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

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

Characterization of High-Fat, Diet-Induced, Non-alcoholic Steatohepatitis with Fibrosis in Rats

An ideal animal model is necessary for a clear understanding of the etiology, pathogenesis, and mechanisms of human non-alcoholic steatohepatitis (NASH) and for facilitating the design of effective therapy for this condition. We aimed to establish a rat model of NASH with fibrosis by using a high-fat diet (HFD). Male Sprague–Dawley (SD) rats were fed a HFD consisting of 88 g normal diet, 10 g lard oil, and 2 g cholesterol. Control rats were fed normal diet. Rats were killed at 4, 8, 12, 16, 24, 36, and 48 weeks after HFD exposure. Body weight, liver weight, and epididymal fat weight were measured. Serum levels of fasting glucose, triglyceride, cholesterol, alanine aminotransferase (ALT), free fatty acids (FFA), insulin, and tumor necrosis factor-alpha (TNF-α) were determined. Hepatic histology was examined by H&E stain. Hepatic fibrosis was assessed by VG stain and immunohistochemical staining for transforming growth factor beta 1 (TGF-β1), and alpha-smooth-muscle actin (α-SMA). The liver weight and liver index increased from week 4, when hepatic steatosis was also observed. By week 8, the body weight and epididymal fat weight started increasing, which was associated with increased serum levels of FFA, cholesterol, and TNF-α, as well as development of simple fatty liver. The serum ALT level increased from week 12. Steatohepatitis occurred from weeks 12 through 48. Apparent hepatic perisinosodial fibrosis did not occur until week 24, and progressed from week 36 to 48 with insulin resistance. Therefore, this novel model may be potentially useful in NASH study

Measurement of the matrix element for the decay η′→ηπ +π -

The Dalitz plot of η⊃′→ηπ⊃+π⊃- decay is studied using (225.2±2.8)×106 J/ψ events collected with the BESIII detector at the BEPCII e⊃+e⊃- collider. With the largest sample of η⊃′ decays to date, the parameters of the Dalitz plot are determined in a generalized and a linear representation. Also, the branching fraction of J/ψ→γη⊃′ is determined to be (4.84±0.03±0.24)×10⊃-3, where the first error is statistical and the second systematic. © 2011 American Physical Society.published_or_final_versio

Higher-order multipole amplitude measurement in ψ ′→γχ c2

Using 106×106 ψ ′ events collected with the BESIII detector at the BEPCII storage ring, the higher-order multipole amplitudes in the radiative transition ψ ′→γχ c2→γπ +π -/γK +K - are measured. A fit to the χ c2 production and decay angular distributions yields M2=0.046±0. 010±0.013 and E3=0.015±0.008±0.018, where the first errors are statistical and the second systematic. Here M2 denotes the normalized magnetic quadrupole amplitude and E3 the normalized electric octupole amplitude. This measurement shows evidence for the existence of the M2 signal with 4.4σ statistical significance and is consistent with the charm quark having no anomalous magnetic moment. © 2011 American Physical Society.published_or_final_versio

Determination of the number of J/ψ events with J/ψ → inclusive decays

postprin

Observation of \chi_{cJ} decaying into the p\bar{p}K^{+}K^{-} final state

First measurements of the decays of the three $\chi_{cJ}$ states to $p\bar{p}K^{+}K^{-}$ final states are presented. Intermediate $\phi\to K^{+}K^{-}$ and $\Lambda(1520)\to pK^{-}$ resonance states are observed, and branching fractions for $\chi_{cJ}\to \bar{p}K^{+}\Lambda(1520)$, $\Lambda(1520) \bar{\Lambda}(1520)$, and $\phi p\bar{p}$ are reported. We also measure branching fractions for direct $\chi_{cJ}\to p\bar{p} K^{+}K^{-}$ decays. These are first observations of $\chi_{cJ}$ decays to unstable baryon resonances and provide useful information about the $\chi_{cJ}$ states. The experiment uses samples of $\chi_{cJ}$ mesons produced via radiative transitions from 106 million $\psi^{\prime}$ mesons collected in the BESIII detector at the BEPCII $e^+e^-$ collider.Comment: 16 pages, 5 figure

Two-photon widths of the χ c0,2 states and helicity analysis for χ c2→γγ

Based on a data sample of 106×106 ψ ′ events collected with the BESIII detector, the decays ψ ′→γχ c0,2, χ c0,2→γγ are studied to determine the two-photon widths of the χ c0,2 states. The two-photon decay branching fractions are determined to be B(χ c0→γγ)=(2. 24±0.19±0.12±0.08)×10 -4 and B(χ c2→γγ)=(3.21±0.18±0. 17±0.13)×10 -4. From these, the two-photon widths are determined to be Γ γγ(χ c0)=(2. 33±0.20±0.13±0.17)keV, Γ γγ(χ c2)=(0.63±0.04±0. 04±0.04)keV, and R=Γ γγ(χ c2)/ Γ γγ(χ c0)=0.271±0. 029±0.013±0.027, where the uncertainties are statistical, systematic, and those from the PDG B(ψ ′→γχ c0,2) and Γ(χ c0,2) errors, respectively. The ratio of the two-photon widths for helicity λ=0 and helicity λ=2 components in the decay χ c2→γγ is measured for the first time to be f 0/2=Γγγλ= 0(χ c2)/Γγγλ=2(χ c2)=0. 00±0.02±0.02. © 2012 American Physical Society.published_or_final_versio

Search for a light exotic particle in J/psi radiative decays

Using a data sample containing 1.06x10^8 psi' events collected with the BESIII detector at the BEPCII electron-positron collider, we search for a light exotic particle X in the process psi' -> pi^+ pi^- J/psi, J/psi -> gamma X, X -> mu^+ mu^-. This light particle X could be a Higgs-like boson A^0, a spin-1 U boson, or a pseudoscalar sgoldstino particle. In this analysis, we find no evidence for any mu^+mu^- mass peak between the mass threshold and 3.0 GeV/c^2. We set 90%-confidence-level upper limits on the product-branching fractions for J/psi -> gamma A^0, A^0 -> mu^+ mu^- which range from 4x10^{-7} to 2.1x10^{-5}, depending on the mass of A^0, for M(A^0)<3.0 GeV/c^2. Only one event is seen in the mass region below 255 MeV/c^2 and this has a mu^+mu^- mass of 213.3 MeV/c^2 and the product branching fraction upper limit 5x10^{-7}.Comment: 7 pages, 3 figures, submitted to Physical Review