. doi:10.1080/00207170600654554Richard, J.-P. (2003). Time-delay systems: an overview of some recent advances and open problems. Automatica, 39(10), 1667-1694. doi:10.1016/s0005-1098(03)00167-5Wang, Q.-G., Lee, T. H., & Tan, K. K. (1999). Finite-Spectrum Assignment for Time-Delay Systems. Lecture Notes in Control and Information Sciences. doi:10.1007/978-1-84628-531-8He, Y., Wu, M., Han, Q.-L., & She, J.-H. (2008). Delay-dependentH∞control of linear discrete-time systems with an interval-like time-varying delay. International Journal of Systems Science, 39(4), 427-436. doi:10.1080/00207720701832531Yue, D., & Han, Q.-L. (2005). Delayed feedback control of uncertain systems with time-varying input delay. Automatica, 41(2), 233-240. doi:10.1016/j.automatica.2004.09.006Zhang, B., Xu, S., & Zou, Y. (2008). Improved stability criterion and its applications in delayed controller design for discrete-time systems. Automatica, 44(11), 2963-2967. doi:10.1016/j.automatica.2008.04.01

Luminescent Organic–Inorganic Hybrids of Functionalized Mesoporous Silica SBA-15 by Thio-Salicylidene Schiff Base

Novel organic–inorganic mesoporous luminescent hybrid material N, N′-bis(salicylidene)-thiocarbohydrazide (BSTC-SBA-15) has been obtained by co-condensation of tetraethyl orthosilicate and the organosilane in the presence of Pluronic P123 surfactant as a template. N,N′-bis(salicylidene)-thiocarbohydrazide (BSTC) grafted to the coupling agent 3-(triethoxysilyl)-propyl isocyanate (TESPIC) was used as the precursor for the preparation of mesoporous materials. In addition, for comparison, SBA-15 doped with organic ligand BSTC was also synthesized, denoted as BSTC/SBA-15. This organic–inorganic hybrid material was well-characterized by X-ray diffraction, Fourier transform infrared spectroscopy, transmission electron microscopy (HRTEM), and photoluminescence spectra, which reveals that they all have high surface area, uniformity in the mesostructure. The resulting materials (BSTC-SBA-15 and BSTC/SBA-15) exhibit regular uniform microstructures, and no phase separation happened for the organic and the inorganic compounds was covalently linked through Si–O bonds via a self-assemble process. Furthermore, the two materials have different luminescence range: BSTC/SBA-15 presents the strong dominant green luminescence, while BSTC-functionalized material BSTC-SBA-15 shows the dominant blue emission

Validation and refinement of two interpretable models for coronavirus disease 2019 prognosis prediction

Objective: To validate two proposed coronavirus disease 2019 (COVID-19) prognosis models, analyze the characteristics of different models, consider the performance of models in predicting different outcomes, and provide new insights into the development and use of artificial intelligence (AI) predictive models in clinical decision-making for COVID-19 and other diseases. Materials and Methods: We compared two proposed prediction models for COVID-19 prognosis that use a decision tree and logistic regression modeling. We evaluated the effectiveness of different model-building strategies using laboratory tests and/or clinical record data, their sensitivity and robustness to the timings of records used and the presence of missing data, and their predictive performance and capabilities in single-site and multicenter settings. Results: The predictive accuracies of the two models after retraining were improved to 93.2% and 93.9%, compared with that of the models directly used, with accuracies of 84.3% and 87.9%, indicating that the prediction models could not be used directly and require retraining based on actual data. In addition, based on the prediction model, new features obtained by model comparison and literature evidence were transferred to integrate the new models with better performance. Conclusions: Comparing the characteristics and differences of datasets used in model training, effective model verification, and a fusion of models is necessary in improving the performance of AI models

Evaluation of image quality with four positron emitters and three preclinical PET/CT systems

Background We investigated the image quality of C-11, Ga-68, F-18 and Zr-89, which have different positron fractions, physical half-lifes and positron ranges. Three small animal positron emission tomography/computed tomography (PET/CT) systems were used in the evaluation, including the Siemens Inveon, RAYCAN X5 and Molecubes beta-cube. The evaluation was performed on a single scanner level using the national electrical manufacturers association (NEMA) image quality phantom and analysis protocol. Acquisitions were performed with the standard NEMA protocol for F-18 and using a radionuclide-specific acquisition time for C-11, Ga-68 and Zr-89. Images were assessed using percent recovery coefficient (%RC), percentage standard deviation (%STD), image uniformity (%SD), spill-over ratio (SOR) and evaluation of image quantification. Results Ga-68 had the lowest %RC ( 85%) and lowest %STD for the 5 mm rod across all systems. For C-11 and Zr-89, the maximum %RC was close (> 76%) to the %RC with F-18. A larger SOR were measured in water with C-11 and Ga-68 compared to F-18 on all systems. SOR in air reflected image reconstruction and data correction performance. Large variation in image quantification was observed, with maximal errors of 22.73% (Zr-89, Inveon), 17.54% (Zr-89, RAYCAN) and - 14.87% (Ga-68, Molecubes). Conclusions The systems performed most optimal in terms of NEMA image quality parameters when using F-18, where C-11 and Zr-89 performed slightly worse than F-18. The performance was least optimal when using Ga-68, due to large positron range. The large quantification differences prompt optimization not only by terms of image quality but also quantification. Further investigation should be performed to find an appropriate calibration and harmonization protocol and the evaluation should be conducted on a multi-scanner and multi-center level

Synthesis and Photoluminescence Property of Silicon Carbide Nanowires Via Carbothermic Reduction of Silica

Silicon carbide nanowires have been synthesized at 1400 °C by carbothermic reduction of silica with bamboo carbon under normal atmosphere pressure without metallic catalyst. X-ray diffraction, scanning electron microscopy, energy-dispersive spectroscopy, transmission electron microscopy and Fourier transformed infrared spectroscopy were used to characterize the silicon carbide nanowires. The results show that the silicon carbide nanowires have a core–shell structure and grow along <111> direction. The diameter of silicon carbide nanowires is about 50–200 nm and the length from tens to hundreds of micrometers. The vapor–solid mechanism is proposed to elucidate the growth process. The photoluminescence of the synthesized silicon carbide nanowires shows significant blueshifts, which is resulted from the existence of oxygen defects in amorphous layer and the special rough core–shell interface

Highly Efficient Near-IR Photoluminescence of Er3+ Immobilized in Mesoporous SBA-15

SiO2 mesoporous molecular sieve SBA-15 with the incorporation of erbium ions is studied as a novel type of nanoscopic composite photoluminescent material in this paper. To enhance the photoluminescence efficiency, two schemes have been used for the incorporation of Er3+ where (1) Er3+ is ligated with bis-(perfluoromethylsulfonyl)-aminate (PMS) forming Er(PMS)x-SBA-15 and (2) Yb3+ is codoped with Er3+ forming Yb-Er-SBA-15. As high as 11.17 × 10−21cm2 of fluorescent cross section at 1534 nm and 88 nm of “effective bandwidth” have been gained. It is a 29.3% boost in fluorescent cross section compared to what has been obtained in conventional silica. The upconversion coefficient in Yb-Er-SBA-15 is relatively small compared to that in other ordinary glass hosts. The increased fluorescent cross section and lowered upconversion coefficient could benefit for the high-gain optical amplifier. Finally, the Judd–Ofelt theory has also been used for the analyses of the optical spectra of Er(PMS)x-SBA-15

Stepwise Maturation of Lytic Granules during Differentiation and Activation of Human CD8+ T Lymphocytes

During differentiation, cytotoxic T lymphocytes (CTL) acquire their killing potential through the biogenesis and maturation of lytic granules that are secreted upon target cell recognition. How lytic granule load in lytic molecules evolves during CTL differentiation and which subsets of lytic granules are secreted following activation remains to be investigated. We set up a flow cytometry approach to analyze single lytic granules isolated from primary human CTL according to their size and molecular content. During CTL in vitro differentiation, a relatively homogeneous population of lytic granules appeared through the progressive loading of Granzyme B, Perforin and Granzyme A within LAMP1+ lysosomes. PMA/ionomycin-induced lytic granule exocytosis was preceded by a rapid association of the docking molecule Rab27a to approximately half of the lytic granules. Activated CTL were found to limit exocytosis by sparing lytic granules including some associated to Rab27a. Our study provides a quantification of key steps of lytic granule biogenesis and highlights the potential of flow cytometry to study organelle composition and dynamics