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

Calculation Of The Giant Magnetocaloric Effect In The Mnfep 0.45as0.55 Compound

We report the theoretical investigations on the giant magnetocaloric compound MnFeP0.45As0.55. The magnetic state equation used takes into account the magnetoelastic effect that leads the magnetic system to order under first order paramagnetic-ferromagnetic phase transition. The model parameters were determined from the magnetization data adjustment and used to calculate the magnetocaloric thermodynamic quantities. The theoretical calculations are compared with the available experimental data.709944101-094410-5Yu, B.F., Gao, Q., Zhang, B., Mang, X.Z., Chen, Z., (2003) Int. J. Refrig., 26, p. 622Gschneidner Jr., K.A., Pecharsky, V.K., (1997) Rare Earths: Science, Technology and Application III, , edited by R. C. Bautista, C. O. Bounds, T. W. Ellis, and B. T. Kilbourn The Minerals, Metals & Materials Society, WarendaleBrown, G.V., (1976) J. Appl. Phys., 47, p. 3673Pecharsky, V.K., Gschneidner Jr., K.A., (1997) Phys. Rev. Lett., 78, p. 4494Tegus, O., Brück, E., Buschow, K.H.J., De Boer, F.R., (2002) Nature, 415, p. 150. , LondonMorellon, L., Algarabel, P.A., Ibarra, M.R., Blasco, J., García-Landa, B., Arnold, Z., Albertini, F., (1998) Phys. Rev. B, 58, pp. R14721Rodbell, D.S., (1961) Phys. Rev. Lett., 7, p. 1Bean, C.P., Rodbell, D.S., (1961) Phys. Rev., 126, p. 104Bacmann, M., Soubeyroux, J.-L., Barrett, R., Fruchart, D., Zach, R., Niziol, S., Fruchart, R., (1983) J. Magn. Magn. Mater., 134, p. 59Brück, E., Tegus, O., Li, X.W., Deboer, F.R., Buschow, K.H.J., (2003) Physica B, 327, p. 431Tegus, O., Brück, E., Zhang, L., Dagula, Buschow, K.H.J., De Boer, F.R., (2002) Physica B, 319, p. 174Zach, R., Guillot, M., Tobola, J., (1998) J. Appl. Phys., 83, p. 7237Tegus, O., (2003) Novel Materials for Magnetic Refrigeration, , PhD thesis, Van der Waals-Zeeman Instituut, Universiteit van Amsterdam, Printer Partners Ipskamp B. V., ISBN: 9057761076, OctoberVon Ranke, P.J., Grangeia, D.F., Caldas, A., De Oliveira, N.A., (2003) J. Appl. Phys., 93, p. 4055Wada, H., Tanabe, Y., (2001) Appl. Phys. Lett., 79, p. 3302Wada, H., Morikawa, T., Taniguchi, K., Shibata, T., Yamada, Y., Akishige, Y., (2003) Physica B, 328, p. 11

Smallest eigenvalues of Hankel matrices for exponential weights

AbstractWe obtain the rate of decay of the smallest eigenvalue of the Hankel matrices ∫Itj+kW2(t)dtj,k=0n for a general class of even exponential weights W2=exp(−2Q) on an interval I. More precise asymptotics for more special weights have been obtained by many authors

Four-body baryonic decays of B→ppˉπ+π−(π+K−)B\to p \bar{p} \pi^+\pi^-(\pi^+K^-) and Λpˉπ+π−(K+K−)\Lambda \bar{p} \pi^+\pi^-(K^+K^-)

We study the four-body baryonic $B\to {\bf B_1 \bar B_2}M_1 M_2$ decays with $\bf B_{1,2}$ ($M_{1,2}$) being charmless baryons (mesons). In accordance with the recent LHCb observations, each decay is considered to proceed through the $B\to M_1 M_2$ transition together with the production of a baryon pair. We obtain that ${\cal B}(B^-\to \Lambda\bar p \pi^+\pi^-)=(3.7^{+1.5}_{-1.0} )\times 10^{-6}$ and ${\cal B}(\bar B^0\to p\bar p \pi^+\pi^-,p\bar p \pi^+ K^-)=(3.0\pm 0.9,6.6\pm 2.4)\times 10^{-6}$, in agreement with the data. We also predict ${\cal B}(B^-\to\Lambda\bar p K^+ K^-)=(3.0^{+1.3}_{-0.9})\times 10^{-6}$, which is accessible to the LHCb and BELLE experiments.Comment: 11 pages, 3 figure

Measurement of the spectral function for the τ- →k-KSντ decay

open238siThe decay tau(-) -> K- K(S)v(tau) has been studied using 430 x 10(6) e(+) e(-) -> tau(+) tau(-) events produced at a center-of-mass energy around 10.6 GeV at the PEP-II collider and studied with the BABAR detector. The mass spectrum of the K- K-S system has been measured and the spectral function has been obtained. The measured branching fraction B(tau(-) -> K- K(S)v(tau)) = (0.739 +/- 0.011 (stat) +/- 0.020 (syst)) x 10(-3) is found to be in agreement with earlier measurements.openLees, J.P.; Poireau, V.; Tisserand, V.; Grauges, E.; Palano, A.; Eigen, G.; Brown, D.N.; Kolomensky, Yu.G.; Fritsch, M.; Koch, H.; Schroeder, T.; Hearty, C.; Mattison, T.S.; McKenna, J.A.; So, R.Y.; Blinov, V.E.; Buzykaev, A.R.; Druzhinin, V.P.; Golubev, V.B.; Kozyrev, E.A.; Kravchenko, E.A.; Onuchin, A.P.; Serednyakov, S.I.; Skovpen, Yu.I.; Solodov, E.P.; Todyshev, K.Yu.; Lankford, A.J.; Gary, J.W.; Long, O.; Eisner, A.M.; Lockman, W.S.; Panduro Vazquez, W.; Chao, D.S.; Cheng, C.H.; Echenard, B.; Flood, K.T.; Hitlin, D.G.; Kim, J.; Li, Y.; Miyashita, T.S.; Ongmongkolkul, P.; Porter, F.C.; Röhrken, M.; Huard, Z.; Meadows, B.T.; Pushpawela, B.G.; Sokoloff, M.D.; Sun, L.; Smith, J.G.; Wagner, S.R.; Bernard, D.; Verderi, M.; Bettoni, D.; Bozzi, C.; Calabrese, R.; Cibinetto, G.; Fioravanti, E.; Garzia, I.; Luppi, E.; Santoro, V.; Calcaterra, A.; De Sangro, R.; Finocchiaro, G.; Martellotti, S.; Patteri, P.; Peruzzi, I.M.; Piccolo, M.; Rotondo, M.; Zallo, A.; Passaggio, S.; Patrignani, C.; Lacker, H.M.; Bhuyan, B.; Mallik, U.; Chen, C.; Cochran, J.; Prell, S.; Gritsan, A.V.; Arnaud, N.; Davier, M.; Le Diberder, F.; Lutz, A.M.; Wormser, G.; Lange, D.J.; Wright, D.M.; Coleman, J.P.; Gabathuler, E.; Hutchcroft, D.E.; Payne, D.J.; Touramanis, C.; Bevan, A.J.; Di Lodovico, F.; Sacco, R.; Cowan, G.; Banerjee, Sw.; Brown, D.N.; Davis, C.L.; Denig, A.G.; Gradl, W.; Griessinger, K.; Hafner, A.; Schubert, K.R.; Barlow, R.J.; Lafferty, G.D.; Cenci, R.; Jawahery, A.; Roberts, D.A.; Cowan, R.; Robertson, S.H.; Seddon, R.M.; Dey, B.; Neri, N.; Palombo, F.; Cheaib, R.; Cremaldi, L.; Godang, R.; Summers, D.J.; Taras, P.; De Nardo, G.; Sciacca, C.; Raven, G.; Jessop, C.P.; Losecco, J.M.; Honscheid, K.; Kass, R.; Gaz, A.; Margoni, M.; Posocco, M.; Simi, G.; Simonetto, F.; Stroili, R.; Akar, S.; Ben-Haim, E.; Bomben, M.; Bonneaud, G.R.; Calderini, G.; Chauveau, J.; Marchiori, G.; Ocariz, J.; Biasini, M.; Manoni, E.; Rossi, A.; Batignani, G.; Bettarini, S.; Carpinelli, M.; Casarosa, G.; Chrzaszcz, M.; Forti, F.; Giorgi, M.A.; Lusiani, A.; Oberhof, B.; Paoloni, E.; Rama, M.; Rizzo, G.; Walsh, J.J.; Zani, L.; Smith, A.J.S.; Anulli, F.; Faccini, R.; Ferrarotto, F.; Ferroni, F.; Pilloni, A.; Piredda, G.; Bünger, C.; Dittrich, S.; Grünberg, O.; Heß, M.; Leddig, T.; Voß, C.; Waldi, R.; Adye, T.; Wilson, F.F.; Emery, S.; Vasseur, G.; Aston, D.; Cartaro, C.; Convery, M.R.; Dorfan, J.; Dunwoodie, W.; Ebert, M.; Field, R.C.; Fulsom, B.G.; Graham, M.T.; Hast, C.; Innes, W.R.; Kim, P.; Leith, D.W.G.S.; Luitz, S.; Macfarlane, D.B.; Muller, D.R.; Neal, H.; Ratcliff, B.N.; Roodman, A.; Sullivan, M.K.; Va'Vra, J.; Wisniewski, W.J.; Purohit, M.V.; Wilson, J.R.; Randle-Conde, A.; Sekula, S.J.; Ahmed, H.; Bellis, M.; Burchat, P.R.; Puccio, E.M.T.; Alam, M.S.; Ernst, J.A.; Gorodeisky, R.; Guttman, N.; Peimer, D.R.; Soffer, A.; Spanier, S.M.; Ritchie, J.L.; Schwitters, R.F.; Izen, J.M.; Lou, X.C.; Bianchi, F.; De Mori, F.; Filippi, A.; Gamba, D.; Lanceri, L.; Vitale, L.; Martinez-Vidal, F.; Oyanguren, A.; Albert, J.; Beaulieu, A.; Bernlochner, F.U.; King, G.J.; Kowalewski, R.; Lueck, T.; Nugent, I.M.; Roney, J.M.; Sobie, R.J.; Tasneem, N.; Gershon, T.J.; Harrison, P.F.; Latham, T.E.; Prepost, R.; Wu, S.L.Lees, J. P.; Poireau, V.; Tisserand, V.; Grauges, E.; Palano, A.; Eigen, G.; Brown, D. N.; Kolomensky, Yu. G.; Fritsch, M.; Koch, H.; Schroeder, T.; Hearty, C.; Mattison, T. S.; Mckenna, J. A.; So, R. Y.; Blinov, V. E.; Buzykaev, A. R.; Druzhinin, V. P.; Golubev, V. B.; Kozyrev, E. A.; Kravchenko, E. A.; Onuchin, A. P.; Serednyakov, S. I.; Skovpen, Yu. I.; Solodov, E. P.; Todyshev, K. Yu.; Lankford, A. J.; Gary, J. W.; Long, O.; Eisner, A. M.; Lockman, W. S.; Panduro Vazquez, W.; Chao, D. S.; Cheng, C. H.; Echenard, B.; Flood, K. T.; Hitlin, D. G.; Kim, J.; Li, Y.; Miyashita, T. S.; Ongmongkolkul, P.; Porter, F. C.; Röhrken, M.; Huard, Z.; Meadows, B. T.; Pushpawela, B. G.; Sokoloff, M. D.; Sun, L.; Smith, J. G.; Wagner, S. R.; Bernard, D.; Verderi, M.; Bettoni, D.; Bozzi, C.; Calabrese, R.; Cibinetto, G.; Fioravanti, E.; Garzia, I.; Luppi, E.; Santoro, V.; Calcaterra, A.; De Sangro, R.; Finocchiaro, G.; Martellotti, S.; Patteri, P.; Peruzzi, I. M.; Piccolo, M.; Rotondo, M.; Zallo, A.; Passaggio, S.; Patrignani, C.; Lacker, H. M.; Bhuyan, B.; Mallik, U.; Chen, C.; Cochran, J.; Prell, S.; Gritsan, A. V.; Arnaud, N.; Davier, M.; Le Diberder, F.; Lutz, A. M.; Wormser, G.; Lange, D. J.; Wright, D. M.; Coleman, J. P.; Gabathuler, E.; Hutchcroft, D. E.; Payne, D. J.; Touramanis, C.; Bevan, A. J.; Di Lodovico, F.; Sacco, R.; Cowan, G.; Banerjee, Sw.; Brown, D. N.; Davis, C. L.; Denig, A. G.; Gradl, W.; Griessinger, K.; Hafner, A.; Schubert, K. R.; Barlow, R. J.; Lafferty, G. D.; Cenci, R.; Jawahery, A.; Roberts, D. A.; Cowan, R.; Robertson, S. H.; Seddon, R. M.; Dey, B.; Neri, N.; Palombo, F.; Cheaib, R.; Cremaldi, L.; Godang, R.; Summers, D. J.; Taras, P.; De Nardo, G.; Sciacca, C.; Raven, G.; Jessop, C. P.; Losecco, J. M.; Honscheid, K.; Kass, R.; Gaz, A.; Margoni, M.; Posocco, M.; Simi, G.; Simonetto, F.; Stroili, R.; Akar, S.; Ben-Haim, E.; Bomben, M.; Bonneaud, G. R.; Calderini, G.; Chauveau, J.; Marchiori, G.; Ocariz, J.; Biasini, M.; Manoni, E.; Rossi, A.; Batignani, G.; Bettarini, S.; Carpinelli, M.; Casarosa, G.; Chrzaszcz, M.; Forti, F.; Giorgi, M. A.; Lusiani, A.; Oberhof, B.; Paoloni, E.; Rama, M.; Rizzo, G.; Walsh, J. J.; Zani, L.; Smith, A. J. S.; Anulli, F.; Faccini, R.; Ferrarotto, F.; Ferroni, F.; Pilloni, A.; Piredda, G.; Bünger, C.; Dittrich, S.; Grünberg, O.; Heß, M.; Leddig, T.; Voß, C.; Waldi, R.; Adye, T.; Wilson, F. F.; Emery, S.; Vasseur, G.; Aston, D.; Cartaro, C.; Convery, M. R.; Dorfan, J.; Dunwoodie, W.; Ebert, M.; Field, R. C.; Fulsom, B. G.; Graham, M. T.; Hast, C.; Innes, W. R.; Kim, P.; Leith, D. W. G. S.; Luitz, S.; Macfarlane, D. B.; Muller, D. R.; Neal, H.; Ratcliff, B. N.; Roodman, A.; Sullivan, M. K.; Va'Vra, J.; Wisniewski, W. J.; Purohit, M. V.; Wilson, J. R.; Randle-Conde, A.; Sekula, S. J.; Ahmed, H.; Bellis, M.; Burchat, P. R.; Puccio, E. M. T.; Alam, M. S.; Ernst, J. A.; Gorodeisky, R.; Guttman, N.; Peimer, D. R.; Soffer, A.; Spanier, S. M.; Ritchie, J. L.; Schwitters, R. F.; Izen, J. M.; Lou, X. C.; Bianchi, F.; De Mori, F.; Filippi, A.; Gamba, D.; Lanceri, L.; Vitale, L.; Martinez-Vidal, F.; Oyanguren, A.; Albert, J.; Beaulieu, A.; Bernlochner, F. U.; King, G. J.; Kowalewski, R.; Lueck, T.; Nugent, I. M.; Roney, J. M.; Sobie, R. J.; Tasneem, N.; Gershon, T. J.; Harrison, P. F.; Latham, T. E.; Prepost, R.; Wu, S. L

Characteristic features of the temperature dependence of the surface impedance in polycrystalline MgB2_2 samples

The real $R_s(T)$ and imaginary $X_s(T)$ parts of the surface impedance $Z_s(T)=R_s(T)+iX_s(T)$ in polycrystalline MgB$_2$ samples of different density with the critical temperature $T_c\approx 38$ K are measured at the frequency of 9.4 GHz and in the temperature range $5\le T<200$ K. The normal skin-effect condition $R_s(T)=X_s(T)$ at $T\ge T_c$ holds only for the samples of the highest density with roughness sizes not more than 0.1 $\mu$m. For such samples extrapolation $T\to 0$ of the linear at $T<T_c/2$ temperature dependences $\lambda_L(T)=X_s(T)/\omega\mu_0$ and $R_s(T)$ results in values of the London penetration depth $\lambda_L(0)\approx 600$ \AA and residual surface resistance $R_{res}\approx 0.8$ m$\Omega$. In the entire temperature range the dependences $R_s(T)$ and $X_s(T)$ are well described by the modified two-fluid model.Comment: 7 pages, 3 figures. Europhysics Letters, accepted for publicatio

(Non-)existence of Polynomial Kernels for the Test Cover Problem

The input of the Test Cover problem consists of a set $V$ of vertices, and a collection ${\cal E}=\{E_1,..., E_m\}$ of distinct subsets of $V$, called tests. A test $E_q$ separates a pair $v_i,v_j$ of vertices if $|\{v_i,v_j\}\cap E_q|=1.$ A subcollection ${\cal T}\subseteq {\cal E}$ is a test cover if each pair $v_i,v_j$ of distinct vertices is separated by a test in ${\cal T}$. The objective is to find a test cover of minimum cardinality, if one exists. This problem is NP-hard. We consider two parameterizations the Test Cover problem with parameter $k$: (a) decide whether there is a test cover with at most $k$ tests, (b) decide whether there is a test cover with at most $|V|-k$ tests. Both parameterizations are known to be fixed-parameter tractable. We prove that none have a polynomial size kernel unless $NP\subseteq coNP/poly$. Our proofs use the cross-composition method recently introduced by Bodlaender et al. (2011) and parametric duality introduced by Chen et al. (2005). The result for the parameterization (a) was an open problem (private communications with Henning Fernau and Jiong Guo, Jan.-Feb. 2012). We also show that the parameterization (a) admits a polynomial size kernel if the size of each test is upper-bounded by a constant