1,377 research outputs found

    Abóbora-gila (cucurbita ficifolia), uma hortaliça pouco convencional cultivada no Rio Grande do Sul.

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    The weak core inverse

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    [EN] In this paper, we introduce a new generalized inverse, called weak core inverse (or, in short, WC inverse) of a complex square matrix. This new inverse extends the notion of the core inverse defined by Baksalary and Trenkler (Linear Multilinear Algebra 58(6):681-697, 2010). We investigate characterizations, representations, and properties for this generalized inverse. In addition, we introduce weak core matrices (or, in short, WC matrices) and we show that these matrices form a more general class than that given by the known weak group matrices, recently investigated by H. Wang and X. Liu.In what follows, we detail the acknowledgements. D.E. Ferreyra, F.E. Levis, A.N. Priori - Partially supported by Universidad Nacional de Rio Cuarto (Grant PPI 18/C559) and CONICET (Grant PIP 112-201501-00433CO). D.E. Ferreyra F.E. Levis - Partially supported by ANPCyT (Grant PICT 201803492). D.E. Ferreyra, N. Thome -Partially supported by Universidad Nacional de La Pampa, Facultad de Ingenieria (Grant Resol. Nro. 135/19). N. Thome -Partially supported by Ministerio de Economia, Industria y Competitividad of Spain (Grant Red de Excelencia MTM2017-90682-REDT) and by Universidad Nacional del Sur of Argentina (Grant 24/L108). We would like to thank the Referees for their valuable comments and suggestions which helped us to considerably improve the presentation of the paperFerreyra, DE.; Levis, FE.; Priori, AN.; Thome, N. (2021). The weak core inverse. Aequationes Mathematicae. 95(2):351-373. https://doi.org/10.1007/s00010-020-00752-zS351373952Ben-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(6), 681–697 (2010)Baksalary, O.M., Trenkler, G.: On a generalized core inverse. Appl. Math. Comput. 236(1), 450–457 (2014)Campbell, S.L., Meyer Jr., C.D.: Generalized Inverses of Linear Transformations. SIAM, Philadelphia (2009)Ceryan, N.: Handbook of Research on Trends and Digital Advances in Engineering Geology, Advances in Civil and Industrial Engineering. IGI Global, Hershey (2018)Chen, J.L., Mosić, D., Xu, S.Z.: On a new generalized inverse for Hilbert sapce operators. Quaest. Math. (2019). https://doi.org/10.2989/16073606.2019.1619104Cvetković-Ilić, D.S., Mosić, D., Wei, Y.: Partial orders on B(H)B(H). Linear Algebra Appl. 481, 115–130 (2015)Djikić, M.S.: Lattice properties of the core-partial order. Banach J. Math. Anal. 11(2), 398–415 (2017)Doty, K.L., Melchiorri, C., Bonivento, C.: A theory of generalized inverses applied to robotics. Int. J. Robot. Res. 12(1), 1–19 (1993)Drazin, M.P.: Pseudo inverses in associative rings and semigroups. Am. Math. Mon. 65(7), 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(2), 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)Ferreyra, D.E., Levis, F.E., Thome, N.: Characterizations of kk-commutative equalities for some outer generalized inverses. Linear Multilinear Algebra 68(1), 177–192 (2020)Hartwig, R.E., Spindelböck, K.: Matrices for which A∗A^* and A†A^\dagger conmmute. Linear Multilinear Algebra 14(3), 241–256 (1984)Liu, X., Cai, N.: High-order iterative methods for the DMP inverse. J. Math. Article ID 8175935, 6 p (2018)Malik, S., Thome, N.: On a new generalized inverse for matrices of an arbitrary index. Appl. Math. Comput. 226(1), 575–580 (2014)Malik, S., Rueda, L., Thome, N.: The class of mm-EP and mm-normal matrices. Linear Multilinear Algebra 64(11), 2119–2132 (2016)Manjunatha Prasad, K., Mohana, K.S.: Core EP inverse. Linear Multilinear Algebra 62(6), 792–802 (2014)Mehdipour, M., Salemi, A.: On a new generalized inverse of matrices. Linear Multilinear Algebra 66(5), 1046–1053 (2018)Mitra, S.K., Bhimasankaram, P., Malik, S.: Matrix Partial Orders, Shorted Operators and Applications, Series in Algebra, vol. 10. World Scientific Publishing Co. Pte. Ltd., Singapore (2010)Mosić, D., Stanimirović, P.S.: Composite outer inverses for rectangular matrices. Quaest. Math. (2019). https://doi.org/10.2989/16073606.2019.1671526Penrose, R.: A generalized inverse for matrices. Math. Proc. Cambr. Philos. Soc. 51(3), 406–413 (1955)Rakić, D.S., Dincić, N.C., Djordjević, D.S.: Core inverse and core partial order of Hilbert space operators. Appl. Math. Comput. 244(1), 283–302 (2014)Soleimani, F., Stanimirović, P.S., Soleymani, F.: Some matrix iterations for computing generalized inverses and balancing chemical equations. Algorithms 8(4), 982–998 (2015)Tosić, M., Cvetković-Ilić, D.S.: Invertibility of a linear combination of two matrices and partial orderings. Appl. Math. Comput. 218(9), 4651–4657 (2012)Wang, X.: Core-EP decomposition and its applications. Linear Algebra Appl. 508(1), 289–300 (2016)Wang, H., Chen, J.: Weak group inverse. Open Math. 16(1), 1218–1232 (2018)Wang, H., Liu, X.: The weak group matrix. Aequ. Math. 93(6), 1261–1273 (2019)Xiao, G.Z., Shen, B.Z., Wu, C.K., Wong, C.S.: Some spectral techniques in coding theory. Discrete Math. 87(2), 181–186 (1991)Zhou, M., Chen, J., Stanimirović, P., Katsikis, V.N., Ma, H.: Complex varying-parameter Zhang neural networks for computing core and core-EP inverse. Neural Process. Lett. 51, 1299–1329 (2020)Zhu, H.: On DMP inverses and mm-EP elements in rings. 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    Transferibilidade de marcadores microssatélites de coco (Cocos nucifera) para butiá (Butia odorata)

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    Pt(IV)Ac-POA: new platinum compound Induced caspase independent apoptosis In B50 neuroblastoma stem cells

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    Neuroblastoma is a tumour that affects adults and children, characterized by a stem cells component. To date, cisplatin is the main antitumor agent used in the clinical treatment of this tumour; however, it induces side effects such as neurotoxicity in healthy cells and induces chemo resistance to therapy in cancer cells. New platinum-based compounds, platinum (II) have recently been synthesized, and due to their chemical characteristics, they are able to identify new cellular targets. These complexes act as prodrugs and performing their cytotoxic effect as platinum (II) after a reduction reaction within the hypoxic tumour cells. Among these prodrugs, Pt(IV)Ac-POA appears to be very promising, thanks to the presence of ligand (2 propinyl)octanoic acid (POA), which acts as an inhibitor of histone deacetylase (HDACi) and leads to the increase of histone acetylation, decreasing the interactions between histone and DNA, so as to produce chemo-sensitization to DNA-damaging agents. The greater cytotoxic effect of Pt(IV)Ac-POA on tumour cells, would therefore be mainly due to the mechanism of inhibition of histone deacetylase, which would increase the accessibility of DNA to platination mechanisms that induce cell death. In this study the results show that Pt(IV)Ac-POA, used at a concentration ten times lower than cisplatin, can induce apoptosis in B50 cells in culture both through the intrinsic pathway and through the independent caspase pathway. The data, obtained by immunohistochemical techniques in fluorescence microscopy, show that treatment with Pt(IV)Ac-POA has a greater proapoptotic effect on stem cells compared to the cisplatin standard treatment
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