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

K+ channel openers restore verapamil-inhibited lung fluid resolution and transepithelial ion transport

<p>Abstract</p> <p>Background</p> <p>Lung epithelial Na⁺channels (ENaC) are regulated by cell Ca²⁺signal, which may contribute to calcium antagonist-induced noncardiogenic lung edema. Although K⁺channel modulators regulate ENaC activity in normal lungs, the therapeutical relevance and the underlying mechanisms have not been completely explored. We hypothesized that K⁺channel openers may restore calcium channel blocker-inhibited alveolar fluid clearance (AFC) by up-regulating both apical and basolateral ion transport.</p> <p>Methods</p> <p>Verapamil-induced depression of heterologously expressed human αβγ ENaC in <it>Xenopus </it>oocytes, apical and basolateral ion transport in monolayers of human lung epithelial cells (H441), and <it>in vivo </it>alveolar fluid clearance were measured, respectively, using the two-electrode voltage clamp, Ussing chamber, and BSA protein assays. Ca²⁺signal in H441 cells was analyzed using Fluo 4AM.</p> <p>Results</p> <p>The rate of <it>in vivo </it>AFC was reduced significantly (40.6 ± 6.3% of control, <it>P </it>< 0.05, n = 12) in mice intratracheally administrated verapamil. K_Ca3.1(1-EBIO) and K_ATP(minoxidil) channel openers significantly recovered AFC. In addition to short-circuit current (Isc) in intact H441 monolayers, both apical and basolateral Isc levels were reduced by verapamil in permeabilized monolayers. Moreover, verapamil significantly altered Ca²⁺signal evoked by ionomycin in H441 cells. Depletion of cytosolic Ca²⁺in αβγ ENaC-expressing oocytes completely abolished verapamil-induced inhibition. Intriguingly, K_V(pyrithione-Na), K _Ca3.1(1-EBIO), and K_ATP(minoxidil) channel openers almost completely restored the verapamil-induced decrease in Isc levels by diversely up-regulating apical and basolateral Na⁺and K⁺transport pathways.</p> <p>Conclusions</p> <p>Our observations demonstrate that K⁺channel openers are capable of rescuing reduced vectorial Na⁺transport across lung epithelial cells with impaired Ca²⁺signal.</p

Measurement of the Forward-Backward Asymmetry in the B -> K(*) mu+ mu- Decay and First Observation of the Bs -> phi mu+ mu- Decay

We reconstruct the rare decays $B^+ \to K^+\mu^+\mu^-$, $B^0 \to K^{*}(892)^0\mu^+\mu^-$, and $B^0_s \to \phi(1020)\mu^+\mu^-$ in a data sample corresponding to $4.4 {\rm fb^{-1}}$ collected in $p\bar{p}$ collisions at $\sqrt{s}=1.96 {\rm TeV}$ by the CDF II detector at the Fermilab Tevatron Collider. Using $121 \pm 16$ $B^+ \to K^+\mu^+\mu^-$ and $101 \pm 12$ $B^0 \to K^{*0}\mu^+\mu^-$ decays we report the branching ratios. In addition, we report the measurement of the differential branching ratio and the muon forward-backward asymmetry in the $B^+$ and $B^0$ decay modes, and the $K^{*0}$ longitudinal polarization in the $B^0$ decay mode with respect to the squared dimuon mass. These are consistent with the theoretical prediction from the standard model, and most recent determinations from other experiments and of comparable accuracy. We also report the first observation of the $B^0_s \to \phi\mu^+\mu^- decay and measure its branching ratio${\mathcal{B}}(B^0_s \to \phi\mu^+\mu^-) = [1.44 \pm 0.33 \pm 0.46] \times 10^{-6}$using$27 \pm 6$signal events. This is currently the most rare$B^0_s$ decay observed.Comment: 7 pages, 2 figures, 3 tables. Submitted to Phys. Rev. Let

Measurement of the Bottom-Strange Meson Mixing Phase in the Full CDF Data Set

We report a measurement of the bottom-strange meson mixing phase \beta_s using the time evolution of B0_s -> J/\psi (->\mu+\mu-) \phi (-> K+ K-) decays in which the quark-flavor content of the bottom-strange meson is identified at production. This measurement uses the full data set of proton-antiproton collisions at sqrt(s)= 1.96 TeV collected by the Collider Detector experiment at the Fermilab Tevatron, corresponding to 9.6 fb-1 of integrated luminosity. We report confidence regions in the two-dimensional space of \beta_s and the B0_s decay-width difference \Delta\Gamma_s, and measure \beta_s in [-\pi/2, -1.51] U [-0.06, 0.30] U [1.26, \pi/2] at the 68% confidence level, in agreement with the standard model expectation. Assuming the standard model value of \beta_s, we also determine \Delta\Gamma_s = 0.068 +- 0.026 (stat) +- 0.009 (syst) ps-1 and the mean B0_s lifetime, \tau_s = 1.528 +- 0.019 (stat) +- 0.009 (syst) ps, which are consistent and competitive with determinations by other experiments.Comment: 8 pages, 2 figures, Phys. Rev. Lett 109, 171802 (2012

Measurements of the properties of Lambda_c(2595), Lambda_c(2625), Sigma_c(2455), and Sigma_c(2520) baryons

We report measurements of the resonance properties of Lambda_c(2595)+ and Lambda_c(2625)+ baryons in their decays to Lambda_c+ pi+ pi- as well as Sigma_c(2455)++,0 and Sigma_c(2520)++,0 baryons in their decays to Lambda_c+ pi+/- final states. These measurements are performed using data corresponding to 5.2/fb of integrated luminosity from ppbar collisions at sqrt(s) = 1.96 TeV, collected with the CDF II detector at the Fermilab Tevatron. Exploiting the largest available charmed baryon sample, we measure masses and decay widths with uncertainties comparable to the world averages for Sigma_c states, and significantly smaller uncertainties than the world averages for excited Lambda_c+ states.Comment: added one reference and one table, changed order of figures, 17 pages, 15 figure

Search for a New Heavy Gauge Boson Wprime with Electron + missing ET Event Signature in ppbar collisions at sqrt(s)=1.96 TeV

We present a search for a new heavy charged vector boson $W^\prime$ decaying to an electron-neutrino pair in $p\bar{p}$ collisions at a center-of-mass energy of 1.96\unit{TeV}. The data were collected with the CDF II detector and correspond to an integrated luminosity of 5.3\unit{fb}^{-1}. No significant excess above the standard model expectation is observed and we set upper limits on $\sigma\cdot{\cal B}(W^\prime\to e\nu)$. Assuming standard model couplings to fermions and the neutrino from the $W^\prime$ boson decay to be light, we exclude a $W^\prime$ boson with mass less than 1.12\unit{TeV/}c^2 at the 95\unit{%} confidence level.Comment: 7 pages, 2 figures Submitted to PR

RhoH Regulates Subcellular Localization of ZAP-70 and Lck in T Cell Receptor Signaling

RhoH is an hematopoietic-specific, GTPase-deficient Rho GTPase that plays a role in T development. We investigated the mechanisms of RhoH function in TCR signaling. We found that the association between Lck and CD3ζ was impaired in RhoH-deficient T cells, due to defective translocation of both Lck and ZAP-70 to the immunological synapse. RhoH with Lck and ZAP-70 localizes in the detergent-soluble membrane fraction where the complex is associated with CD3ζ phosphorylation. To determine if impaired translocation of ZAP-70 was a major determinant of defective T cell development, Rhoh-/- bone marrow cells were transduced with a chimeric myristoylation-tagged ZAP-70. Myr-ZAP-70 transduced cells partially reversed the in vivo defects of RhoH-associated thymic development and TCR signaling. Together, our results suggest that RhoH regulates TCR signaling via recruitment of ZAP-70 and Lck to CD3ζ in the immunological synapse. Thus, we define a new function for a RhoH GTPase as an adaptor molecule in TCR signaling pathway

Mechanisms of T cell organotropism

F.M.M.-B. is supported by the British Heart Foundation, the Medical Research Council of the UK and the Gates Foundation

Search for heavy bottom-like quarks decaying to an electron or muon and jets in ppˉp\bar{p} collisions at s=1.96\sqrt{s}=1.96 TeV

We report the most sensitive direct search for pair production of fourth-generation bottom-like chiral quarks ($b'$) each decaying promptly to $tW$. We search for an excess of events with an electron or muon, at least five jets (one indentified as due to a $b$ or $c$ quark) and an imbalance of transverse momentum using data from $p\bar{p}$ collisions collected by the CDF II detector at Fermilab with an integrated luminosity of 4.8 fb$^{-1}$. We observe events consistent with background expectation and calculate upper limits on the $b'$ pair production cross section ($\sigma_{b\bar{b'}}\lesssim 30$ fb for $m_{b'}>$375 GeV/$c^2$) and exclude $m_{b'}<372$ \gevcc at 95% confidence level.Comment: For submission to PR